yoursmahboob.wordpress · 2018-06-29 · yoursmahboob.wordpress.com NON-VERBAL REASONING 18. Series...

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ordpress.comVERBAL REASONING

1. Analogy & Classification 1-7

2. Series 8-12

3. Alphabet & Number Test 13-19

4. Coding-Decoding 20-23

5. Blood Relations 24-28

6. Direction and Distance 29-32

7. Time Sequence, Number & Ranking Test 33-34

8. Logical Sequence of Words 35

9. Number Puzzles 36

10. Venn Diagram 37-39

11. Mathematical Operation Arithmetical Reasoning 40-41

12. Coded Inequalities 42-47

13. Problem Solving 48-57

14. Input and Output 58-68

15. Syllogism 69-78

16. Cube & Dice 79-84

17. Analytical Decision Making 85-90

Index

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NON-VERBAL REASONING

18. Series 91-95

19. Mirror & Water Images 96-99

20. Paper Cutting and Folding 100-101

21. Completion of Figure 102

22. Hidden / Embedded Figures 103

23. Figure Formation and Analysis 104-105

24. Visual Reasoning 106-110

ANALYTICAL REASONING

25. Evaluating Inferences 111-114

26. Statement & Arguments 115-126

27. Statement & Assumptions 127-131

28. Statement & Conclusions 132-133

29. Courses of Action 134-140

30. Critical Reasoning` 141-152

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Shortcuts in Quantitative Aptitude with EBooks is an attempt of Disha Publication to provide Quality Material to aspirants. The book will help in learning the various tips and tricks of Quantitative Aptitude. The book emphasizes on the short cut methods through which one can solve any problem before time. Each chapter covers basic theory followed by shortcut approaches and formula.The book is supported by ample practice material through E-books which covers:(a) Chapter-wise Solved Examples

(b) Chapter-wise Practice Exercises with Hints and Solutions(c) Chapter-wise Tests(d) Past Solved Papers (IBPS PO/Clerk, SBI PO/Clerk, SSC, CDS exams etc.)

Disha’s Tips and Techniques in English (with 3 eBooks) for all Competitive Exams is a short book designed to cater to every student appearing for competitive exams. The chapters also include Spotting errors, Sentence Correction, Choose the Correct Sentence, Synonyms and Antonyms, Sentence Completion, Active and Passive voices, Direct and Indirect speech and Common Errors in English and so on. In short, it focuses on all those scientific yet student-friendly approaches to crack all competitive exams. The practice exercises, solved papers and tests are given in the form of e-books. The book is supported by 3 eBooks:1. Chapter-wise Practice Exercise2. Chapter Tests3. Solved Papers of various exams

The Current Affairs Roundup is the most cost effective quality book ever built for Competitive Exams. The book is empowered with 30+ Online MCQ Tests and 2 eBooks - GK2017 and Current Affairs Update July - December 2016.The book has been designed to capture the day-to-day happenings in and around our country. The book has been divided into 4 parts - Events, Issues, Ideas and People. Further each of the 4 parts is divided month-wise.

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General Competition Books At A Glance

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General Competition Guides At A Glance

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Disha’s General Knowledge At A Glance

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ordpress.comANALOGYThe meaning of analogy is ‘similarproperties’ or similarity. If an object orword or digit or activity shows anysimilarity with another object or word ordigit or activity in terms of properties,type, shape, size, trait etc., then theparticular similarity will be called analogy.The relationship of analogy can beestablished in two ways :

(i) A : B : : C : D

(ii) A : B : : C : D

Word AnalogyLetter AnalogyNumber AnalogyMixed Analogy

Types of Analogy

WORD ANALOGYIn word analogy, candidates have to findthe relationship between given words ina pair.

Remember

1. Tool & Object Based AnalogyThis establishes a relationshipbetween a tool and the object inwhich it works.

EXAMPLE

Scissors : Cloth2. Synonym Based Analogy

In such type of analogy two wordshave similar meaning.

EXAMPLE

Huge : Gigantic3. Worker & Tool Based

AnalogyThis establishes a relationshipbetween a particular tool and theperson of that particular professionwho uses that tool.

EXAMPLE

Writer : Pen4. Worker & Product Based

AnalogyThis type of analogy gives arelationship between a person ofparticular profession and his/hercreations.

EXAMPLE

Writer : Book5. Causes & Effect Based

AnalogyIn such type of analogy 1st wordacts and the 2nd word is the effectof that action.

EXAMPLE

Work : Tiredness

Analogy &Classification

Chapter

1

VERBAL REASONING

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Analogy & Classification26. Opposite Relationship

(Antonym) Based AnalogyIn such type of analogy the twowords of the question pair areopposite in meaning.

EXAMPLE

Poor : Rich

7. Gender Based AnalogyIn such type of analogy, one wordis masculine and another word isfeminine of it or It is a ‘male andfemale’ or ‘sex’ relationship.

EXAMPLE

Man : Woman

8. Classification Based AnalogyThis type of analogy is based onbiological, physical, chemical or anyother classification. In suchproblems the 1st word may beclassified by the 2nd word and vice-versa.

EXAMPLE

Oxygen : Gas

9. Function Based AnalogyIn such type of analogy, 2nd worddescribes the function of the 1st

word.EXAMPLE

Singer : Sings

10. Quantity and Unit BasedAnalogyIn such type of analogy 2nd word isthe unit of the first word and vice-versa.

EXAMPLE

Distance : Mile

11. Finished Product & RawMaterial Based AnalogyIn such type of analogy the 1st wordis the raw material and 2nd word isthe end product of that raw materialand vice-versa.

EXAMPLE

Yarn : Fabric12. Utility Based Analogy

In such type of analogy the 2nd

word shows the purpose of the 1st

word or vice-versa.EXAMPLE

Pen : Writing13. Symbolic Relationship

Based Analogy

In such type of analogy, the 1st wordis the symbol of the 2nd word andvice-versa.

EXAMPLE

White : Peace

14. Adult & Young One BasedAnalogyIn such type of analogy, the 1st wordis the adult one and 2nd word is theyoung one of the 1st word or vice-versa.

EXAMPLE

Cow : Calf

15. Subject & Specialist BasedAnalogyIn such type of analogy the 2nd

word is the specialist of 1st word(subject) or vice-versa.

EXAMPLE

Heart : Cardiologist

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Analogy & Classification 316. Habit Based Analogy

In this type of analogy 2nd word isthe habit of 1st and vice-versa.

EXAMPLE

Cat : Omnivorous17. Instrument and

Measurement BasedAnalogyWe see in this type of analogy, the1st word is the instrument to measurethe 2nd word and vice-versa:

EXAMPLE

Hygrometer: Humidity

18. Individual & Group BasedAnalogySecond word is the group of 1st

word (or vice-versa) in such typeof analogy.

EXAMPLE

Cow : Herd

19. State & Capital BasedAnalogy1st word is the state and 2nd word isthe capital of that state (1st word)(or vice-versa) in the analogy likethis.

EXAMPLE

Bihar : Patna20. Analogy Based on Individual

& Dwelling PlaceIn such type of analogy 1st word isthe individual & 2nd word is thedwelling place of that individual (1st

word) and vice-versa.EXAMPLE

Horse : Stable

21. Analogy Based on Workerand Working PlaceIn this type of analogy the 1st wordrepresents a person of particularprofession and 2nd word representsthe working place of that person (1st

word) and vice-versa.

EXAMPLE

Doctor : Hospital22. Analogy Based on Topic

Study1st word is the study of the 2nd word(or vice-versa) in the analogy likethis.

EXAMPLE

Birds : Ornithology

LETTER ANALOGYIn this, candidate has to find out therelationship between given letters orgroup of letters.Analogy Based on Letters (orMeaningless Words)Case I : Forward alphabetical sequence

EXAMPLE

CD : FG : : PQ : UVHere, CD and FG are in the naturalalphabetical sequence. Similarly, PQ &UV are in the natural alphabeticalsequence.Case II: Backward or Oppositealphabetical sequence

EXAMPLE

DC : GF : : QP : VUIn fact this case is opposite of case ICase III: Vowel – Consonant relation

EXAMPLE

ATL : EVX : : IPR : ORS

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Analogy & Classification4Here, the 1st two words start with the 1st

two vowels A & E and the next two wordsstart with the next two vowels I & O.Last two letter of every word areconsonants.Case IV: Skip letter relation

EXAMPLE

ABC : FGH : : IJK : NOPHere, between ABC & FGH two lettersskip and they are D & E. Similarly,

between IJK & NOP two letters skip andthey are L & M.Case V: Jumbled letters relation

EXAMPLE

(i) LAIN : NAIL : : EVOL : LOVEHere, the 1st term gets reveresed toproduce the 2nd term and similarrelation is shown in between 3rd and4th term.

q Shortcut ApproachI: While solving the problems based on alphabet, you must have in your mind

the exact positions of every letters of alphabet in forward order as well as inbackward or reverse order as given below:Letters positions in forward alphabetical order:

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

D E F G H I J K L M N O P Q R S T U V W X Y Z1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

Letters positions in backward or reverse alphabetical order:

Z Y X W V U T S R Q P O N M L K J I 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

K J I H G F E D C B A5 16 17 18 19 20 21 22 23 24 25 26

II: Just keep in mind, the following positions of the letters in the English alphabet(forward order).

(i)

15 20 25105

E J O T Y

EJOTY Remember this word

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Analogy & Classification 5

(ii)

CFILORUX Remember

3 6 9 12 15 18 21 24

C F I L O R U X

(iii)

16 20 2484

D H P T X

DHLPTX Remember

12

L

NUMBER ANALOGYIn this, candidate has to find out therelationship the number or group ofnumbers.

Remember• Even and Odd numbers

EXAMPLE 84 : 51 : : 72 : 37(Here, 84 & 72 are even and 51 & 37are odd numbers respectively)

• Addition and subtraction ofnumbers.

EXAMPLE 234 : 9 : : 136 : 10(Here, 2 + 3 + 4 = 9 and 1 + 3 + 6 = 10)

• Multiplication and Division ofnumbers

EXAMPLE 3 : 21 : : 5 : 35(Here, 3 × 7 = 21 and 5 × 7 = 35)

• Squares & Cubes of numbersEXAMPLE 4 : 16 : : 8 : 64

(here, 42 = 16 and 82 = 64)

MIXED ANALOGYIn this, candidate has to find out therelationship between the given group ofletters and a number on one side.

EXAMPLE AB : 12 : : CD : : 34(Here, A B C D ̄ ¯ and ¯ ¯ 1 2 3 4

(positional (positional value) vlaue)

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Analogy & Classification6CLASSIFICATIONIn classification we take out an elementout of some given elements and theelement to be taken out is different fromthe rest of the elements in terms ofcommon properties, shapes, sizes, types,nature, colours, traits etc. In this way,the rest of the elements form a group andthe element that has been taken out isnot the member of that group as thissingle element does not possesses thecommon quality to be possessed by restof the elements.

Types of Classification(1) Letter/meaningless word based

classification(2) Meaningful word based

classification(3) Digit based classification(4) General knowledge based

classification

1. Letter/Meaningless WordBased ClassificationSuch classifications are based onletters of English alphabet. So manygroups of letters are given in thequestion in which one group isdifferent from remaining groups andhence the different group will be ouranswer.

EXAMPLE

(a) PQT (b) UVY(c) DEH (d) IJN(e) FGJ

Sol. (a) Here, P Q R S T

2 letter gap

(b) U V W X Y

2 letter gap

(c) D E F G H

2 letter gap

(d) I J K L M N

3 letter gap

(e) F G H I J

2 letter gap

2. Meaningful Words BasedClassificationIn such type of classification wehave to take odd word out of thegiven group of meaningful words.

EXAMPLE

(a) Slim (b) Trims(c) Greets (d) Grid(e) Fight

Sol. (a) Here, Sl i m

1 vowel(b)

Tr i ms

1 vowel

(c)Gr ee ts

2 vowels(d)

Gr i d

1 vowel

(e)F i ght

1 vowel3. Digit Based Classification

In such type of classifications digitsor numbers are given to find out onenumber that is not a part of thegroup of remaining numbers.

EXAMPLE

(a) 122 (b) 128(c) 199 (d) 200(e) 388

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Analogy & Classification 7Sol. 199 is an odd number while all the

other options are even numbers.

4. General Knowledge BasedClassificationSuch classification is done on thebasis of our general knowledge. Nodoubts that this is a word basedclassification but without havinggeneral knowledge this type ofquestions can not be solved.

EXAMPLE

(a) Cat (b) Dog(c) Tiger (d) Octopus(e) Lion

Sol. Octopus is the only animal out ofgiven options which is a wateranimal. Rest of the options are landanimals.

q Shortcut ApproachStep I : See all the given options with aserious eye.Step II : Try to make relation of similarityamong the given options.Step III :Find out the one word nothaving the common similarity like otherfour options and that one word will beyour answer.

ebooks Reference Page No.

Practice Exercises with Hints & Solutions – P-1-7Chapter Test – C-1- 2Past Solved Papers

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Series8

INTRODUCTIONA series is a sequence of numbers/alphabetical letters or both which follow aparticular rule. Each element of series is called ‘term’. We have to analyse thepattern and find the missing term or next term to continue the pattern.

Types of series are explained in the following chart:

SERIES

Numberseries

A series that ismade by only

number or digit

A series that ismade by only

alphabetic letters

A series in which both

alphabets andnumbers are

used

A series of letters, which follow a certain pattern, is given with four /five times blankspaces in between. The order of missing lettersis correct answer.

1. Ascending series2. Descending series3. Oscillating series

Alphabetseries

Alpha-numericseries

Mixedseries

Continuous Patternseries

Correspondenceseries

A series which is created by

the combination of two or more than two series

A series consists ofthree sequence withthree different elements (for ex.capital letters, numbers and smallletters). An elementof each sequence iscorrespond to theelement of othersequence on the basis of the similarityin position.

Series

Chapter

2

NUMBER SERIESNumber series is a form of numbers ina certain sequence, where somenumbers are mistakenly put into theseries of numbers and some number ismissing in that series, we need toobserve first and then find the accuratenumber to that series of numbers.

Remember· Even and odd numbers.· Prime and composite numbers.· Square and square roots of a

numbers.

· Cube and cube roots of a numbers.

·

Arithmetic Operations

AdditionSubtractionDivisionMultiplication

Types of Number Series

1. Perfect Square SeriesThis type of serics are based onsquare of a number which is insame order and one square numberis missing in that given series.

EXAMPLE 841, ?, 2401, 3481, 4761Sol. 292, 392, 452, 592, 692

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Series 92. Perfect Cube series

Perfect Cube series is aarrangement of numbers is acertain order, where some numberwhich is in same order and onecube is missing in that givenseries.

EXAMPLE 4096, 4913, 5832, ?, 8000Sol. 163, 173, 183, 193, 203

3. Mixed number seriesMixed number series is aarrangement of numbers in acertain order. This type of seriesare more than are different orderwhich arranged in alternatively insingle series or created accordingto any non conventional rule.

EXAMPLE 6, ?, 33, 69, 141, 285Sol. × 2 + 3, × 2 + 3, × 2 + 3, × 2 + 3,

× 2 + 3, × 2 + 34. Geometric Series

Geometric Number series is aarrangement of numbers in acertain order, where some numbersare this type of series are based onascending or descending order ofnumbers and each continuesnumber is obtain by multiplicationor division of the previous numberwith a static number.In geometric series number is acombination of number arranged.

EXAMPLE 21, 84, 336, ?, 5376

Sol. 21 × 4 = 8484 × 4 = 336336 × 4 = 13441344 × 4 = 5376

5. Prime seriesWhen numbers are a series ofprime numbers.

EXAMPLE 2, 3, 5, 7, 11, 13, __ , 19

Sol. Here, the terms of the series are theprime numbers in order. The primenumber, after 13 is 17. So, theanswer to this question is 17.

6. Alternate PrimesIt can be explained by belowexample.

EXAMPLE 2, 11, 17, 13, __, 41

Sol. Here, the series is framed by takingthe alternative prime numbers.After 23, the prime numbers are 29and 31. So, the answer is 31.

7. The difference of any termfrom its succeding term isconstant (either increasingseries or decreasing series):

EXAMPLE 4, 7, 10, 13, 16, 19, __, 25

Sol. Here, the differnce of any termfrom its succeding term is 3.7 – 4 = 310 – 7 = 3So, the answer is 19 + 3 = 22

8. The difference between twoconsecutive terms will beeither increasing or decreasingby a constant number:

EXAMPLE 2, 10, 26, 50, 82, __

Sol. Here, the difference between twoconsecutive terms are10 – 2 = 826 – 10 = 1650 – 26 = 2482 – 50 = 32

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Series10Here, the difference is increasedby 8 (or you can say the multiplesof 8). So the next difference will be40 (32 + 8). So, the answer is 82 +40 = 122

9. The difference between twonumbers can be multiplied bya constant number:

EXAMPLE 15, 16, 19, 28, 55, __Sol. Here, the differences between two

numbers are16 – 15 = 119 – 16 = 328 – 19 = 955 – 28 = 27Here, the difference is multipliedby 3. So, the next difference will be81. So, the answer is 55 + 81 = 136

10. The difference can bemultiples by number whichwill be increasing by a constantnumber:

EXAMPLE 2, 3, 5, 11, 35, __Sol. The difference between two

number are3 – 2 = 15 – 3 = 211 – 5 = 635 – 11 = 24

11. Every third number can be thesum of the preceding twonumbers :

EXAMPLE 3, 5, 8, 13, 21, __Sol. Here, starting from third number

3 + 5 = 85 + 8 = 138 + 13 = 21So, the answer is 13 + 21 = 34

12. Every third number can be theproduct of the preceeding twonumbers :

EXAMPLE 1, 2, 2, 4, 8, 32. __

Sol. Here, starting from the third number1 × 2 = 22 × 2 = 42 × 4 = 84 × 8 = 32So, the answer is 8 × 32 = 256

13. Every succeeding term is got bymultiplying the previous termby a constant number ornumbers which follow aspecial pattern.

EXAMPLE 5, 15, 45, 135, __

Sol. Here,5 × 3 = 1515 × 3 = 4545 × 3 = 135So, the answer is 135 × 3 = 405

14. In certain series the terms areformed by various rule(miscellaneous rules). By keenobservation you have to findout the rule and theappropriate answer.

EXAMPLE 4, 11, 31, 90, __

Sol. Terms are,4 × 3 – 1 = 1111 × 3 – 2 = 3131 × 3 – 3 = 90So, the answer will be 90 × 3 – 4= 266

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Series 11q Shortcut Approach

· First check the direct formulas.

· If all the numbers are even, odd orprime.

· If all the number are perfect squaresor cubes.

· If all the numbers have a particulardivisibility.

· If all the numbers are succeedingby some additions or subtractionor multiplications or divisions by aparticular number or addition oftheir cubes and squares.

Remember· When the difference between the

consecutive numbers is same/constant or the number series is inarithmetic progression.

a, a + d, a + 2d, ..., a + ( n – 1) d.

Where 'a' is first term, d is thecommon difference.

· When any number series is in theform a, a + (a + 1), a + (a + 1) + (a + 2),.. . , n th term of the series be

( 1)2

n n +é ùê úë û

q Shortcut Approach(i) If numbers are in ascending order

in the number series.· Numbers may be added or

multiplied by certain numbersfrom the first number.

(A) 19 23 26 30 33 ?19 23 26 30 33 37

×4 ×3 ×4 ×3 ×4

(B) 1 3 12 60 ?1 3 12 60 360

×3 ×4 ×5 ×6

(ii) If numbers are in descendingorder in the number series,

· Numbers may be subtracted ordivided by certain numbers fromthe first number.

(A) 34 18 10 6 4 ?34 18 10 6 4 3–16 –8 –4 –2 –1

(B) 720 120 24 6 2 1 ?720 120 24 6 2 1 1/6 /5 /4 /3 /2

(iii) If numbers are in mixing order(increasing and decreasing) inthe number series.

· Numbers may be in addition,subtraction, multiplication anddivision in the alternate numbers.

200 165 148 117 104 ?200 165 148 117 104 77(14) 2+4 (13) 2–4 (12) 2+4 (11) 2–4 (10) 2+4 (9) 2–4

Step 1: Check whether it is ascending,descending or mixed order.Step 2: It is in mixing order. So it maybe in addition, subtraction, divisionand multiplication, squares and cubes.Step 3: In above series it is mixing ofsquare, addition and subtraction.(14)2 = 196 + 4 = 200(13)2 = 169. By adding 4 it gives 173.Try subtraction.169 – 4 = 165Here we found it is in order of squaringa number, adding by 4 and subtractingby 4.Hence, the answer for above series is 77.

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Series12

200 165 148 117 104 ?

–35 –17 –31 –13

+18 –14 –18 –14\ = – 13 – 14 = – 27 ? = 104 – 27 = 77

(B)14 17 31 48 ? 12714 17 31 48 79 12714+17=31 17+31=48 31+48=79

ALPHABET SERIESA series that is made by only alphabeticletters.

EXAMPLE G, H, J, M, ?

Sol. G H J M Q

+ 1 + 2 + 3 + 4

q Shortcut Approach· Remember all the alphabets and

their place number.· Intervals like :E J O T Y , C F I L O R U X

5 10 15 20 25 3 6 9 12 15 18 21 24

ALPHA NUMERIC SERIESThese kind of problems used bothmathematical operation and position ofletters in the alphabet in forward,backward order.

EXAMPLE K 1, M 3, P 5, T 7, ?Sol. Alphabets follow the sequence

+2 +3 +4 +5

K M P T Y

And numbers are increasing by 2.

MIXED SERIES

EXAMPLE Z, L, X, J, V, H, T, F, __, __Sol. The given sequence consists of

two series(i) Z, X, V, T, __(ii) L, J, H, F, __. Both consistingof alternate letters in the reverseorder.\ Next term of (i) series = R, andNext term of (ii) series = D

CONTINUOUS PATTERNSERIESIt is a series of small/capital letters thatfollow a certain pattern like repetition ofletters.

EXAMPLE b a a b – a b a – b b a – –Sol. b a a b b a / b a a b b a / b a

q Shortcut Approach· Firstly, count the number of blanks

and given letters.· Divide the whole sum of blanks and

letters by a multiple.· Note down the pattern common to

all groups separately.


Practice Exercise with Hints & Solutions – P-8-14Chapter Test – C-3-4Solved Papers

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ordpress.comINTRODUCTIONAs we know that English alphabet is agroup of English letters, hence theproblems based on alphabet are theproblems based on English letters.

Types of Problems(1) General series of alphabet(2) Random series of alphabet(3) Problems of word formation(4) Problems of letter gap(5) Finding Digits after rearrangement.

1. GENERAL SERIES OFALPHABET

EXAMPLE 1. Which of the followingoptions is seventh to the right of the 13th

letter from the left in a forward Alphabetseries?Sol. 1st of all we will write the forward

alphabet series as given below:

A B C D E F G H I J K L M

13th letter from left

N O P Q R S T U V W X Y Z

7th letter

From the above series it is clear thatM is the 13th letter from left and tothe right of M (13th letter from left),T is the 7th letter.

Here, we have solved this problemwith a general method. But this typeof problem can also be approachedthrough quicker method that willhelp you save some extra consumedtime.

q Shortcut Approach

(a) If both the directions are same thensubtraction of numbers takesplace.

(b) If the directions are opposite thenaddition of numbers takes place.

SHORTCUT METHOD FOR ABOVEEXAMPLE :Now, for solving the example we applythis rule. As we want to find out the 7th

letter to the right of the 13th letter fromthe left, the directions are opposite andthus shortcut (b) will be applied here.Hence, we add 7 + 13 = 20. Therefore, theanswer will be 20th from left. Also, 20th

from left less mean 26 – 20 + 1 = 7th fromright. We can easily see,\ 20th letter from left = TAlso 7th letter from right = TAfter solving the example, you musthave noticed that the above mentionedtrick is to calculate the actual positionof the required letter before going tosearch for it.

Alphabet &Number Test

Chapter

3

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Alphabet & Number Test14Remember

mth element to be counted from left to right of a series of x characters is equal to(x + 1 – m)th element to be counted from right to left of that series. This rule can bebetter illustrated by an example which is given below:Let us take the forward order alphabet series,A B C D E F G H I J K L M N O P Q R S T U V W X Y Z1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26As we know that English alphabet has 26 characters, hence, we have x = 26.Now suppose, we have to find out the position of K in the above given seriescounting from right to left.Position of ‘K’ in the English alphabet from left to right is 11. Thus m = 11\ Position of K in the above given series from right to left would be (26 + 1 – 11) = 16

How to solve problems when letters are dropped or deleted at regularintervals?

EXAMPLE 2. If every 3rd letter from left to right of English alphabet is deleted,then what would be the 6th letter from left in the new series obtained?Sol. General method:

A B C D E F G H I J K L M N O P Q R T U V W X Y ZSHere, deleted letters have been encircled and we find the new series as givenbelow:A B D E G H J K M N P Q S T V W Y Z1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 D E G H J K M N P Q S T V W Y Z

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18It is clear, that 6th letter from left in the new series is H.

q Shortcut ApproachNo doubt, above general method gives the correct answer. But we need to saveextra consumed time and this is the reason we go for a quicker approach.

As per the example, every third letter is deleted in the original series. It doesmean that we are left of two letters after every deletion. Here, ‘2’ is the key digit forus and we have to find out 6th letter from the left in the new obtained series.Therefore, we have to find a digit which is just less than 6 but divisible by 2. Forthis question the digit just less than 6 and divisible by 2 is 4. Now, we follow theoperation given below:

6th letter from the left in the new series = 462

+

= 8th letter from the left in the original series, which is it.In the same manners, we can find out any letter at a particular position in the

new obtained series.

\ 16th letter from the left in the new obtained series = 14162

+

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Alphabet & Number Test 15

= 23rd letter from the left in the original series which is W.18th letter from the left in the new obtained series

= 16182

+

= 26th letter from the left in the original series which is Z.The sample example can be asked in following way also.“If every third letter from left to right in English alphabet is dropped (or deleted),

then find out the 13th letter from right in the new obtained series”.To solve this, we find first of all the number of letters in the new obtained series.As every third letter is dropped, hence we have

2626 – 26 – 8 18

3æ ö = =ç ÷è ø

letters in the new series.

Point to be noted here that we divide 26 by 2 as every 3rd letter is dropped and

after division we take approximate value of 263

in round figure (approximate value

of 263

will be 8).

As per the example we have to find out 13th letter from right in the newlyobtained series. This loss mean (18 + 1 – 13) = 6th letter from left which is H.

Note that : This shortcut approach can also be applied to the dropping of every 4th,5th, 6th, 7th..... and so on letters from left to right at regular intervals.

How to solve problems based on the backward (reversed) alphabetseries?

While solving problems based on general series of alphabet, we come acrossthe various cases. In some cases we see that whole alphabet series is reversed butin some other cases 1st half of the series is reversed, or second half of the series isreversed or many segments of the alphabet series are reversed.

Let us take a case when a forward order alphabet series get reversed in threesegments. In 1st segment 8 letters get reversed; in 2nd segment the next 8 letters getreversed and in the 3rd segment the remaining 10 letters get reversed. Just see thepresentation given below:

A B C D E F G H

Get reversed

H G F E D C B A

(8 letters)

I J K L M N O P

Get reversed

P O N M L K J I

(8 letters)

Q R S T U V W X Y Z

Get reversed

Z Y X W V U T S R Q

(10 letters)

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Alphabet & Number Test16Now if you are asked to find out the 4th letter from left in the new obtained

series, then through general method, we simply do counting from left in the newseries and find out our required answer as ‘E’ because ‘E’ is at 4th position from leftin the new obtained series. But while solving such type of problems, we have to dosome time consuming formalities like (a) writing the original series (b) writing andreversing the letters of original series as per the question says and (c) countingthem to get the required answer. Such time consuming processes can be avoided ifwe go through “Remember” and solve the question with shortcut approach.

q Shortcut ApproachIt is clear that 4th letter from left in the new obtained series falls into first segmentwhich has 8 letters. Hence, 4th letter in the new obtained series = (8 + 1 – 4) = 5th letterfrom the left in the original series. As we know that exact position of 5th letter from leftin the original alphabet series is the position of E. Hence, E is our required answer.

If we have to find out 18th letter from left in the new obtained series, then that willbe 16 + (10 + 1 – 2) = 25th letter from left in the original alphabet series (why?) which is Y.

In fact, while finding out 18th letter, we can easily see that 18th letter is the 2nd

letter of 3rd segment and hence it will be not affected by 1st two segments having 8letters each. In other words to find out 18th letter in the new obtained series, we haveto find out the 2nd letter in the 3rd segment. This is the reason we find out the 2nd letterin the 3rd segment and then add the 16 letters of 1st two segment to get the 18th letterin the new obtained series. From this, we find that 18th letter from left in the newobtained series is the 25th letter from left in the original series. As 25th letter from leftin the original series is Y. So, (Y) will be our required answer.

Readers are advised to practice such type of problems as you much as possibleand after a certain time will notice that you have got a skill to solve such problemsin a few seconds and that too, without the use of pen and paper.

How to solve if positions of letters are interchanged?There is no any rule for such type of problems. Only the hard practice can given youa skill to solve such questions in a quick time.

EXAMPLE 3. If A and C interchange their places, B and D interchange theirplaces, F and H interchange their places and so on, then which letter will be 5th tothe left of Q?Sol. As per the question the interchanges take place as follows:

A B C D E F G H I J K L M N O P

Q R S T U V W X Y Z

Here we can see that Q interchanges with S. Then to left of Q, the 5th letterwould be P because P interchanges with N.

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Alphabet & Number Test 17How to find the Middle Letter?

q Shortcut ApproachCase I : Remember that if mth and nthletter from the left in the Englishalphabet are given then

Middle letter = 2m n+æ ö

ç ÷è ø th letter from

the left.

EXAMPLE 4. Which letter will bemidway between 8th letter from the leftand 16th letter from the left in theEnglish alphabet?Sol. Here, m = 8 and n = 16

then middle letter = 8 16 24

2 2+

=

= 12th letter from left in the alphabet= L

q Shortcut ApproachCase II: Remember that if mth and nthletter from the right in the Englishalphabet are given thenMiddle letter

= th2

m n+æ öç ÷è ø

letter from right

26 1 – 27 – th2 2

m n m né + ù é + ùæ ö æ ö= + =ç ÷ ç ÷ê ú ê úè ø è øë û ë û

letter from the left in the English alphabet.

EXAMPLE 5. Which letter will bemidway between 8th letter from the rightand 16th letter from the right in theEnglish alphabet.

Sol. Middle letter 8 1627 –2

é + ùæ ö= ç ÷ê úè øë û th

letter from left in the alphabet.or middle letter = (27 – 12) = 15th

letter from left = 0

Note : In case I and case II (m + n) mustbe divisible by 2.

q Shortcut ApproachCase III :Remember that if the mth letterfrom the left and the nth letter from theright are given then middle letter

= ( – ) 27

2m n +é ù

ê úë û th letter from the

left in the alphabet.

EXAMPLE 6. Which letter will bemidway between 8th letter from the leftand 15th letter from the right?Sol. Here, m = 8 and n = 15

Then middle letter (8 –15) 272

+é ù= ê úë û

202

é ù= ê úë û= 10th

letter from left in the Englishalphabet = J.

Note : In case III (m – n) + 27 must bedivisible by 2.

2. RANDOM SERIES OFALPHABETThis series is not in the propersequence and letters take theirposition in the series in jumbledmanner. Further, there is also apossibility that all the 26 letters ofEnglish alphabet are not availablein the series. Even same letters maybe repeated in the series.

EXAMPLE 7. How many letters in thefollowing series are immediatelypreceded by B but not immediatelyfollowed by D?

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Alphabet & Number Test18

\ Only the two times A fulfill thegiven condition and those A havebeen marked with the correct sign(ü). Those not fulfilling the conditionhave been marked with the crosssign (×). \ Required answer is 2.

3. PROBLEMS ON WORDFORMATIONIn such problems, a word is givenand you have to find out the numberof words to be formed out of someletters drawn from that particularword.

EXAMPLE 8. How many meaningfulwords can be formed from the 3rd, 4th, 6th

and 8 th letter of the word‘CONTROVERSIAL’?Sol.

C O N T R O V E R S I A L

3rd 4th 6th 8th

Now, from letters N, T, O and E,two words ‘NOTE’ and ‘TONE’ canbe formed.

4. PROBLEMS OF LETTERGAP

Case II:

EXAMPLE 9. How many pairs of lettersare there in the word ‘DREAMLAND’which have as many letters between themas in the English alphabet?

Sol. Here, we are asked to solve problemaccording to English alphabet. Inthis case we have to count bothways. It does mean that we have tocount from left to right and from rightto left. Let us see the followingpresentation:

D R E A M L A N D

The above presentation makes itclear that the required pairs of lettersare 4. (Pairs: DA, EA, ML and LN)

Case II:

EXAMPLE 10. How many pairs ofletters are there in the word‘DREAMLAND’ which have the samenumber of letters between them as inthe English alphabet in the samesequence.Sol. Here, we are asked to solve problems

according to the alphabeticalsequence. It does mean that wehave to do counting only from leftto right. Let us, see the followingpresentation:

D R E A M L A N D

The above presentation makes itclear that the required pair of lettersis only 1 (Pair: LN)

R S P Q B A H M A C F B A D N O P B A C D.

Sol. R S P Q B A H M A C F B A D N O P B A C D

× ×

ü ü

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Alphabet & Number Test 195. FINDING DIGITS AFTER

REARRANGEMENTIn this type of problems, a specifiedorder or pattern is used to rearrangethe positions of digits of thenumber. Then, either the number ofthose digits is found out whosepositions remain unchanged afterrearrangement or the digit atparticular place from left or right ofthe number is to be found out.

EXAMPLE : (Direction (Qs. 11-15)Following questions are based on thefive three-digit numbers given below:

713 361 458 932 72411. If the positions of the first and the

third digits are interchanged ineach of these numbers, then whichof these will be an even number.

Sol. According to the question,7 1 3 3 6 1 4 5 8 9 3 2 7 2 4

3 1 7 1 6 3 8 5 4 2 3 9 4 2 7

Original Numbers :

New Arrangement :

So, here only one number is eveni.e., 854.

12. What is the difference between thesum of the three digits of thehighest and that of the secondhighest number?

Sol. Highest number = 932Second highest number = 724So, the required difference= (9 + 3 + 2) – (7 + 2 + 4)= 14 – 13 = 1

13. If all the three digits are arrangedin ascending order (from left toright) within the number, in eachof these numbers, then which ofthese will be second lowest ?


1 3 7 1 3 6 4 5 8 2 3 9 2 4 7

Original number :

New arrangement :

So, the second lowest number willbe 137.

14. If the positions of the second andthe third digits are interchangedin each of these numbers, thenwhich of these will be exactlydivisibly by 2 ?


7 3 1 3 1 6 4 8 5 9 2 3 7 4 2

Original Numbers :

New Arrangement :

So, two numbers will be exactlydivisible by 2, i.e., 316 and 742.

15. If the following numbers arearranged in descending order, thenwhat will be the square of the digitssum of the third number from theright end of the new arrangement ?


9 3 2 7 2 4 7 1 3 4 5 8 3 6 1

Original Numbers :

New Arrangement :

3 from the right endrd

Now, digits sum of the 3rd numberfrom the right= 7 + 1 + 3 = 11\ Square of the digits sum = (11)2 =121.



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Coding-Decoding20

INTRODUCTION

In this segment of commonsensereasoning, secret messages or wordshave to be decoded. They are coded asper a definite pattern/ rule which shouldbe identified first. Then the same isapplied to decode another coded word.

TYPE-1 CODING BY LETTERSHIFTING

Pattern 1:

Coding in forward sequence

EXAMPLE 1. If ‘GOOD’ is coded as‘HPPE’, then how will you code ‘BOLD’?Sol. Here,every letter of the word

‘GOOD’ shifts one place in forwardalphabetical sequence.

G

H

+1O

P

+1O

P

+1D

E

+1

Similarly, every letter in the word‘BOLD’ will move one place inforward alphabetical sequence asgiven below:

B

C

+1O

P

+1L

M

+1D

E

+1

\ Code for ‘BOLD’ will be ‘CPME’.

Pattern 2:Coding in backward sequence.

EXAMPLE 2. If ‘NAME’ is coded as‘MZLD’, then how will code 'SAME'?Sol. Here, every letter of the word

‘MZLD’ moves one place inbackward alphabet sequence. Let ussee:

N

M

–1A

Z

–1M

L

–1E

D

–1

Similarly, every letter of the word‘SAME’ will move one place inbackward alphabet sequence. Let ussee :

S

R

–1A

Z

–1M

L

–1E

D

–1

\ Code for ‘SAME’ will be ‘RZLD’.

Pattern 3:Coding based on skipped sequence.

EXAMPLE 3. If the word ‘FACT’ iscoded as ‘IDFW’; then how will you code‘DEEP’?Sol. Here, every letter of the word shifts

three place in forward alphabeticalorder.

F

I

+3A

D

+3C

F

+3T

W

+3

Coding-Decoding

Chapter

4

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Coding-Decoding 21Similarly, ‘DEEP’ can be coded. Letus see :

D

G

+3E

H

+3E

H

+3P

S

+3

\ Code for ‘DEEP’ will be ‘GHHS’.

q Shortcut Approach• Observe alphabets given in the

code carefully.• Find the sequence it follows

whether it is ascending/descending• Detect the rule in which the

alphabets follow.• Fill the appropriate letter in the

blank given.

TYPE-2 : CODING BYSUBSTITUTIONIn this coding, some words are replacedby some substituted words and on thebasis of substituted word the code isderived.

EXAMPLE 4. If 'cages' are called'rockets', 'rockets' are called 'traps','traps' are called 'planets', 'planets' arecalled 'aeroplanes', 'aeroplanes' arecalled 'cycles' are cycles' are called'cars', what is Earth

(a) Cycles (b) Rockets(c) Planet (d) Aeroplanes(e) Cars

Sol. Earth is a planet and here planetsare called aeroplanes. So, earth willbe called aeroplanes.

TYPE-3 : CODING BYREVERSING LETTERSIn this coding, all letters of a word hasbeen reversed.

EXAMPLE 5. If ‘TEMPERATURE’ iscoded as ‘ERUTAREPMET’, then howwill you code ‘EDUCATION’ followingthe same scheme.Sol. Here, the word ‘TEMPERATURE’has been reversed. Hence, the code for‘EDUCATION’ will be ‘NOITACUDE’.

TYPE 4 : CODING IN FICTIONLANGUAGEIn some cases of coding-decoding,fictions language is used to code somewords. In such questions, the codes fora group of words is given. In such typesof problems, codes for each word can befound by eliminating the common words.

EXAMPLE 6. In a certain codelanguage ‘over and above’ is written as‘da pa ta’ and ‘old and beautiful’ is writtenas ‘Sa na pa’. How is ‘over’ written inthat code language?

Sol. Over and above ® da Pa ta

Old and beautiful ® Sa na Pa

Clearly, ‘and’ is common in both anda common code is ‘Pa’.\ Code for ‘and’ must be ‘Pa’.Code for ‘over’ = ‘da’ or ‘ta’.Code for above = ‘da’ or ‘ta’.Code for old = ‘Sa’ or ‘na’Code for beautiful = ‘Sa’ or ‘na’\ We can’t certainly say what willbe exact code for ‘over’. But it issure that code for ‘over’ must beeither ‘da’ or ‘ta’.

q Shortcut Approach

• Firstly, write the words and theircodes as given in the question instraight line with an arrow inmiddle.

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Coding-Decoding22

EXAMPLE 8. In a certain code 3 iscoded as ‘R’, 4 is coded as ‘D’, 5 is codedas ‘N’, 6 is coded as ‘P’, then find thecode for ‘53446’.Sol. As per the given condition

3 4 5 6R D N P

Now,5 3 4 4 6N R D D P

\ Code for 53446 = NRDDP.

TYPE-6 : MATHEMATICALOPERATIONS WITH THEPOSITION NUMBERS OFLETTERS

EXAMPLE 9. In a certain code, if‘TALE’ is written as 38, then how willyou code ‘CAME’ using the same codingscheme?Sol. Look at the numbered alphabet

and write down the numbercorresponding to the letters of theword ‘TALE’.T A L E

20 1 12 5The fact that the code for ‘TALE’ is38, gives you a clue that the code isprobably obtained by performing anarithmatical operations of thenumbers of each other. Let us see :20 + 1 + 12 + 5 = 38Thus, the code for ‘CAME’ isC A M E 3 + 1 + 13 + 5 = 22\ Code for ‘CAME’ = 22

• Now, find the common words andtheir corresponding codes.

• Encircle each pair with the sameshape.

• Finally, we have each word andits corresponding code.

TYPE-5 : CODING BASEDON NUMBERS

Pattern 1:

When numerical values are given to words.

EXAMPLE 7. If in a certain languageA is coded as 1, B is coded as 2. C iscoded as 3 and so on, then find the codefor AEECD.

Sol. As given the letters are coded asbelow:

A B C D E F G H I1 2 3 4 5 6 7 8 9

Now, A E E C D1 5 5 3 4

\ Code for AEECD = 15534

q Shortcut Approach

• First you have to observe thenumber code.

• Now, notice the position ofnumber.

• Search the common pattern.

Pattern 2:

When alphabetical code value are givenfor numbers.

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Coding-Decoding 23Remember• If the letters in the code look the

same as in the original text, it will bea scramble type coding.

• If more than one codes are giventhen likely the required code can bedrived from the question itself andyou will not need to solve itmathematically.

• If the code for a word is a one digitnumber then likely the position ofthe letters are added and the digitsare summed up until the one digitnumber is arrived at.

TYPE-7 : MATRIX CODING

In this type of questions two matricesare given. In each matrix there are 25 cellsand these cells contain two classes ofalphabets. The columns and rows ofmatrix I are numbered from 0 to 4 andthat of matrix II from 5 to 9. A letter fromthese matrices can be represented firstby its row number and next by its columnnumber. For example. ‘A’ Can berepresented by 32 or 43.

EXAMPLE 10.

Directions: In each of the followingquestions find out the correct set ofnumber pairs for the given word from thetwo matrices given above.

Matrix I

0 1 2 3 40 I A U E O1 E U O A I2 O A I E U3 E U A O I4 E I O A U

Matrix II

5 6 7 8 95 K R L M N6 M R K N L7 K N M L R8 M L K R N9 N R L K M

1. MONK(a) 58, 33, 67, 98(b) 65, 02, 59, 67(c) 65, 04, 89, 75(d) 65, 20, 89, 68

Sol.A ® 01, 13, 21, 32, 43E ® 03, 10, 23, 30, 40I ® 00, 14, 22, 34, 41O ® 04, 12, 20, 33, 42U ® 02, 11, 24, 31, 44K ® 55, 67, 75, 87, 98L ® 57, 69, 78, 86, 97M ® 58, 65, 77, 85, 99N ® 59, 68, 76, 89, 95R ® 56, 66, 79, 88, 96So, 65, 04, 89, 75 is correct



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Blood Relations24

INTRODUCTIONBlood relation does mean biologicalrelation. Remember a wife and husbandare met biologically related but they arebiological parents of their own children.Similarly, brother, sister, paternalgrandfather, paternal grandmothermaternal grandfather, maternalgrandmother, grandson, granddaughter,niece, cousin etc. are our blood relatives.

TYPES OF BLOODRELATIONSThere are mainly two types of bloodrelatives:(i) Blood relation from paternal side(ii) Blood relation from maternal side(i) Blood relation from paternal

side:

This type of blood relation can befurther subdivided into threetypes:

(a) Past generations of father : Greatgrandfather, great grandmother,grandfather, grandmother etc.

(b) Parallel generations of father:Uncles (Brothers of father), Aunts(sisters of father) etc.

(c) Future generations of father:Sons, daughters, grandsons,granddaughters etc.

(ii) Blood relation frommaternal side:This type of blood relations canalso be subdivided into threetypes:

(a) Past generations of mother:Maternal great grandfather,maternal great grandmother,maternal grandfather, maternalgrandmother etc.

(b) Parallel generations of mother:Maternal uncles, maternal aunts etc.

(c) Future generations of mother:Sons, daughters, grandsons,granddaughters etc.

1 Son of father or mother Brother2 Daughter of father or mother Sister3 Brother of father Uncle4 Brother of mother Maternal uncle5 Sister of father Aunt6 Sister of mother Aunt7 Father of father Grandfather8 Father of father's father Great grand father 9 Father of grandfather Great grandfather

Table of Blood Relations

Blood Relations

Chapter

5

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Blood Relations 25

10 Mother of father Grandmother11 Mother of father's mother Great grandmother12 Mother of grandmother Great grandmother13 Father of mother Maternal grandfather14 Father of mother's father Great maternal grand father

16 Mother of mother Maternal grandmother17 Mother of mother, mother Great maternal grandmother18 Mother of maternal grandmother Great maternal grandmother19 Wife of father Mother20 Husband of mother Father21 Wife of Grandfather Grandmother22 Husband of Grandmother Grandfather23 Wife of son Daughter-in-law24 Husband of daughter Son-in-law25 Brother of Husband Brother-in-law26 Brother of wife Brother-in-law27 Sister of Husband Sister-in-law28 Sister of wife Sister-in-law29 Son of brother Nephew30 Daughter of brother Niece31 Wife of brother Sister-in-law32 Husband of sister Brother-in-law33 Son of sister Nephew34 Daughter of sister Niece35 Wife of uncle Aunt36 Wife of maternal uncle Aunt37 Son/daughter of uncle/Aunt Cousin

Cousin

Father of maternal grandfather Great maternal grandfather

Cousin

Son/daughter of sister of Fathar Cousin

40

39

38

15

Son/daughter of sister of Mother

Son/daughter of maternal uncle/maternal aunt

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Blood Relations26

41 Only son of grandfather Father42 Only daughter of maternal Mother

grandfather43 Daughter of grandfather Aunt44 Sons of grandfather other Uncle

than father45 Son of maternal grandfather Maternal Uncle.

/maternal grand mother46 Only daughter in law of Mother

grandfather/ grandmother47 Daughters in law of Aunt other than mother

grandfather/ grandmother 48 Daughters-in-law of Aunt maternal

maternal grandfather/ grandmother49 Neither brother nor sister Self

Some Important Informationabout Blood RelationA. Without the information of gender,

no relationship can be establishedbetween two people. For example,If given that R is the child of P &Q, then we can only say that P &Q are the parents of R. But we cannot find out:(i) R is the son of P & Q or R is

the daughter of P & Q.(ii) Who is mother of R and who

is father of R.But if we have given that P is amale, Q is a female and R is male,then we can easily say that R isthe son of P and Q. Further we canalso say that P is father of R and Qis mother of R.

B. Gender can not be decided on thebasis of name. For example, in Sikhcommunity the names like Manjit,Sukhvinder etc. are the names ofboth male and female. Similarly, in

the Hindu Community ‘Suman’ isthe name of both male and female.

q Shortcut Approach• While solving blood relation

based question, first of all find outthat two persons between whoma relationship has to beestablished.

• Next, try to find out middle relation.• Finally, find out the relationship

between two persons to beidentified for this purpose.

TYPES OF PROBLEMS(1) General Problems on Blood Relation(2) Blood Relation based on Family

Tree(3) Coded Blood Relation(1) General Problem on Blood

Relation

EXAMPLE 1. Pointing towards aphotograph, Mr. Sharma said, “She is the

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Blood Relations 27only daughter of mother of my brother’ssister.” How is Mr. Sharma related to thelady in the photograph?Sol. Here, we have to find relationship

between Mr. Sharma & the lady inthe photograph.Mother of my brother’s sister doesmean my (Mr. Sharma’s) mother.Only daughter of Mr. Sharma’smother does mean “sister of Mr.Sharma”.

q Shortcut Approach

• Read the statement from right toleft to develop the relation byusing blood relation table.

(2) Blood Relation based onFamily Tree

EXAMPLE 2. Q is the brother of C andC is the sister of Q. R and D are brotherand sister. R is the son of A while A & Care wife and husband. How is Q relatedwith D.Sol. For such type of question a family

tree is made in which somesymbols are used as below:‘Û’ is used for husband & wife.‘___’ is used for brother & sister‘ | ’ is used for parents (father ormother). Parents are put on topwhile children are put at thebottom.‘–’ or minus sign is used for female‘+’ or plus sign is used for male.Now, adopting and using theabove given symbols we can makea family tree and solve the givenproblem, let us see the family tree :

Family tree :

A C Q

R

+ – +

+ D–

As per the question Q is the brother of Cand C is the sister of Q. Hence, relationbetween C & Q has been presented as

( )–C — Q+ where ‘–’ sign above C

makes it clear that C is a female and ‘+’sign above ‘Q’ makes it clear that Q is amale. Similarly, for R and D. The

presentation +R — D-æ öç ÷è ø

has been

made. Further according to the question,

A and C are having a husband and wiferelationship and hence this has been

presented as A C+

-æ öÛç ÷è ø

. As it is already

given that C is the sister of Q and A andC are wife and husband, this becomesclear that A is the male member of thefamily and this is the reason A has ‘+’ asits gender sign. Lastly, the vertical linegives father and son relationship and has

been presented as A

R|+

+

æ öç ÷ç ÷è ø

. Now from this

family tree it becomes clear that C is themother of R and D and as Q is the brotherof C, then Q will definitely be the maternaluncle of R & D. Hence, we can say thatQ is the maternal uncle of D and this isthe required answer for our question.

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Blood Relations28

q Shorcut Approach• Follow the symbols for male (+)

and (–) female.• Remember the generations and

relations.Note : In solving family tree basedrelations make sure that your diagramis in correct representation.(3) Codded Blood Relations –

EXAMPLE 3. If P + Q means P ishusband of Q, P/Q means P is the sisterof Q, P*Q means P is the son of Q. flowis D related to A in D*B + C/A ?Sol. C/A – C is sister of A.

B + C/A – B is brother-in-law of A(Sister's husband – broter-in-law)D*B + C/A – D is nephew of A(Sister's husband's son meanssister's son i.e., nephew)So, D is nephew to A.

Shortcut Method :By using symbols and generationrelations :

Couple Sister

SonNephew

B(+)

D

(–)C A

(+)

So, it is clearly shown that D isnephew to A.

q Shortcut Approach• The best way to solve blood

relation questions, you try and

relate every statement to'yourself'. The starting name ofthe statement could be assumedas your name or you.

• When the statement is very long,it can get confusing. So, breakdown every statement in thequestion into sub statements andsolve the question.

• Do not assume the gender of anyperson in the question just basedon the names given in thequestion.

• Draw a family tree where peopleof the same generation are placedat the same level and the entirediagram is in the form of ahierarchy.

Remember• Concentrate on points which give

maximum definite information.• Read the questions carefully and

try identifying the personsbetween whom relationship is tobe established. Possibly putyourself in given character so thatit becomes easy for you tounderstand.

• Whilst concluding the relationshipbetween two people be carefulabout the gender of the personbeing talked about as it is possibleto commit mistake by assuming thegender of the person which is notgiven in the data or which can't beextracted from the data/information given.



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ordpress.comINTRODUCTIONThis part of reasoning comes under thecategory of common sense reasoning.In fact, this segment gauges the senseof direction of a candidate.

CONCEPT OF DIRECTIONIn our day to day life, we make ourconcept of direction after seeing theposition of sun. In fact, this is a truththat sun rises in the East and goes downin the West. Thus when we stand facingsunrise, then our front is called East whileour back is called West. At this positionour left hand is in the Northward and theright hand is in the Southward. Let ussee the following direction map that willmake your concept more clear.

Direction Map

North

North-East

East

South-East

SouthSouth-West

West

North-West

q Shortcut ApproachTo remember four maindirections, always remember theword 'NEWS.'

Note: On paper North is always on topbe while South is always in bottom.

CONCEPT OF DEGREELet us see the following picture:

0º

45º

90º

135º

180º

225º

270º

315º

360º

Clo

ckw

ise

(CW

)

0º

315º

270º

225º

180º

135º

90º

45º

360º

Anti clockw

ise (AC

W)

Direction andDistance

Chapter

6

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Direction and Distance30Remember• Angle between two consecutive

main directions is always 90°.• Angle between two consecutive

subdirections is always 90°.• Angle between a main direction

and a subdirection is always 90°.

CONCEPT OF TURNRight turn = Clockwise turnLeft turn = Anticlockwise turnLet us understand it throughpictorial representation:

Right turn R

ight turn

Right turn

Righ

t tur

n

(i)Left turn

Left turn

Left turn

Left

turn

(ii)

Right turn

(iii)

Left turn

(iv)

EXAMPLE 1. Raman walked 2 kmWest from his office and then turnedSouth covering 4 km. Finally, he waked3 km towards East and again move 1 kmWest. How far is Raman from his initialposition.Sol. Raman starts from his office A,

moves 2 km West upto B, then 4km to the South upto C, 3 km Eastupto D and finally 1 km West uptoE, Thus his distance from the initialposition AE = BC = 4 km.

A

2 kmC ED

B 2 km

1 km

4 km

Remember• If our face is towards North, than

after left turn our face will be towardsWest while after right turn, it will betowards East.

• If our face is towards South, thenafter left turn our face will be towardsEast and after right turn it will betowards West.

• If our face is towards East, then afterleft turn our face will be forwardsNorth and after right turn it will betowards South.

• If our face is towards West, thenafter left turn our face will be towardsSouth and after right turn it will betowards North.

• If our face is towards North-West,then after left turn our face will betowards South-West and after rightturn it will be towards North-East.

• If our face is towards South-West,then after left turn our face will betowards South-East and after rightturn it will be towards North-West.

• If our face is towards South-East,then after left turn our face will betowards North-East and after rightturn it will be towards South-West.

• If our face is towards North-East,then after left turn our face will betowards North-West and after right-turn it will be towards South-East.

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Direction and Distance 31CONCEPT OF MINIMUMDISTANCEMinimum distance betweeninitial and last point

2 2 2h b P= +

where,

h = Hypotenuse

b = Base

A

P h

B b C

P = Perpendicular

Remember this important rule isknown as ‘Pythogoras Theorem’

EXAMPLE 2. Rashmi walks 10 kmtowards North. She walks 6 km towardsSouth then. From here she moves 3 kmtowards East. How far and in whichdirection is she with reference to herstarting point?Sol. It is clear, Rashmi moves from A 10

km Northwards upto B, thenmoves 6 km Southwards upto C,then turns towards East and walks3 km upto D.Then, AC = (AB – BC) = 10 – 6 = 4kmCD = 3km.

6 km3 km

C D

A

B

10 km

\ Rashmi’s distance from startingpoint A

= AD = 2 2 2 2AC +CD 4 3= +

16 9 25 5km.= + = =

From figure, D is to the North-Eastof A.

SHADOW CASE

In Morning/Sunrise Time(a) If a person facing towards Sun, the

shadow will be towards his backor in West.

(b) If a person facing towards South,the shadow will be towards hisright.

(c) If a person facing towards West,the shadow will be towards hisfront.

(d) If a person facing towards North,the shadow will be towards his left.

In Evening/Sunset Time(a) If a person facing towards Sun, the

shadow will be towards his backor in East.

(b) If a person facing towards North,the shadow will be towards hisright.

(c) If a person facing towards East,the shadow will be towards hisfront.

(e) If a person facing towards South,the shadow will be towards his left.

Note : At 12:00 noon there is noshadow because the rays of the sunare vertically downward.

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Direction and Distance32

EXAMPLE 3. Early morning aftersunrise, Rajesh was standing infront ofhis house in such a way that his shadowas falling exactly behind him. He startswalking straight and walks 5 m. Heturns to his left and walks 3 m and againturning to his left walks 2m. Now inwhich direction is he from his startingpoint?Sol. The shadow of Rajesh was fallingexactly behind him. So, he was facingtowards East. Diagram clearly showsthat Rajesh was in North-East withreference to the starting point.

2 m

2 m

5 m

Star

ting p

oint

q Shortcut Approach

• Draw four lines and write alldirections on each edge of itsame.

• Think the 'you' are standing at allarrow head facing outward fromcentre.

• Read the statement line by line.• Move yourself as per statement

asked and prepare a diagram asper line by line statement.

• Show, check and verify thedirection and distance of youfrom starting point.



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ordpress.comTIME SEQUENCEIn time sequence, we have to defect exacttime from the given time sequence.To solve problems related to timesequence, let us gather first thefollowing informations :

1 Minute = 60 seconds1 Hour = 60 minutes1 Day = 24 hours1 Week = 7 days1 Month = 4 weeks1 Year = 12 months1 Ordinary year = 365 days1 Leap year =366 days1 Century = 100 years

Remember• A day is the period of the earth’s

revolution on its axis.• A ‘Solar year’ is the time taken the

earth to travel round the sun. It isequal to 365 days, 5 hours, 48

minutes and 1472

seconds nearly..

• A ‘Lunar month’ is the time takenby the moon to travel round theearth. It is equal to nearly 28 days.

Leap Year• If the number of a given year is

divisible by 4, it is a leap year.Hence, the years like 1996, 2008,2012 are leap years. But years like1997, 1991, 2005, 2007 are notdivisible by 4 and therefore, suchyears are not leap years.

• In a leap year, February has 29 days.• A leap year has 52 weeks and 2 days.

Therefore, a leap year has 2 odd days.

Ordinary year• An ordinary year has 12 months.• An ordinary year has 365 days.• An ordinary year has 52 weeks

and 1 day. Therefore, an ordinaryyear has 1 odd day.

CENTURY (100 YEARS)• A century has 76 ordinary years

and 24 leap years.• A century has 5 odd days.Odd daysOdd days in an ordinary year = 1Odd days in a leap year = 2Odd days in 100 years = 5Odd days in 200 years = (5 × 2)

= 1 week + 3 days = 3Odd days in 300 years = (5 × 3)

= 2 weeks + 1 day = 1Odd days in 400 years = (5 × 4 + 1)

= 21 days= 3 weeks + 0 day = 0

Similarly, each 800, 1600, 2000, 2004, etc.has 0 odd days.

EXAMPLE 1. Neena returned homeafter 3 days earlier than the time shehad told her mother. Neena’s sisterVeena reached five days later than theday Neena was supposed to return. IfNeena returned on Thursday, on whatday did Veena return ?Sol. Neena returned home on Thursday.

Neena was supposed to return 3days later, i.e., on Sunday.Veena returned five days later fromSunday. i.e., on Friday.

Time Sequence, Number& Ranking Test

Chapter

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Time Sequence, Number & Ranking Test34NUMBER TESTIn such test, generally you are given along series of numbers. The candidateis required to find out how many times anumber satifying the conditionsspecified in the question occurs.

EXAMPLE 2. How many 8s are therein the following number sequence whichare immediately preceded by 5 but notimmediately followed by 3?

3 8 5 8 4 5 8 3 9 8 8 5 8 8 8 9 3Sol. Let use see the following :

3 8 8 4 5 8 3 9 8 8 5 88 8 9 3Clearly, two such 8s are there.

RememberThere is no rule as how to attempt thesequestions but we can practice thesequestions :

Left < > Right

A is preceding B C is the following B

A B C

RANKING TESTIn such problems, the ranks of a personboth from the top and from the bottomare given and on the basis of this the totalnumber of persons is asked. Sometimesquestion is twisted also and positionof a particular person is asked.

q Shortcut ApproachFormulas to determine the positioningof a person(1) Left + Right = Total + 1(2) Left = Total + 1 – Right(3) Right = 1 + 1 – left(4) Total = left + Right

Note : The above formulas are only fora single person's position

EXAMPLE

1 2 3 4 5|

3rd from left3rd from right

Total = 3 + 3 – 1

q Shortcut Approach

Same for Vertical &Horizontal(1) Total + 1 = Top + Bottom(2) Top = Total + 1 – Bottom(3) Botom = Total + 1 – Top(4) Total = Top + Bottom

EXAMPLE 3. In a row of 40 students,A is 13th from the left end, find therank from right end.Sol. Total = 40

A 13L

A's rank from right side= Total + 1 – left= 40 – 13 + 1= 27 + 1= 28

ebooks Reference Page No.Practice Exercises with Hints & Solutions – P-46-50Chapter Test – C-13- 14Past Solved Papers

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ordpress.comINTRODUCTION

In this particular type of problems,certain inter-related words are given andnumbered, followed by varioussequences of the numbers denotingthem, as alternatives.

TYPES OF SEQUENCE

(i) Sequence of occurence ofevents or various stages in aprocess.

EXAMPLE 1. Consultation2. Illness3. Doctor4. Treatment5. Recovery

Sol. Clearly illness occurs first. Onethen goes to a doctor and afterconsultation with him,undergoes treatment to finallyattain recovery.

(ii) Sequence of objects in aclass or group

EXAMPLE 1. Member2. Country3. Community4. Family5. Locality

Sol. Member ® Family ®Community® Locality®Country

(iii) Sequence in Ascending orDescending order

EXAMPLE 1. Furniture2. Forest3. Wood4. Country5. Trees

Sol. Country ® Forest ® Trees®Wood ® Furniture.

(iv) Sequential order of wordsAccording to Dictionary

EXAMPLE 1. Direct2. Divide3. Divest4. Devine5. Divisons

Sol. Devine ® Direct ® Divest ®Divide ® Divisons.

q Shortcut Approach • Remember all English alphabets

in forward and reverse order • Knowledge of our nature or

surroundings

Chapter

8Logical Sequence

of Words


Practice Exercises with Hints & Solutions – P-51-54Chapter Test – C-15-16Past Solved Papers

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ordpress.comINTRODUCTIONIn this, the questions are based ondifferent number. This type of problemhaving figure which follows a particularrule for their different number. We havethen asked to find a missing number byusing same rule.TYPES OF NUMBER PUZZLEPATTERN 1 : SINGLE FIGUREPATTERN

4416 10

685 33?

Here, a clockwise pattern is beingfollowed. If we move clockwise we cansee that numbers are increasing. If weobserve it more closely, we can crack thepattern which isAs, 4 × 2 + 2 = 10, 10 × 3 + 3 = 33So, 33 × 4 + 4 = 136PATTERN 2 : MULTIPLE FIGUREPATTERN

110

65

30

75

(i)

25

?

103

67

82

99

97

80

(ii) (iii)Here, a series of figure is given. Checkingthe pattern in the first two figures, wehave to find missing number in the third.If we observe the first two figureproperly, we get an idea of the pattern.As, 110 + 30 – 75 = 65, 97 + 82 – 80 = 99So, 103 + 25 – 67 = 61.

q Shortcut Approach

• The first step is to observe thefigure and check if there is anyfamiliar pattern in the givenquestion.

• The second step is finding out thepattern.

• Ther is no need to memorize anypattern.

• All you need is to understand theconcept and decipher the pattern.



Number PuzzlesChapter

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Venn Diagram 37

INTRODUCTIONVenn diagrams are pictorial way ofrepresent the set of article. There aredifferent regions which needs properunderstanding for solving problemsbased on given Venn diagrams.

TYPES OF VENN DIAGRAM

Analysis BasedVenn Diagram

Identification of RelationBased Venn Diagram

(i) ANALYSIS BASED VENNDIAGRAM -In this type, generally a venndiagram comprising of differentgeometrical figures is given. Eachgeometrical figure in the diagramrepresents a certain class.

q Shortcut ApproachCase - I:Two articles:

P Q

IA IIAB IB

Here, IA represents only P IB represents only QIIAB represents P and Q

EXAMPLE

12

3

– represents student passedin English

– represents student passedin Reasoning.1 – represents student passed inEnglish only2 – represents student passed inReasoning only3 – represents student passed in

both English Reasoning both.

q Shortcut Approach Case: - II Three articles

P Q

R

1 2

3

4

5

67

1 – represents P only2 – represents Q only3 – represents R only4 – represents Q and R (not P)5 – represents P and Q (not R)6 – represents P and R (not Q)7 – represents P, Q and R

Venn Diagram

Chapter

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Venn Diagram38EXAMPLE

1 2

3

4

5

67

Engineer Doctor

Farmer

1 ® Engineer2 ® Doctor3 ® Farmer4 ® Doctor who is farmer also5 ® Engineer who is doctor also6 ® Engineer who is farmer also7 ® Person who is Engineer,doctor and farmer.

(ii) Identification of Relation BasedVenn Diagram -In this type, some standardrepresentations for groups ofthree items with different casesof venn diagrams are given.

q Shortcut Approach

When one class of items is completelyincluded in the another class of itemthen it is represented by the givendiagram

I

II

EXAMPLE

I – MangoII – Fruit

Here, all mango are fruit.

q Shortcut ApproachIf two classes of item are completelydifferent from each other but they allare completely included in third classthen the relationship is represent of thediagram.

III

I II

EXAMPLE

I – represent potatoII – represent onionIII – represent vegetable

q Shortcut Approach• If two group of items having some

common relationship and both ofthem are all included in thirdclass then the relationship isrepresented by the diagram.

III

I II

EXAMPLE Brother, Father, Male.

I ® BrotherII ® FatherIII ® MaleSome Brother may be Father andall are male.

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Venn Diagram 39

q Shortcut ApproachWhen one class of item is completelyincluded in another group while thirdis not related to both of them then suchcondition are diagrammati-callyrepresented by

I

II

III

EXAMPLE

Cricketer, player and farmerI – CricketerII – PlayerIII – FarmerAll cricketers are players butfarmers not.

q Shortcut ApproachIf three group of things are related toeach other

I II

III

EXAMPLE

Graduate, Engineer and DoctorGraduate may be Engineer andDoctor.

q Shortcut ApproachWhen two group of items arecompletely unrelated to each otherwhile they are partly related with thirdgroup of item

I II III

EXAMPLE Cloth, Red, Flowers.Some cloth are Red and also someFlowers are red.

q Shortcut ApproachWhen group of items are completelydifferent from each other

I

III

II

EXAMPLE

Red, Yellow, BlackThese are all different colour.



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Mathematical Operation Arithmetical Reasoning40

INTRODUCTIONIn this type of problem, usuallymathematical symbol are converted intoanother form by either interchanging thesymbol or using different symbol inplace of usual symbol and then calculatethe equation according to the givencondition.

RememberWhile simplifying a mathematicalproblem follow 'VBODMAS' ruleV - Viniculum bracketB - BracketO - OfD - DivisionM - MultiplicationA - AdditionS - Subtraction

TYPES OF MATHEMATICALOPERATION

(i) SYMBOL SUBSTITUTIONIn this, various mathematical

symbols, followed by a questioninvolving calculation of an expression.It is required to put in the real signs inthe given equation and then solve thequestion.

EXAMPLE 1. If ‘+’ stands for division,‘×’ stands for addition, ‘–’ stands formultiplication, and ‘¸’ stands forsubtraction, then which of the followingequation is correct?

(a) 36 × 6 + 7 ̧ 2 – 6 = 20(b) 36 + 6 – 3 × 5 ̧ 3 = 24(c) 36 ¸ 6 + 3 × 5 – 3 = 45(d) 36 – 6 + 3 × 5 ̧ 3 = 74

Sol. 36 × 6 ̧ 3 + 5 – 3Þ 36 × 2 + 5 – 3 = 74

(ii) INTERCHANGE OF SIGNS &NUMBERSIn this, the given equation

becomes correct and fully balancedwhen either two signs of the equation orboth the numbers and the signs of theequations are interchanged.

EXAMPLE 2. Given interchange :sign ‘+’ and ‘–’and numbers 5 and 8.Which of the following is correct?

(a) 82 – 35 + 55 = 2(b) 82 – 35 + 55 = 102(c) 85 – 38 + 85 = 132(d) 52 – 35 + 55 = 72

Sol. 52 + 38 – 88 = 2(iii) BALANCING THE EQUATION

In this, the signs given in one ofthe alternatives are required to full upthe blank spaces for the signs in orderto balance the given equation.

Mathematical OperationArithmetical Reasoning

Chapter

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Mathematical Operation Arithmetical Reasoning 41EXAMPLE 3. Select correct

combination of mathematical sign toreplace ‘*’ sign to balance the equation.

9 * 4 * 22 * 14(a) × = –(b) × – =(c) = – ×(d) – × =

Sol. 9 * 4 * 22 * 149 × 4 – 22 = 14

q Shortcut Approach • Begin with replacing coded

operators with their meanings.Write the entire expressions withcorrect operators and operand.

• When sowing always rememberVBODMAS.

• If any interchnages are suggested,apply then before you start soling.

ARITHMETICAL REASONINGArithmetical Reasoning tests the abilityto solve basic arithmetic problemsencountered in everyday life. These

problems require basic mathematicalskills like addition, subtraction,multiplication, division etc. The testsinclude operations with whole numbers,rational numbers, average ratio andproportion, interest and percentage, andmeasurement. Arithmetical reasoning isone factor that helps characterizemathematics comprehension, and it alsoassesses logical thinking.

EXAMPLE 4 : The total of the ages ofAmar, Akbar and Anthony is 80 years.What was the total of their ages threeyears ago ?Sol. Here, required sum = (80 – 3 x 3)

years = (80 – 9) years = 71 years.

q Shortcut Approach

If ages of n persons in a group are x1,x2, x3 ... , xn yr, then average age of thegroup

= 1 2 3 nx x x ... xn

+ + + +



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Coded Inequalities42

INTRODUCTIONAs we know,

3 × 3 = 9Now, we can say that the result ofmultiplication between 3 and 3 is equalto 9. Therefore, 3 × 3 = 9 is a case ofequality. But when we multiply 3 × 4, weget 12 as a result of this multiplication. Itdoes mean that

3 × 4 ¹ 9As 3 × 4, is not equal to 9, it is a case ofinequality.When, we come to know that one thingis not equal to another; there can be onlytwo possibilities:-(i) One thing is greater than another

thing.or

(ii) One thing is less than the anotherthing.

When, we denote (i) and (ii) mathematically,then we will write.(i) One thing > another thing.

or(ii) One thing < another thing.where ‘>’ denotes ‘greater than’.and ‘<’ denotes ‘less than’Hence, you can write,

3 × 4 > 94 × 1 < 9

( 3 × 4 > 9) means ‘Product of 3 and 4 isgreater than 9’.(4 × 1 < 9) means ‘Product of 4 and 1 isless than 9’.

Sometimes we come across two numberswhere, we do not know the exact state ofinequality between them.Let us see :m ³ n means m is either greater than orequal to n.m £ n means n is either less or equal tom.Hence, we can summarise the signs tobe used in inequalities as below:

‘=’ denots equal to ‘>’ denots greater than ‘³’ denots greater than or equal to ‘<’ denots less than ‘£’ denots less than or equal to

CHAIN OF INEQUALITIESSometimes two or more inequalities arecombined together to create a singleinequality having three or more terms.Such combination is called chain ofinequalities.

Note : If you see the given problemformat (Example). You will find thatyour primarily task is to combine twoor more inequalities to create a singleinequality.

Conditions for CombiningTwo InequalitiesCondition I: Two inequalities will be

combined if and only ifthey have a commonterm.

Coded InequalitiesChapter

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Coded Inequalities 43Condition II: Two inequalities will be

combined if and only ifthe common term isgreater than (or ‘greater’than or equal to’) one andless than (or ‘less than orequal to’) the other.

EXAMPLE 14 > 13, 13 > 12 can beeasily combined as ‘14 > 13 > 12’.

Coded InequalitiesHere,

14 > 13 > 12

Common termClearly, 14 > 13 and 13 > 12 have commonterm 13 and this common term is greaterthan 12 and less than 14. Hence, 14 > 13and 13 > 12 have been combined into14 > 13 > 12 as per the conditions I and II.

EXAMPLE 17 < 19, and 19 < 20 can beeasily combined as 17 < 19 < 20.Here,

17 < 19 < 20

Common term

Clearly, 17 < 19 and 19 < 20 have commonterm 19 and this common term is greaterthan 17 and less than 20. Hence, 17 < 19and 19 < 20 have been combined into 17< 19 < 20 as per the conditions I and II.Now, let us see some examples ofinequalities which can not be combined.Some such examples are given below:i. 14 > 12, 19 > 18ii. 18 < 20, 22 < 25iii. 100 > 99, 80 > 77iv. 100 < 115, 118 < 119

Clearly, (i), (ii), (iii) and (iv) can not becombined as they do not have anycommon term and therefore, they do notfollow condition I and condition II.

How to Derive Conclusionsfrom a Combined Inequalities?

To derive conclusion from a combinedinequality, you have to eliminate thecommon term.For example,(a) If we have

m > l > nthen, our conclusion is

m > n

(b) When, we havem < l < nthen, our conclusion is

m < n

(c) When, we have ‘³’ signs in thecombined inequalities then youhave to think a little bit more. Letus consider the combinedinequality given below:m ³ l > nHere, m is either greater than l orequal to l.Hence, the minimum value for m isequal to l. But l is always greaterthan n. Therefore, m is alwaysgreater than n.

\ Our conclusion is m > n

(d) When, we have the followinginequalities:-m > l ³ n

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Coded Inequalities44In this case, m is always greaterthan l and l is either greater thann or equal to it. When l is greaterthan n; m will obviously be greaterthan n. Even when l is equal to n;m will be greater than n as m isalways greater than l.

\ Our conclusion is m > n

(e) When, we have combine inequalitym ³ l ³ nHere, m is either greater than l orequal to l.

When m is greater than l; we have m > l³ n, which gives the conclusion.

m > n — (A)

When m is equal to l; we havem = l ³ n, which gives the conclusion

m ³ n — (B)

Combining (A) and (B), we have the finalconclusion as

m ³ n

From (a), (b), (c), (d) and (e), we get arule for deriving conclusions from acombined inequality, we may say it‘Golden Rule’.

GOLDEN RULE

The conclusion inequality will have an '³' sign or a '£' sign if and only if both the signs in the combined inequality are '³' or '£' sign

Clearly, in (a), (b), (c), (d) and (e) onlyone inequality (e) (m ³ l ³ n) has ‘³’ asits both the sign.

Remember• If m > n, then n < m must be true.• If m < n, then n > m must be true.• If m ³ n, then n £ m must be true.• If m £ n, then n ³ m must be true.

EITHER CHOICE RULESI. When your derived conclusion is

of the type m ³ n (or m £ n) thencheck if the two conclusions arem > n and m = n (or, m < n andm = n). If yes, choice “eitherfollows” is true.

II. If neither of the given conclusionsseems correct. Then try to check ifthe given conclusions form acomplementary pair. Givenconclusions form a complementarypair in the 4 cases given below:-(i) m ³ n and m < n(ii) m > n and m £ n(iii) m £ n and m > n(iv) m < n and m ³ n

In such case, the choice “either follows”is correct.

q Shortcut ApproachSteps for Solving Problems

Step I: Decode the given symbols like@, $, d, #, *, etc.

Step II: Take one conclusion at a timeand make an idea that whichstatements are relevant forevaluating it.

Step III: Use conditions I and II and the‘Golden Rule’ to combine therelevant statements and derivea conclusion from it. They are:

Condition I: There must be a commonterm.

Condition II: The common term mustbe less than or equal toone term and greater thanor equal to another.

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Coded Inequalities 45GOLDEN RULE:The conclusion — inequality isobtained by letting the common termbe eliminated and it has a ‘³’ or a ‘£’sign if and only if both the inequalitiesin 2nd step had a ‘³’ or a ‘£’ sign. In allother cases, there will be a ‘>’ or a ‘<’sign in the conclusion.

After performing the above mentionedthree steps, if a conclusion is establishedand verified, it is well and good. But ifdoes not happen so, then you have toperform 4 more new steps given below:New Step I: Check if the given

conclusion directlyfollows from anyonesingle statement.

New Step II: Check if the conclusion— inequality you get isessentially as same as thegiven conclusion butwritten differently.

New Step III: Check if the derivedconclusion follows‘Either choice Rule I’.

New Step IV: If neither of theconclusions has beenproved correct till now,then check ‘Either choiceRule II’.

EXAMPLE 1: In the following question,the symbols ©, @, =,* and $ areused with the following meanings :P © Q means ‘P is greater than Q’;P @ Q means ‘P is greater than orequal to Q’;P = Q means ‘P is equal to Q’;P * Q means ‘P is smaller than Q’;P $ Q means ‘P is either smallerthan or equal to Q’.

Now in each of following questions,assuming the given statements to betrue, find which of the two conclusions Iand II given below them is/are definitelytrue.Give answer :

(a) if only conclusion I is true;(b) if only conclusion II is true;(c) if either I or II is true;(d) if neither I nor II is true.(e) if both I and II are true.Statements : P © T, M $ K, T = KConclusions : I. T © M II. T = M

Sol. Given statements :P > T, M £ K, T = K.T = K, K ³ M Þ T ³ MÞ T > M or T = M Complementary

pairÞ T © M or T = MSo, either I or II is true.

DIRECT INEQUALITYIn this type of questions, direct relationbetween two or more than two elementsare given in a meaningful inequality.Candidates are required to establish therelation between elements with the helpof used signs between the elements.

EXAMPLE 2 : Which of the followingsymbols should replace the questionmark in the given expression in order tomake the expressions. ‘I > L’ as well as‘M ³ K’ definitely true?

I > J ³ K ? L £ N = M(a) > (b) <(c) £ (d) =(e) Either < or £

Sol. On putting sign (=) in place ofquestion mark (?)

I > J ³ K = L £ N = MÞ means I > L and M ³ K

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Coded Inequalities46Remember

Inequality depends upon combiningmore than two element with a commonterm. Now observe the below diagramthoroughlyAccordance to this diagramDefinite Conclusion· > = ® > · < = ® <· ³ = ® ³ · £ = ® £· ³ > ® > · £ < ® <· < = £ ® < · > = ³ ® >Indefinite Conclusion· > < ® No relation · ³ £ ® No relation· > £ ® No relation · ³ < ® No relation

q Shortcut Approach

Case 1. < OR >Two signs opposite to each other willmake the conclusion wrong But againif the signs are in same manner that willnot make it wrong.

EXAMPLE

If A > B < C > D then A < C = False,C > A = False .ButIf E > F > G > H then E > G = True , F >H = True , E > H = True.Statement: A < D > C < E > BConclusions:• C > B ® False• A < E ® False• D > B ® FalseIn simple way, whenever these two signcomes in opposite direction the answerwill be false.q Shortcut Approach

Case 2. £ OR ³Two signs opposite to each other willmake the conclusion wrong But againif the signs are same then it will be true.

EXAMPLE

If A ³ B £ C thenA £ C = False, C ³ A = FalseButIf A ³ B ³ C thenA ³ C = True, C £ A = True.Statement: B ³ D £ A ³ F ³ CConclusions :I. A ³ C ® TrueII. B £ F ® FalseIII. D ³ C ® False

q Shortcut Approach

Case 3. Sets Priority1st Priority : < or >2nd Priority: £ or ³3rd Priority: =Statement: P ³ R > Q = T ³ SConclusions :

I. P ³ Q ® False II. P > Q ® True III. Q ³ S ® True

Case 4.When it occurs to you that the statementof order is opposite just change thesign into similar opposite direction.Then change the sign into similaropposite /corresponding / alternativedirection.If A > B > F > C < D < E

than F < A ® True

EXAMPLE

[Q A > B > F = F < B < A]Statements : A > B > F > C; D > E > CConclusions:I. C < A ® TrueII. C > A ® False

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Coded Inequalities 47

Case 5. > or < and ³ or £Whenever there is two conclusionswhich are false then check for thesetwo symbols (> or < and ³ or £). Inmost of case where two conclusionsare false and these two similar signsare not there respectively then thatstatement can call it as either or butshould check there variable it shouldsame.(A)Either Or :Note : First thing need to check whetherin conclusion any two or more

Rules:1. Both conclusion should False2. Check the symbolsIf both the rules are satisfied then writeit as " Neither Nor' other wise leave it.

EXAMPLEStatement : P > Q ³ S = RConclusion : I. P ³ R

Neither norII. R > QStatement : L = T £ J ³ KConclusion : I. L > K Neither norII. T £ KStatement : V < L ³ J £ TConclusion : I. V < J Neither norII. L = TStatement : G £ K £ F < MConclusion: I. G > F Neither norII. K £ M


EXAMPLE

Statement : H = W £ R > FConclusion : I.R = H

Either OrII.R > HStatement : H > L = E < TConclusion : I.H £ T Either OrII.H > TStatement : S < T ³ R ³ MConclusion : I.M < T Either OrII.M = TStatement : I ³ H = T > S £ RConclusion: I.I > T Either OrII.I = TB. Neither Nor :First thing you need to check whether inyour conclusion any 2 or more conclusionsare wrong then write it as 'Neither Nor'but before checking their symbols.

conclusions are wrong then if it is therethen check whether the two variablesare same. If It happens then write it as'Either or' but after checking theirsymbols.Rules:

1. Both conclusion should False 2. Should have same Predicate or

Variable 3. Check the symbolsIf above conditionsare satisfied thenwrite it as 'Either Or' Other wise leave it.Note : If Rule 3 is satisfied than theconclusions are called 'Either Or'.

Statement :Conclusion :

W < X Y > Z£

I.II.

W < Z W Z³

×× Either Or

Step 2. Bothconclusions are false

Step 1. Check both variable should be same

Step 3. Check symbols likea) '<&=' or '> & =' togetherb) '< & 'or '> & ' together³ £

q Shortcut Approach

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Problem Solving48

INTRODUCTIONIn this chapter you will see some typicalproblems in which you would be given aseries of interlinked information and onthe basis of those informations youwould be expected to reach certainconclusions.

TYPES OF INFORMATIONSIN A GIVEN PROBLEM

1. Basic Informations(Useful secondary informations):It is given in fi r st couple ofsentences of given data are suchthat they give you some basicinformation that is essential togive you general idea of thesituation.

2. Actual InformationsWhatever remains after the basicinformations are known as actualinformation.While trying to solve a problemone should begin with actualinformation and useful secondaryinformation should be solve bymind.

3. Negative InformationsActual informations havingnegative sentences are callednegative information. A negativeinformation does not inform us

anything exactly but it gives achance to eliminate a possibility.

TYPES OF PROBLEMS1. Simple problems (based on

categorisation)2. Problems based on arrangement

(Linear, circular, rectangular/square).

3. Problems based on comparison.4. Problems based on blood

relations.5. Blood relations and profession

based problems.6. Problems based on conditional

selection.

1. SIMPLE PROBLEMS BASEDON CATEGORISATION

Tips to Solve ProblemsThese type of problems can easily besolved by construction of table.

EXAMPLE 1 Directions : Read thefollowing information carefullyand answer the question thatfollows:

1. There are six cities L, M, N, O, Pand Q.

2. L is not a hill station.3. M and P are not historical places.4. O is not an industrial city.5. L and O are not historical cities.6. L and M are not alike.

Problem SolvingChapter

13

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Problem Solving 49Q. Which two cities are industrial centres ?Sol. It can be solved by preparing a table in the manner given below:

L M N O P QHistorical placeIndustrial cityHill station

(2), (3), (4), (5) are negative informations. Therefore as per such informations.We put ‘X’ (not) mark wherever applicable. As a result the table looks like theone below.

L M N O P QHistorical place

× × × ×

Industrial city

×

Hill station ×

As above table gives definite informations about L, O. L is neither a historicalplace nor a hill station. So, it must be an industrial city. In the same manner Ois neither a historical nor an industrial city. So, O must be a hill station. Hence,we put ‘P’ mark at the appropriate place which give the table following look:-

L M N O P Q Historical place

× × × ×

Industrial city

P ×

Hill station × P

Now, as per the condition (6) (L and M are not alike), M can not be an Industrialcity. Also M is not a historical place either. Therefore, it is very obvious that Mis a hill station.Again, in the given problem there is no negative information about N. Hence,we can assume that N is a hill station as well as a historical place and anindustrial city. Combining if these aspects, the following table will be preparedfinally.

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Problem Solving50

L M N O P Q Historical place

× × P × × P

Industrial city

P × P × P P

Hill station

× P P P P P

Now, after analysing the given question we get the answer:-So, P and Q are two industrial centres.

2. PROBLEMS BASED ON ARRANGEMENTIn such problems a group of people, objects, etc, may have to be is arrangedin a row, or in a circle or any other way.

Linear Arrangement

one row sequence(A) When direction of face is not clear, then we take ourself as base and then the

diagram will be as follows

A B C D E

Face Face Face Face Face

RightLeft

Middle

From the above diagram, it is clear that(i) B, C, D, E are right of A but only B is the immediate right of A.(ii) D, C, B, A are left of E but only D is the immediate left of E.

(B) When direction of face is towards you, then the diagram will be as follows

A B C D E

Face Face Face Face Face

LeftRight

From the above diagram, it is clear that(i) B is immediate left of A, C is immediate left of B; D is immediate left of

C and E is immediate left of D.(ii) D is immediate right of E; C is immediate right of D; B is immediate

right of C; and A is immediate right of B.

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Problem Solving 51two rows sequenceLet us see 6 persons seating in two rows

P Q R

S T U

Right

RightLeft

Left

From the above diagram, it is clear that(i) P is sitting opposite S.(ii) Q is sitting opposite T.(iii) R is sitting opposite U.(iv) P and U are sitting at diagonally

opposite positions.(v) S and R are sitting diagonally

opposite positions.Note: Point to be noted that inarrangement problems, the actualinformation can be classified into 2categories:-(a) Definite information

A definite information is one whenthe place of object/man isdefinitely mentioned.

(b) Comparative informationIn such information the place ofobject/man is not mentioneddefinitely but only a comparativeposition is given. In other wordsthe positions of objects/men aregiven in comparision to anotherobjects/men.

q Shortcut ApproachStep I. Sketch a diagram of

empty placesStep II. Fill up as many empty

places as possible using allthe definite informations.

Step III. With the help ofcomparative informationconsider all possibilities

and select the possibilitieswhich does not violate anycondition.

EXAMPLE 2. Directions : Just readthe following informationcarefully to answer the questionsgiven below it:Five friends P, Q, R, S, and T aresitting on a bench.

(1) P is sitting next to Q.(2) R is sitting next to S.(3) S is not sitting with T.(4) T is on the last end of the bench.(5) R is on the 2nd position from the

right.(6) P is on the right of Q and T.(7) P and R are sitting together.Q. All what position is P sitting?Sol.

Here, 4th and 5th sentencesconstitute definite information:Comparative informations are: 1st,2nd, 6th and 7th sentences while 3rd

is a negative information.Now, start with definite information,sketch the following arrangement:-

T __ __ R __Now, this is the time to look for thecomparative informations that tellabout T and R. Such informationsare 2nd, 6th and 7th sentences. Takethe 7th and the 1st sentence. If Pand R are together and also Q andP are together, then P must bebetween Q and R. Now thearrangement take the form as:-

T Q P R ____By the virtue of the 2nd sentence:

T Q P R SSo, P is sitting between Q and R.

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Problem Solving52Circular ArrangementCircle is the most important case from the exam point of view. Most of the timesCircle kind of statements are there in exams.From the exam point of view, in most cases they give 8 persons sitting in the circle.But before solving the important thing is their ' Sitting Position '.Step 1. Knowing NEWS! N= North , E= East , W=West , S= South

W

S

N

E

To remember this just remember combination ' North - South ' & ' West - East ' whichcomes together to each other respectively.Step 2 : Picking Left & Right .• Facing Center • Facing Outside

Clock wise = Left Anti - Clock wise = Right

N NNE NE

E E

SE SES S

SW SW

W W

NW NW

If it is mention in the statement that all isfacing outside then just do opposite ofabove like this:Clock wise = Right & Anti-clock wise

= LeftStep 3 : Solving step wise the statementor Following the statement.

q Shortcut Approach• Imagine yourself as one of the

persons given in the question.• Count how many people are

mentioned in the question. Thendraw a circle with those manylines.

RightLeft

• Imagine yourself at the positionshown by the box.

• Now your left hand is the left sideand right hand is the right side.

• Now, if in question it is given, P issecond to the right of Q, approachas follows.® Imagine yourself as Q.

RightLeft

Q

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Problem Solving 533. PROBLEMS BASED ON

COMPARISONIn such problems comparison ofdifferent objects or persons has tobe made. Such comparisions aredone on the basis of marks, agesheights, etc.

Method to SolveIf you give a serious look to the problemyou will find that such problems are assame as the arrangement problems.Therefore, we have to go likearrangement problem while solvingproblems based on comparison.

EXAMPLE 4. Directions : Read theinformations given below toanswer the given question:(1) 7 students A, B, C, D, E, F and

G take a series of tests.(2) No two students obtain the

same marks.(3) G always scores more than A.(4) A always scores more than B.(5) Each time either C scores the

highest and E gets the least,or alternatively D scores thehighest and F or B scores theleast.

Q. If D is ranked 6th and B is ranked5th, which of the following can betrue?

Sol.In this case, we see there is no definiteinformation. Sentence 5 gives a definiteinformation but it is conditional. Still, wedraw all the possibilities based onsentence 5.

(1) C __ __ __ __ __ __ Eor, (2) D __ __ __ __ __ __ For, (3) D __ __ __ __ __ __ B

® Now, P is second to right ofQ. The right of Q is your right side.So, place P two places from Qtowards its right.

RightLeftQ

P

EXAMPLE 3. Directions Study thefollowing information carefully andanswer the question given below.Bunty, Dev, Manav, Kavya, Payal,Qasturba, Wasir and Himmat are sittingaround a circle facing at the centre.Manav is to the immediate right of Buntywho is 4th to the right of Kavya. Payalis 2nd to the left of Bunty and is 4th tothe right of Wasir. Qasturba is 2nd tothe right of Dev who is 2nd to the rightof Himmat.Q. Who is 3rd to the right of Bunty?Sol.

Kavya

HimmatWasir

Manav

Bunty

Qasturba

Payal

SeatingArrangement

Dev

Now, look at the given question andcheck that you get the answer.So, Himmat is 3rd to the right of Bunty.

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Problem Solving54We see that the two additionalinformations (3) and (4) are inadequateto reach a definite conclusion. Hence,keeping these in mind. We move on tothe given questions.

D is ranked 6th and B is 5th. Thisdoes mean that possibilities (2) and(3) are violated. Hence, possibility(1) must be true. Thus, we have:C ______ B D EAlso by virtue of (3) and (4) we canhave only one arrangement for G,A and B which is GAB. Accordingly,there are two possibilities:

C G F A B D Eor, C G A F B D ESo, if D is ranked 6th and B is ranked5th, then f is ranked 3rd or 4th.

4. PROBLEMS BASED ONBLOOD RELATIONSuch problems involves analysisof certain blood relations.

q Shortcut Approach(i) Vertical/diagonal lines to

represent parent-childrelationships.

(ii) Single/double horizontal linelike ( )/« Û to representmarriages.

(iii) A dashed line (—) for brotherand sister relationship.

(iv) ‘+’ sign for male and ‘–’ signfor femaleFor example.

A+B–

D+ E–

G– +F

or

A+B–

D+

F+G–

E–

or

A+ B–

D+

F+G–

E–

The above diagrams tells us:-(a) A and B are couple; A is the

husband while B is the wife.(b) D is son of A and B while E

is daughter of A and B.(c) D is the brother of E and E is

the sister of D.(d) D has a son F(e) F and G are couple; F is the

husband and G is the wife.(f) F is the grandson of A and

B.(g) G is the daughter in law of

D.(h) E is the aunt (Bua) of F(i) There are 3 males (A, D and

F) and 3 females (B, E, G)

EXAMPLE 5. Directions : Read thefollowing information carefullyand answer the question givenbelow:

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Problem Solving 55There are 6 members in a family.They are M, N, O, P, Q, R aretravelling together. N is the son ofO but O is not the mother of N. Mand O are a married couple. Q isthe brother O. P is the daughter ofM. R is the brother of N.

Q. How many male members are therein the family?

Sol. Here, all the sentences are actualinformation except the first out ofthese the 2nd and the fifthsentences give information onparent child relationship. We canbegin with either of the two. Letus begin with the 6th sentence. Ourdiagram will be as

M(?)

P(–)

As, we do not want to make manydiagrams and instead we wouldprefer to only add to the existingdiagsams. Therefore, we shouldlook for sentences that talk of Mor P. The 3rd sentence talks aboutM. Hence, we add thisinformation, that M and O aremarried couple in our diagram.

M(?)

O

P(–)

(?)

Now, the 2nd sentence talks aboutO. It says that N is the son of Obut O is not the mother of N.Obviously, O must be the father ofN. This means O is a male andhence M must be a female. Nowour diagram takes the form asfollowing:-

M(–)O(+)

P(–)N(+)

Now, we add the two sentences‘Q is the brother of O’ and ‘R is thebrother of N’ and we get the finaldiagram as below:-M(–)

O(+)

P(–)N(+)

Q(+)

R(+)

So, there are 4 male members in thefamily.

5. PROBLEMS BASED ONBLOOD RELATIONSAND PROFESSIONSuch problems are very muchsimilar to the problems related toblood relation. What makes itdifferent is the addition of newdata:- the professions of familymembers. You will get the moreclear idea about this type ofproblem.

EXAMPLE 6. Directions : Read thefollowing information carefullyand answer the question givenbelow it:(1) A, B, C, D, E and P are

members of a family.(2) There are two married

couples.(3) B is an engineer and the father

of E(4) P is the grandfather of C and

is a lawyer.

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Problem Solving56(5) D is the grandmother of E and

is a housewife.(6) There is one engineer, one

lawyer, one teacher, onehousewife and two studentsin the family.

Q. Who is the husband of A?Sol. Here, (1), (2), and (6) are useful

secondary informations. While(3), (4) and (5) are the actualinformations. We start with the 3rd

sentence because it mentions aparent. Child relationship itsdiagram can be made as thefollowing:-

(+, Eng)

E(? ?)

B

B is an Engineerand father of E

Now, we move on to anothersentence that involves either B orE. You see that the 5th sentencegives some information about E. Itsays that D is the grandmother E.Point to be noted that if D is thegrandmother of E, then the son ofD must be father of E and hence Bis the son of D. Now, the diagramtakes the following form.

B(+, Eng)

E(?, ?)

D is a housewifeand grandmother E

D(–, Housewife)

Now, the 4th sentence has theremaining information and diagramfor it is given below:-

(+, Lawyer)

C(? ?)

P

P is a lawyer and grandfather of C(?)

Now, we see that we have endedup with two different component.Then how to resolve this deadlock?The answer is simple: - to resolveit, we make use of the given usefulsecondary information (USI).“There are two married couple inthe family.” Clearly, the twopossible pairs are of grandfather,grandmother and father, mother.Therefore, we combine the twodiagrams into the following way.

P D(+, Lawyer) (–, Housewife)

B(+, Eng)

A(– ?)

C(? ?)

E(? ?)

Point to be noted that theprofessions of A, E and C areyet unknown. However, withreasonable justification, we mayassume that the mother (A) shouldbe the teacher and the two children

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Problem Solving 57E and C should be students. Butthis conclusion can be challengedand has no reason at all.Apart from that the sexes of E andC can not be determined. So, B ishusband of A.

6. PROBLEMS BASED ONCONDITIONAL SELECTION

In this type of problems, a groupof objects/persons has to beselected from a given larger group,as per the given restrictions. Youwill get the better idea of such typeof problem from the problem givenbelow:-

EXAMPLE 7. Directions : Study thefollowing information carefullyand answer the question givenbelow:-From, amongst 6 boys J, K, L, M,N, and O and 5 girls P, Q, R, S andT, a team of 6 is to be selectedunder the following conditions:-(i) J and M have to be together.(ii) L can not go with S.(iii) S and T have to be together.(iv) K can not be teamed with N.(v) M cannot go with P.(vi) K and R have to be together.(vii) L and Q have to be together.

Q. If there be 5 boys in the team, thenthe lone girl member is ------

Sol. Make the group of all the pairs thathave to be together on one sideand the pairs that must not betogether on the other side. Next,read each of the questions andtreat that as an additionalinformation. Finally, analyse thepossibilities and choose thepossibilities that satisfies all theconditions. Let us see the processbelow:-Firstly, we can summarise theconditions in the following way:-

J,M S,T( )( ) ( )( )

GroupK, R L, Q 'must be together '.

( )( ) ( )( )

+ + - - ®

+ - + -

L, S, K, N, M, P(+) (–) (+) (+) (+) (–1) Group never

be together’®

Here, number of boys are 5. Wesee than K and N can never betogether. Therefore, there are onlytwo ways of selecting 5 boys:-JKLMO and JNLMO. But thepossiblity is not possible becauseif K would go then R should alsogo, and if L goes than Q shouldalso go. Hence, JNLMO is the onlypossibility in which L’s friend Qwould be the lone girl member.



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Input and Output58

INTRODUCTIONProblems related to input-output arefrequently asked questions in variousgraduate level competitive examinations.They are not very tough stuff but take agood deal of time to be solved orsometimes students do not take attemptto solve them because of time consumingimpression of such type of questions.But proper understanding of the subjectmakes you believe that such problemsare not as tough and time consuming asthey seem.

CONCEPT OF INPUT-OUTPUT PROBLEMSIn such problems:(a) It is imagined that there is some

kind of computer/word processingmachine.

(b) An input is given to the computer/word processing machine

(c) The computer/word processingmachine performs repeatedoperations as per a certain patternto give different output in differentsteps.

TYPES OF PROBLEMS(i) Problems of shifting(ii) Problems of arrangement(iii) Problems of mathematical

operation(iv) Miscellaneous.

PROBLEM OF SHIFTINGWe know that in such type of problems,a word/number processing machinegenerate output through shifting.Shifting does mean an operation in whichwords or numbers of a given input giveoutputs in different steps throughshifting their place to different place asper a fixed pattern.Note : In shifting problems, the previousstep of any step can possibly bedetermined, so we can move in backwardor reverse order which is not possiblein some of the other type of problems.

Methods to SolveLets take an exampleInput : Blue Cat Good Other Have CakeStep 1 : Blue Other Good Cat Have CakeStep 2 : Blue Other Have Cat Good CakeStep 3 : Cake Other Have Cat Good BlueStep 4 : Cake Cat Have Other Good BlueStep 5 : Cake Cat Good Other Have BlueStep 6 : Blue Cat Good Other Have CakeShifting of element can easily beunderstood by making them equivalentto number likeBlue = 1, Cat = 2, Good = 3, Other = 4,Have = 5, Cake = 6Input can be written as

1 2 3 4 5 6Blue Cat Good Other Have CakeStep-1 : 2 and 4 interchangedStep-2 : 3 and 5 interchangedStep-3 : 1 and 6 interchangedStep-4 : 1, 2 and 3 are repeated again.

Input and Output

Chapter

14

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Input and Output 59

Input :)

1 2 3 4 5 6

Step-1 :)

1 4 3 2 5 6

Step-2 : 1 4 3 2 5 6

Step-3 :)

6 4 5 2 3 1

Step-4 :)

6 2 5 4 3 1

Step-5 : 6 2 3 4 5 1Step-6 : 1 2 3 4 5 6

PROBLEMS ON ARRANGEMENTS1. Word Arrangement from Left Side:

EXAMPLE :Input : mango tango orange banana pearStep I: banana mango tango orange pearStep II: banana mango orange tango pearStep III: banana mango orange pear tangoHere, we start arrangement from the word that comes 1st in the dictionary;then comes the word coming 2nd in the dictionary, then comes the wordcoming 3rd in the dictionary and so on. In this case, the arrangement start fromleft side. This is the reason in step I banana comes 1st as it comes 1st in thedictionary. In the 2nd step, orange comes at 3rd place because after thearrangement of step I the next word coming in the dictionary is mango but itget arranged automatically and hence there is no need to arrange it in step II.This is the reason after arranging banana in step I, we directly come to theword orange (coming 3rd in the dictionary) in step II. In the 3rd step, wearrange the word ‘pear’ (coming 4th in the dictionary) and the word tango getarranged automatically.

2. Word Arrangement from Right:

EXAMPLE :

Input: Name Fame Game Shame JamStep I: Name Game Shame Jam FameStep II: Name Shame Jame Game FameStep III: Shame Name Jam Game FameIn this case, the arrangement starts from right side. The word coming 1st in thedictionary comes at the 1st position from right. At the 2nd position from rightcomes the word coming 2nd in the dictionary and the process goes on till thearrangement gets completed. In the above given example, ‘Fame’ is the 1stword coming in the dictionary and hence it comes at the 1st position from rightin the step I. In the step II, the 2nd word coming in the dictionary (Game)comes at the 2nd position from right. Point to be noted that the word coming

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Input and Output60third in the dictionary will come at the 3rd position from right and this word is‘Jam’. But ‘Jam’ automatically get arranged as per the given pattern when wearrange the word ‘Game’ in II step. This is the reason why we don’t arrange‘Jam’ in the third step and jump directly to arrange the word. ‘Name’ thatcomes 4th in the dictionary. ‘Name’ occupies 4th position from right and theword ‘Shame’ automatically get arranged in the 3rd step. Hence, the word‘Shame’ does not need to get arranged.

3. Word Arrangement from the Left-Right Alternate:

EXAMPLE :

Input: Sachin is a great cricket playerStep I: a Sachin is great cricket playerStep II: a is great cricket player SachinStep III: a cricket is great player SachinStep IV: a cricket great is player SachinHere, the arrangement is made by putting the first word at 1st place, thenalphabetically last word at last place, then alphabetically second word at secondplace from left and the further arrangements goes on in the same manner. Inthe other words, are positioned from the left and from the right alternately. Inthe step I the word coming 1st in the dictionary is ‘a’ and it takes 1st positionfrom left. In the step II, the last word coming alphabetically is Sachin and ittakes last position (1st from right). In step III, the word coming 2nd in dictionaryis ‘cricket’ that comes at 2nd position from left. In step IV, the word coming 3rdlast in the dictionary takes the 3rd position from right. After the step IV, all thewords get arranged in alphabetical order. Point to be noted that after step IV,there is no need to arrange the word ‘great’ as it get arranged automatically isstep IV.

4. Arrangement in Increasing or Decreasing Order:

EXAMPLE :Input: 25 17 18 58 100 35Step I: 17 25 18 58 100 35Step II: 17 18 25 58 100 35Step III: 17 18 25 35 58 100

This arrangement gives a clear idea of arrangement of numbers in increasingorder. In step I, the smallest number (17) comes at the 1st position from leftpushing the remaining to the right. In step II, the 2nd smallest number (18)comes at 2nd position from left pushing the remaining number to the right. Instep III, the 4th smallest number (35) takes 4th position from left and the othertwo numbers 58 and 100 get arranged automatically.

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Input and Output 61Now, let us see decreasing order arrangement:

Input: 25 17 18 58 100 35Step I: 100 25 17 18 58 35Step II: 100 58 25 17 18 35Step III: 100 58 35 25 17 18Step IV: 100 58 35 25 18 17

The same arrangement can take place from right side (or in the reverse order)as follow:

Input: 25 17 18 58 100 35Step I: 25 18 58 100 35 17Step II: 25 58 100 35 18 17Step III: 58 100 35 25 18 17Step IV: 100 58 35 25 18 17

5. Number Arrangment from Left-Right Alternate:Like words left-right alternate arrangement, number arrangement also takesplace. The process of this arrangement is exactly the same as the arrangementtakes place in case of words. Just see the following cases:

Case I :Input: 100 125 26 10 15 35Step I: 10 100 125 26 15 35Step II: 10 100 26 15 35 125Step III: 10 15 100 26 35 125Step IV: 10 15 26 35 100 125

Here, the smallest number (10) takes 1st position from left in step I. In step IIthe largest number takes the last (1st from right) position. Again in step III the2nd smallest number (15) comes at the 2nd position from left. In the step IV, the2nd largest number (100) comes at the 2nd position from right and the remainingnumber (26 and 35) get arranged automatically.

Case II :Input: 100 125 26 10 15 35Step I: 100 26 10 15 35 125Step II: 10 100 26 15 35 125Step III: 10 26 15 35 100 125Step IV: 10 15 26 35 100 125

In case II, the arrangements take place in the same way as the arrangementstake place in case I. But the difference here is that case I is a left-right

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Input and Output62arrangement and case II is the right-left arrangement. In case II, the arrangementstarts with the largest number (125) coming at the 1st position from right andthis is step I. In step II, the smallest number (10) comes at the 1st position fromleft. In step III the 2nd largest number (100) comes at the 2nd position fromright. In step III, the third largest number (35) automatically comes at the 3rdposition from right. In 4th step, the 2nd smallest number (15) comes at the 2ndposition from left and 26 get arranged automatically coming at 3rd positionfrom left.Note: Left-right (or right-left) arrangement of numbers also take place in thesame manner when numbers are arranged in decreasing order.

6. Arrangement of Words and Numbers Simultaneously:Just see the following outputs produced by a word and number machine.Case IInput: 50 32 Vandana Prerna Aradhna 100Step I: 32 50 Vandana Prerna Aradhna 100Step II: 32 Aradhna 50 Vandana Prerna 100Step III: 32 Aradhna 50 Prerna Vandana 100Step IV: 32 Aradhna 50 Prerna 100 VandanaIn such case, numbers and words get arranged alternately. In step I, the smallestnumber (32) comes at the 1st position from left pushing the remaining membersof input towards right. In the step II, the word coming 1st alphabetically (thatis the word ‘Aradhna’) takes the 2nd position from left pushing the remainingmember rightward. Point to be noted that the 2nd smallest number automaticallycomes at the third position from left while arranging the word ‘Aradhna’ andhence, there is no need to arrange the 2nd smallest number ‘50’. In step III, theword (Prerna) coming 2nd alphabetically comes at the 4th position from leftpushing the other members to the right. In step IV, the largest number (100)occupies the 5th position from left and the word (Vandana) coming lastalphabetically comes at last position automatically finishing the completearrangement.Let us see some other cases of this type:Case II:Input: 50 32 Vandana Prerna Aradhna 100Step I: 100 50 32 Vandana Prerna AradhnaStep II: 100 Vandana 50 32 Prerna AradhnaStep III: 100 Vandana 50 Prerna 32 Aradhan

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Input and Output 63In this case, largest number and the word coming last alphabetically getarranged alternately. Then the 2nd longest number and the word coming 2ndlast alphabetically get arranged alternately and the process goes on till thearrangements of all the numbers and words get completed. In this case,arrangement completes in step III.

Case III:Input: 50 32 Vandana Prerna Aradhna 100Step I: Aradhna 50 32 Vandana Prerna 100Step II: Aradhna 32 50 Vandana Prerna 100Step III: Aradhna 32 Prerna 50 Vandana 100In this case, arrangement starts with the word coming 1st alphabetically andsuch word is ‘Aradhna’ that comes at the 1st position from left is step I. In stepII, the smallest number (32) comes at the 2nd position from left. Then, in stepIII, the word coming 2nd alphabetically comes at the 3rd position from left andall the other members get arranged automatically.

Case IV:Input: 50 32 Vandana Prerna Aradhna 100Step I: Vandana 50 32 Prerna Aradhna 100Step II: Vandana 100 50 32 Prerna AradhnaStep III: Vandana 100 Prerna 50 32 AradhnaStep IV: Vandana 100 Prerna 50 Aradhna 32In this case, word coming last alphabetically comes 1st from left in step I andsuch word is ‘Vandana’. In step II, the largest number (100) comes at the 2ndposition from left. In step III, the word coming 2nd last alphabetically occupiesthe 3rd position from left, and such word is ‘Prerna’. As the 2nd largest number(50) automatically get arranged as per the pattern going on and hence this isnot needed to arranged in step IV. In step VI, the word coming Ist alphabeticallycomes at the 5th position from left and such word is ‘Aradhna’. The smallestnumber (32) get arranged automatically coming at the last position from left instep IV. Thus, it is clear that in this case the word coming lst alphabetically andthe greatest number get arranged alternately in 1st two steps; then 2nd lastword alphabetically and 2nd largest number get arranged alternately finishingthe whole arrangement in step IV.

Case V:Input: 50 32 Vandana Prerna Aradhna 100Step I: 32 50 Vandana Prerna Aradhna 100Step II: 32 Vandana 50 Prerna Aradhna 100Step III: 32 Vandana 50 Prerna 100 Aradhna

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Input and Output64In this case, the smallest number comes at the 1st position from left in step Iand such number is 32. In step II, the word (Vandana) coming last alphabeticallyoccupies the 2nd place from left. In the 2nd step, the 2nd smallest number (50)takes the 3rd position from left automatically and also the word coming 2ndlast alphabatically takes the 4th position from left automatically. Hence, thereis no need to arrange ‘50’ and ‘Prerna’. In the III step, the largest number (100)occupies the 5th position from left completing the whole arrangement.Case VI:Input: 50 32 Vandana Prerna Aradhna 100Step I: 100 50 32 Vandana Prerna AradhnaStep II: 100 Aradhna 50 32 Vandana PrernaStep III: 100 Aradhna 50 Prerna 32 VandanaIn this case, the logic is that the greatest number (100) comes at the 1st positionfrom left in step I. In step II the word coming 1st alphabetically takes the 2ndposition from left and the 2nd largest number (50) gets arranged automatically.Hence, in step III, we direct arrange the word coming 2nd last alphabetically(that word is ‘Prerna’) occupies the 4th position from left and the other twomembers (32 and ‘Vandana’) get arranged automatically finishing the wholearrangement.

7. Arrangement Based on the Number of Letters in Words:Just have a look at the following patterns:

Case I :Input: let pattern love fried be matureStep I: be let pattern love fried matureStep II: be let love pattern fried matureStep III: be let love fried pattern matureStep IV: be let love fried mature patternHere, the words get arranged as per increasing number of letters. In otherwords, the word having least number of letters comes 1st from left in step I andsuch word is ‘be’. The word ‘let’ is bigger than ‘be’ and smaller than otherwords letterwise and hence, it takes 2nd position from left but it gets arrangedautomatically when the word ‘be’ is arranged in step I. In 2nd step, the word‘love’ comes at the 3rd position from left as it is bigger than word ‘let’ letterwise.In step III, the letterwise bigger word (fried) than love comes at the fourthposition from left. Similarly, mature comes at the 5th position from left andpattern comes at the last position automatically while arranging the word‘mature’.

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Input and Output 65Case II :Input: let pattern love fried be matureStep I: pattern let love fried be matureStep II: pattern mature let love fried beStep III: pattern mature fried let love beStep IV: pattern mature fried love let be

In this case, the words get arranged in decreasing order in terms of letters. Inother words, the word having the largest number of letters comes 1st from left,then comes the word having 2nd largest number of letters, then comes theword having 3rd largest number of letters and the process goes on till theword having the least number of letters occupies the last position from left.Case III:Input: let pattern gate a set be hopeStep I: a let pattern gate set be hopeStep II: a be let pattern gate set hopeStep III: a be let set pattern gate hopeStep IV: a be let set gate pattern hopeStep V: a be let set gate hope patternHave you noticed something here? Here, the words get arranged in increasingorder of litters. But when it comes to the case of two or more words havingequal number of letters the priority is given alphabetically. It does mean thatthe word coming 1st as per the alphabet will be put before the word coming2nd. Similarly, the word coming 2nd alphabetically will be put before the wordcoming third. This is the reason why ‘let’ has been put before ‘set’ and ‘gate’has been put before ‘hope’.Case IV:Input: let pattern gate a set be hopeStep I: pattern let gate a set be hopeStep II: pattern hope let gate a set beStep III: pattern hope gate let a set beStep IV: pattern hope gate set let a beStep V: pattern hope gate set let be aIn this case, the words get arranged in decreasing order of letters. But when itcomes to the case of two or more words having equal number of letters thepriority is given to the word that comes later alphabetically. It does mean thatthe word coming 1st alphabetically will be put after the word coming 2nd andthe word coming 2nd will be put after the word coming 3rd. This is the reasonwhy ‘hope’ has been put before ‘gate’ and ‘set’ has been put before ‘let’.

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Input and Output66Important Note: The case of arrangement discussed so far are the cases of push. Inall the cases a new word jumps from its place in every step, occupies its new anddue place and gives the remaining words and push either towards left or right asper the requirement of the pattern. But in some cases of arrangement interchangedoes take place and that format is given below:

8. Arrangement with Interchange:

EXAMPLE

Input: the most beautiful girl is VandanaStep I: beautiful most the girl is VandanaStep II: beautiful girl the most is VandanaStep III: beautiful girl is most the VandanaIn this case, the word (beautiful) coming 1st in alphabetical order comes at the1st position from left interchanging its place with the word ‘the’ and this isstep I. In step II, the word (girl) coming 2nd in alphabetical order occupies the2nd position from left interchanging with the word ‘most’. In step III, the wordcoming 3rd (is) comes at the third position from left interchanging with theword ‘the’ and finishing the complete arrangement in alphabetical order.This type of cases can also be seen in number arrangements and in thearrangements of numbers and words simultaneously. The examples of thesetype of arrangements are given below:

EXAMPLE (Increasing order number arrangement)Input: 25 11 50 20 35Step I: 11 25 50 20 35Step II: 11 20 50 25 35Step III: 11 20 25 50 35Step IV: 11 20 25 35 50

Presentation :

Step I: 11 25 50 20 35

Step II: 11 20 2550 35

Step III: 11 20 25 50 35

Step IV: 11 20 25 35 50

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Input and Output 67The presentation gives you the clear idea of how interchange takes place inevery step.

EXAMPLE (Decreasing order number arrangement)Input: 25 11 50 20 35Step I: 50 11 25 20 35Step II: 50 35 25 20 11

Presentation:

Step I: 50 2511 20 35

Step II: 50 35 1125 20

PROBLEMS OF MATHEMATICAL OPERATION—In this type of problems, the input has some numbers. Different steps are obtainedby taking the numbers of the input and different arithmetic operations are performedafter that.

EXAMPLE

Input : 44 35 18 67 22 28 36

Step I : 36 27 10 59 14 20 28

Step II : 16 15 8 42 4 16 18

Step III : 132 105 54 201 66 84 108

Step IV : 50 41 24 73 28 34 42

Step V : 8 8 9 4 4 1 9

Step VI : 64 64 81 169 16 100 81

Step VII : 20 19 12 46 8 20 22

In this case, in step I (each number of the input – 8). In step II, product of thedigits of each number of the input. In step III, each number of the input ismultiplied by 3. In step IV, each number of the input is added by 6. In step V,keep adding the digits of each number of the input till they are converted intosingle digit. In step VI, (digit sum of each number of input)2. In step VII, eachnumber of step II is added by 4.

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Input and Output68MISCELLANEOUS PROBLEMSIn this type of problems, there is no fixed pattern of questions coming under thiscategory. Infact, questions under this category comes before you as a real surprise.

EXAMPLE

Input : every now and then same

Step I : every ow nd hen ame

Step II : ever no an the sam

Step III : vry nw nd thn sm

Step IV : ee o a e ae

Step V : ery w d en me

In this case, in step I, first letter disappear. In step II, last letter disappear. Instep III, vowels disappear. In step IV, consonants disappear. In step V, first twoletters disappear.

q Shortcut Approach1. First of all, observe the given input line of words or numbers and the last step

of rearrangement, so that candidate may get an idea about the changes effectedin various steps of rearrangement.

2. In order to know what changes have been made in each step, observe twoconsecutive steps carefully.

3. Now, correlate the input, the last step and anyone of the middle steps. Thiswill enable you to identify the rule of arrangement.

4. In shifting problems, it is possible to determine the previous/earlier stepsincluding input. We can proceed/move backward or in reverse direction inshifting problems.

5. In shifting problems for convenience, we assign numeric value to given words.



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Syllogism 69

INTRODUCTION

Syllogism is a Greek word that does mean‘inference’ or ‘deduction’. The problemsof syllogism are based on two parts :1. Proposition / Propositions2. Conclusion / Conclusions drawn from

given proposition/ propositions

PROPOSITION

Just consider the sentences given below:

(i) “ ”All lions are pigs

Subject Predicate

(ii) “ ”No cat is rat

Subject Predicate

(iii) “ ”Some girls are beautiful

Subject Predicate

(iv) “ ”Some kites are not birds

Subject Predicate

All the sentences mentioned above givea relation between subject and predicate.Here, it is clear from the sentences that asubject is the part of a sentencesomething is said about, while a predicateis the term in a sentence which is relatedto the subject.Now, let us define the proposition :A proposition is a sentence that makes astatement giving a relation between twoterms. It has three parts :(a) The subject(b) The predicate(c) The relation between subject and

predicate

CATEGORICAL PROPOSITIONLet us see the sentences given below :

“All M are P”“No M are P”“Some M are P”“Some M are not P”

What we notice in all above-Mentionedsentences that they are condition free.These type of sentences are calledCategorical Propositions. In otherwords a categorical proposition has nocondition attached with it and it makesdirect assertion. It is different from non-categorical proposition which is in theformat

“If M then P”

SyllogismChapter

15

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Syllogism70

TYPES OF CATEGORICAL PROPOSITION:

Categorical proposition

Universal

Positive Positive

All M are P (A type)

Some M are P(I type)

No M are P (E type)

Some M are not P(O type)

Particular

Negative Negative

Therefore, it is clear, that universalpropositions either completely includethe subject (A type) or completelyexclude it (E type). On the other hand,particular propositions either only partlyinclude the subject (I type) or only partlyexclude the subject (O type).Now, we can summarise the four typesof propositions to be used while solvingthe problems of syllogism :

Format TypeAll M are P ANo M are P ESome M are P ISome M are not P O

q Shortcut ApproachAll M are P (A type):

M, PM

Pand

[Possibility]No M are P (E type):

M

P

Some M are P (I type):Either:

M P

Some M are P[Some M are not P]

Or :

MP

Some M are P[All P are M]

Some M are not P (O type):Either:

M P

Some M are not P[Some M are P]

Or:

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Syllogism 71

MP

Some M are not P[All P are M]

HIDDEN PROPOSITIONS

(A) A type:

Apart from ‘all’ it starts with every,each and any.

EXAMPLE

Every girl is beautiful.[All girls are beautiful.]

(i) A positive sentence with aparticular person as its subject isA type.

He should be amended Bharat Ratna

Subject Predicate

Amitabh Bacchan is a great actor.

Subject Predicate

(ii) A sentence in with a definiteexception is A type :

definite exception

“All girls except Reeta are healthy.”

(B) E type:

Apart from ‘no’ this type ofpropositions starts from ‘no one’,‘none’, ‘not a single’ etc.

EXAMPLE

No one (student) is studious.[No student is studious]

(i) A negative sentence with aparticular person as its subject isE type propoistion.

He does not deserve Bharat Ratna

Subject Predicate

Amitabh Bacchan is not a great actor.

Subject Predicate(ii) Sentences in following formats are

E type :“No student except

Reena has failed”

definite exception

“Is there any truth left in theworld”[No truth is left in the world.]

(C) I type:

Apart from some it also starts withwords such as often, frequently,almost, generally, mostly, a few,most etc.

EXAMPLE

(i) Almost all the girls are beautiful.[Some girls are beautiful].

(ii) Most of the garments arehandmade.[Some of the garments arehandmade].It is clear from the above examplesthat negative sentences beginingwith words like ‘few’, ‘rarely’,‘seldom’, etc. (Also ‘hardly’,‘scarcely’, ‘little’ etc.) are to bereduced to I type.

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Syllogism72Just see the other formates given below

All girls except a few are beautiful.

Not a definite exception as name ofgirls are not given.

[Some girls are beautiful]

All girls except 5 have passed

Not a definite exception as name ofgirls are not given.

[Some girls have passed]Therefore, a positive proposition withan indefinite exception is reduced to Itype.

(D) O type :Apart from “Some ....... not’ thistype of statements start with wordslike ‘all’, ‘every’, ‘any’, ‘each’, etc.

EXAMPLE

(i) All girls are not beautiful.[Some girls are not beautiful]

(ii) Poor are usually not healthy.[Some poor are not healthy]

Now, it is clear from the above mentionedexamples that negative propositions withwords such as ‘almost’, ‘frequently’,‘most’, ‘mostly’, ‘a few’, generally, etc.are to be reduced to the O–typepropositions.Again, positive propositions startingwith words like ‘few’, ‘scarcely’, ‘rarely’,‘little’, ‘seldom’ etc. are said to be O–type.

EXAMPLE

Seldom are women jealous.[Some women are not jealous]

Also, see the following formates :

three are beautiful.No girls except

No definite exception as name ofgirls are not given.

[Some girls are not beautiful.]

a few are housewife.No women except

No definite exception as name ofwomen are not given.

Therefore, a negative proposition withan indefinite exception, is reduced to Otype.

EXCLUSIVE PROPOSITIONSSuch propositions start with ‘only’,‘alone’, ‘none else but’, ‘none but’ etc.and they can be reduced to either A or Eor I format.

EXAMPLE

Only graduates are ProbationaryOfficers.Þ No graduate is Probationary

Officer (E type)Þ All Probationary Officers are

graduates. (A type)Þ Some graduates are Probationary

Officers (I type)General format of sentences given in theexaminations :

All M are P (A type)No M are P (E type)Some M are P (I type)Some M are not P (O type)

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Syllogism 73Note : General format given above arefrequently asked formats in theexaminations. But students must beready for other hidden formates of A,E, I and O types of propositions asproblems in hidden formates can alsobe given in question papers.

CONVERSION OFPROPOSITIONSBefore solving the problems of syllogismit is must to know the conversion rules ofall A, E, O, and I types of propositions :(i) Conversion of A type :

“ ”All M are P (A type)

PredicateSubject

After conversion it becomes.

“ ”Some P are M (I type)

PredicateSubject

Therefore, it is clear that A type ofpropositions get converted into I type.(ii) Conversion of E type :

“ ”No M are P (E type)

PredicateSubject

After conversion it becomes

“ ”No P are M (E type)

PredicateSubject

Therefore, E gets converted into E.(iii) Conversion of I type :

“ ”Some M are P (I type)

PredicateSubject

After conversion it becomes

“ ”Some P are M (I type)

PredicateSubject

Therefore, I gets converted into I.

(iv) Conversion of O type :O type of proposition can’t beconverted.

Note : In each conversion, subjectbecomes predicate and predicatebecomes subject.In fact, conversion is an immediateinference that is drawn from a singleproposition while inference drawn fromtwo propositions are called mediateinference.

q Shortcut Approach Table of conversion :

A IE EI IO

Type of proposition

Get converted into

Never get converted Rule to draw conclusion :After knowing conversion ofpropositions, we must learn the rulesto draw conclusions. In problems ofsyllogism, conclusions are drawn eitherfrom single propositions or from twoproposition or from both. But aconclusion from single proposition isjust a conversion of that propositionwhile to get conclusion from twopropositions a certain table is used thattells us what type of conclusion (in formof proposition) we get out of twopropositions. To understand it, let ussee the following conclusion table :

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Syllogism74Conclusion TableI Proposition II Proposition ConclusionA A AA E EE A (O)R

E I (O)R

I A II E O

EXAMPLE

Statements :

I. No pen is chair..

II. Some tables are pen .

EXAMPLE

Statements :

I. Some women are men .

II. No men is chair..

In all the above mentioned example, wenotice that in two statements of everyexample, there is a common term. Inexample 1 the word ‘girl’ is common; inexample 2 the word ‘pen’ is commonwhile in example 3 the word ‘men’ iscommon.Now, the aligning of the two statements(propositions) does mean that the pairof statements must be written in such away that the common term is thepredicate of the 1st sentence and thesubject of the 2nd.Just think over the following examples :Statements :I. Some girls are cute .

II. All cute are tall.

Note :(a) Apart from above 6 pairs of

propositions, no other pair willgive any conclusion.

(b) The conclusion drawn out of twopropositions is itself a propositionand its subject is the subject ofthe Ist statement while itspredicate is the predicate of the2nd statement. The common termget disappeared.

(c) (O)R does mean that theconclusion is O type but is inreverse order. In this case, thesubject of the inference orconclusion is the predicate of the2nd proposition and the predicateof the conclusion is the subject ofthe Ist sentence or statement.

(d) The conclusion table givescorrect conclusions or inferenceif and only if the two propositionsare aligned properly.

WHAT IS ALIGNING ?Let us see the following examples :

EXAMPLE

Statements :

I. All girls are beautiful.

II. Some girls are Indian.

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Syllogism 75Here, the common term cute is thepredicate of the I statement and subjectof the 2nd statement. Therefore, the twostatements (I & II) are properly aligned.But see another example.Statements :I. Some bats are chairs.

II. Some cats are bats .Here, the sentences are not aligned asthe predicate of the 1st statement is notthe subject of the 2nd.Then how to align it ? In such type ofcases we change the order of sentences.In another words we put I sentence inplace of II and II in place of I :

II. Some cats are bats .

I. Some bats are chairs.

Therefore, as per the requirement andnature of the sentence the alignment isdone.

(i) only by changing the orderof sentences.

or(ii) only by converting of the

sentences.or

(iii) By changing the order of thestatements and thenconverting one of thesentences.

IEA RuleAlignment must be done in IEA order. Itdoes mean that if the two statements areI & E then the conversion must be donefor I and for E & I it will be done for E.After discussing all the minute thingsabout this chapter, now we have comeat the position of solving the problemsof syllogism.

METHODS:(1) By Analytical Method(2) By Venn Diagram

(1) Analytical method :This method has two main steps:(a) Aligning the pair of sentences.(b) Using conclusion table to

draw conclusion.

EXAMPLE Statements :I. All rats are cats.II. All rats are men.When aligned it takes the form as

I. Some cats are rats [I type]

II. All rats are men [A type]

Now we use the conclusion tablegiven in this chapter that says

I + A = I type of conclusion.Therefore, the drawn conclusionmust be“Some cats are men”

It is clear that the conclusion drawn“Some cats are men” is a mediateinference as it is the result of twopropositions. But in actual problemimmediate inferences are also given inconclusion part and that format is givenbelow :

EXAMPLE : Statements:I. All rats are cats.II. All rats are men.Conclusion:(i) Some cats are men.(ii) Some men are cats.(iii) Some rats are cats.(iv) Some cats are rats.(v) Some rats are men.(vi) Some men are rats.

Here, all the options are correct.conclusion (i) follows because it is themediate inference of statements I & II.

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Syllogism76Conclusion (ii) is the conversion ofconclusion (i) conclusion (iii) is theimmediate inference (conversion) ofstatement I while conclusion (iv) is theconversion of conclusion (iii).Conclusion (v) is the immediate inference(conversion) of statement II whileconclusion (vi) is the conversion ofconclusion (v).Further, in some problemscomplementary pairs are also seen in the conclusion part in the forms of sentencegiven below:(a) (i) Some cats are rats.

(ii) Some cats are not rats I - O pair(b) (i) All cats are rats.

(ii) Some cats are not rats. A - O pair(c) (i) Some cats are rats.

(ii) No cats are rats. I- E pairApart from I - O, A - O and I - E pair thetwo sentences must have some subjectand predicates as are the abovementioned pairs. for these pairs we writethe form 'Either (i) or (ii) follows.

METHOD TO SOLVE(a) First step is aligning the

sentences.(b) Second step is using conclusion

table.(c) Third step is checking immediate

inferences.(d) Fourth step is checking through

the conversion of immediateinferences & immediate inferences.

(e) First step is checking thecomplementary pairs.

(2) Venn diagram method for solvingproblems :Students will have to adopt threesteps to solve the syllogismproblems through Venn diagrammethod :

METHOD TO SOLVE(a) 1st step is sketching all possible

pictorial representation for thestatements separately.

(b) 2nd step is combining possiblepairs of these representations ofall the statements into one.

(c) 3rd and final step is makinginterpretation of this combinedfigure.Conclusions are true if they aresupported by all the combinedfigures in 2nd step.

EXAMPLE

Statements :A. All chairs are books.B. All books are ties.Conclusions :I. Some ties are books.II. Some ties are chairs.1st Step :

cb

1A

bt

1B

c, b

2A

b, t

2B

Here, 1A and 2A are representations forstatement A while 1B and 2B arerepresentations for statement B. In theserepresentations

b = booksc = chairst = ties

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Syllogism 772nd step :Let us combine all the possible pairs ofthis pictorial representations :

cb t

(1A + 1B)

cb t

(1A + 2B)

c, bt

(2A + 1B)

c, b t

(2A + 2B)3rd step :When we interpret the pictures in stepII, we find that all the pictures supportboth the conclusions. Therefore,conclusion I :“Some ties are books” andconclusion II.“Some ties are chairs”both are true.Note : In the Venn diagram method,any conclusion given with anyproblem will be true if and only if it issupported by all the combinedpictorial representations through 2ndstep. If any pictorial representationcontradicts the given conclusion, itwill be put in the category of incorrector wrong conclusion.

POSSIBILITYPossibility is a concept of inconsistencyfor an event which is not yet verified butif true would explain certain facts orphenomena.Generally, the meaning of possibility isprobability, viz. possibility exists wherenothing is certain between the objects.In general language determination ofpossibility exist easily in that conditionwhen between two objects have nocertainty or the truth facts accordingly.Let's understand below table in whichpossibility exists where no definiterelation occurs between the objects anddefinite or proper relation between theobjects eliminate existance of anypossibility. In simple way givencondition eliminates the possibility andimproper condition favours thepossibility. Here, we can go through withan example which will also clear the termpossibility.

Condition PossibilityGiven facts cannot be determinedImaginary facts can be determined

EXAMPLE

Statements Some boxes are treesSome trees are hens.

ConclusionsI. Some boxes being hens is a

possibilityII. All trees being hens is a

possibility

Boxes TreesHens

Hens

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Syllogism78In Conclusion I, before deciding the possibility between boxes and hens, wemust notice the relation between both, we find that there is no relation betweenboxes and hens, so possibility favours the condition and the conclusion I is truefor possibility and in Conclusion II we must notice the relation between treesand hens. We find that both have some type of relation between them so thepossibility of ‘All between trees and hens is true. Hence, both the ConclusionsI and II follow.

q Shortcut Approach

Given Exclusive Proposition DesiredProposition

Possibility

All All ´

Some Some ´No No ´No Some not ´Some All ü

No proper relation Some All ü

Note: Improper relation between two objects favours the possibility (In aboveexample Conclusion I)

SPECIAL CASES OF EXCLUSIVE PROPOSITION

If the statement is of Conversion Illustration MeaningfulConversion

Much, more, many, very, a few, most, almost

Some Most A are B.A few X are Y.

Some A and B.Some X or Y.

Atleast Some Atleast some A are B. Some A and B.

Definitely No use Some A are definitely B.Some X are definitely not Y.

Some A are B.Some X are not Y.

Only Only A are B. All B are A.1% to 99% Some 38% A are B.

98% X are Y. Some A are B.Some X are Y.



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Cube & Dice 79

CUBE

INTRODUCTIONA cube is three dimensional figure whoselength, breadth and height are equal andany two adjacent faces are inclined toeach other at 90°. It has 6 faces, 8 cornersand 12 edges.

A B

EF

G H

CD

• Corners of the cube are A, B, C, D,E, F, G and H.

• Edges of the cube are AB, BE, EF,AF, AD, CD, BC, EH, CH, GH, DGand FG.

• Faces of the cube are ABCD,EFGH, CDGH, BCHE, ABEF andADFG.

When a cube is painted on all ofits faces with any colour andfurther divided into varioussmaller cubes of equal size, weget following results :(i) Smaller cubes with no face painted

will present inside faces of theundivided cube.

(ii) Smaller cubes with one facepainted will present on the facesof the undivided cube.

(iii) Smaller cubes with two facespainted will present on the edgesof undivided cube.

(iv) Smaller cubes with three facespainted will present on the cornersof the undivided cube.

Cube withthree sidespainted

Cube withtwo sidespainted

Cube withone sidepainted

The above figure may be analysed by dividing it into three horizontal layers :

Cube & DiceChapter

16

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Cube & Dice80Layer I or top layer :The central cube has only one face coloured, four cubes at the corner havethree faces coloured and the remaining 4 cubes have two faces coloured.

Top layer

Bottom unpainted

Layer II or middle layer :The central cube has no face coloured, the four cubes at the corner have twofaces coloured and the remaining 4 cubes have only face coloured.

Middle layer

Bottom unpainted

Unpainted cube

Top unpainted

Layer III or bottom layer :The central cube has only one face coloured, four cubes at the corner havethree faces coloured and the remaining 4 cubes have two faces coloured.

Bottom layer

Bottom unpainted

Also, if n = no. of divisions on the faces of cube

= Length of the edge of undivided cube .

Length of the edge of one smaller cube

q Shortcut Approach

Æ Number of smaller cubes with no face painted = (n – 2)3

Æ Number of smaller cubes with one face painted = (n – 2)3 × 6

Æ Number of smaller cubes with two faces painted = (n – 2) × 12

Æ Number of smaller cubes with three faces painted = 8

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Cube & Dice 81

EXAMPLE 1. A cube is painted blueon all faces is cut into 125 cubes ofequal size. Now, answer the followingquestion :How many cubes are not painted on anyface?Sol. Since, there are 25 smaller cubes

of equal size, therefore, n = numberof divisions on the face ofundivided cube = 5.Number of cubes with no facepainted = (n – 2)3

= (5 – 2)3 = 27

DICE

INTRODUCTIONA dice is three-dimensional figure with6 surfaces. It may be in the form of acube or a cuboid. After observing thesefigures, we have to find the different side(opposite or adjacent sides) of the dice.

Dice Formation A Dice is formed by folding a sheet ofpaper. These forms may be

Form 1:1

32 4

5

6

Number 1 is opposite to 5.Number 2 is opposite to 4.Number 3 is opposite to 6.

Form 2: 21

3

4

5 6


Form 3: 1

2

3 4

5

6


Form 4:1

32

4

5 6


Form 5: 1

32

4

6

5


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Cube & Dice82

ORDINARYDICE

STANDARDDICE

TYPES OF DICE

1. Ordinary Dice :

In this type of dice, the sum of opposite sides is not 7 but the sum of twoadjacent sides are seven.

3

45

Ordinary Dice

4+3 = 7

2. Standard Dice:

In such type of dice, the sum of opposite sides is 7 or sum of adjacent side isnot 7.

3

45

Ordinary Dice

1

54

Opposite of 1 ........6 (since 1+6 =7)Opposite of 5 ........2 (since 5+2 =7)Opposite of 3 ........4 (since 3+4 =7)

Here,1+4 =54+5=91+5=6

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Cube & Dice 83

IMPORTANT RULES Rule- 1 : If two sides of cubes are common( has same numbers or symbols), then theremaining two will be opposites of each other.

3

4 51

5 4

In above shown two dices, number 4 and 5 arecommon in both dices, hence, 3 and 1

will be apposite to each other.

Rule 2: If one side of dices is commonIf one side of given dices are common then list these sides (numbers on them)either in clock-wise or anti-clockwise. Comparing the numbers obtained from bothdices will give you the opposite numbers.

2

4 13

2 6

In this figure, number 2 is common in both dices. Now, writing the remaining no,in clock-wise direction, we get:2.............1...............4 (dice 1)2.............3...............6 (dice 2)Through the above observed data, we can say that:1 is opposite to 34 is opposite to 62 is opposite to 5

Rule 3 : If one side is common and it's place is same in bothdices.

If one side is common in both cubes and it's place is same in both of these dices,then the remaining two sides of respective dices which appear in figure will be theopposite of each other.

31

2

6

2

4

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Cube & Dice84As you can see, number 2 is common inboth of these dices and it appears in thesame face in both these dices. In suchcase, the remaining two sides in bothdices will be opposite to each other. Inthis figure, the opposite sides are :4 is opposite to 3 (as the position of 4 and3 are same on two dices)6 is opposite to 1 (as the position of 6 and1 are same on two dices)2 is opposite to 5 (we already know theposition of 1, 6, 3, 4 and 2. The only oneremaining is 5)

EXAMPLE 2. Two positions of a diceare shown, when 4 is at the bottom, whatnumber will be on the top?

1 1

3 52 6

(i) (ii)

(a) 1 (b) 2(c) 5 (d) 6

Sol. From the two figures it is clear thatthe numbers 2, 3, 5 and 6 cannotappear opposite 1. So, 4 appearsopposite 1. Therefore, when 4 is atthe bottom, 1 will be on the top.



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Analytical Decision Making 85

INTRODUCTIONAnalytical Decision Making is based ona set of relationships laid out, generallyarbitrarily, from which new informationcan be deduced. This involves twosteps-first of analysis and second ofreasoning. Analytical decision makingdeals with questions in which you haveto decide upon the course of actiontaken upon a candidate who has appliedfor a post or membership to an institutionkeeping in mind the essential requisitesand the data given for the candidate.

CATEGORIES OFANALYTICAL DECISIONMAKINGCategory IIn this type a vacancy is beingdeclared. The necessary qualificationsrequired by the recruiting agencies aregiven with certain exceptions. Thequalifications and the merits of thecandidates are mentioned. The decisionabout each candidate has to be madefrom amongst the five choices given,which state the courses of action to betaken as per the candidate's potential.

Category IIHere, the eligibility conditions for joininga course or availing certain benefits etcare given as against the vacanciesmentioned in the former category. The

qualifications of the candidates are alsomentioned. The decision about eachcandidate is to be made from amongstthe five answer choices given.

FORMAT OF THE QUESTIONExample (Directions): Read carefuly theinformations given below and answer thequestions based on it:The following are the given conditionsfor the recruitment of a candidate as afamily member in a computer institute:(i) The candidate must be in the age

range of 23 years to 28 years as on1st November, 2013.

(ii) The candidate must have workexperience as a teacher orprogramming experience of at least2 years.

(iii) The candidate must have a PGdegree in computer application,[MCA, M.Tech. or M.Sc.(computer science)] with not lessthan 60% marks.

(iv) Out of total 50 marks in theinterview, the candidate mustobtain 50%. In the case when acandidate

(v) Fulfils the above conditions, he/she shall be appointed as seniorteacher.

(vi) Has less than 60% but more than50% marks in his/her PG degree incomputer application, he/she willbe appointed as junior teacher.

Analytical DecisionMaking

Chapter

17

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Analytical Decision Making86(vii) Is of age more than 28 years but

less than 32 years as on 1st

November, 2013, the case may bereffered to the GM of the institute.

On the basis of the above mentionedconditions and information about eachof the candidates in the question below,you have to decide which of thefollowing courses of action should bethan against each candidate. Point to benoted that nothing extra will be assumedexcept the given information. Thedecision must be based only on the dataprovided.Mark your answer:(a) If the candidate is to be selected

as a Junior teacher(b) If the candidate is to be selected

as a Senior teacher(c) If the case will be reffered to the

GM of the institute.(d) If the data are inadequate(e) If the candidate is not to be

selected.

QUESTIONS:1. Mukesh Verma was born on 31st

July, 1985. He is an M.Tech. incomputer engineering with 70%marks. He has been working in aninstitution as a programmer for thelast 7 years.

2. Karishma Tiwari is MCA with72% marks. Her date of birth is 14th

August, 1990. She has worked asa computer teacher for 4 years. Shehas got 35 marks in interview.

What You See in the givenQuestion Format?

In the given format you can see thefollowing things:(1) Informations about some

candidates have been provided.

(2) Some conditions have been givenfor candidates to fulfil in order toget selected for a particular job/post. In case of the given format,four conditions have been given.

(3) When a candidate fulfils all thecriteria except some, then differentcourse of action has to be takenfor him.

Some more things tounderstand

Basic conditions: In the given questionformat, there are four basic conditions— (i), (ii), (iii) and (iv). They are calledbasic conditions because they are theoriginal conditions.

Additional conditions: In the givenquestion format, there are two moreconditions apart from the basicconditions and they are (vi) and (vii).point to be noted that (v) will not be onadditional condition as it does not talkof exceptions. In fact (v) is only atotality of the four basic or originalconditions given in the questionformat.

What is data inadequacy?As one of the answer is given as ‘datainadequate’ we must be clear about whatexactly does data inadequacy mean?When details given about any candidateprovide no information as required bythe basic conditions/additionalconditions then this would be the caseof data inadequacy, For example, let ussee the first question given in the format.No information is given about whatmarks have been obtained by MukeshVerma in the interview. Hence, the datais inadequate here.

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Analytical Decision Making 87How to solve a givenproblem?Let us consider the questions given inthe format and start one stepwiseprocess.STEP IWrite the name of the candidates in theleft side and then write the symbols (i, ii,iii, iv) of the basic conditions to the topright. Now, put the symbols of theadditional conditions (vi and vii) belowthe symbols of that basic condition withwhich these might be related. Forexample, (vi) is a condition abouteducational qualification and so, it is anexception of (iii). Hence (vi) should bewritten below (iii). Similarly, (vii) shouldbe written below (i). Now, after thecompletion of step I, the following formatwill be prepared:

i (vii)

ii iii (vi)

iv

1 Mukesh Verma

2 Karishma Tiwari

3 Brijesh Shankar

4 Mansi Ranjan

5 Subodh Saxena

NOTE : To differentiate between basicconditions and additional conditions.The additional conditions have beenencircled.STEP IIAt the 2nd step just see the given answerchoices carefully and decide whichcombination of the conditions leads towhich conclusion. If we see the given

question format with serious eye, we findthat the following combination can beformed.

i + ii + iii + iv ® 2 [Senior teacher]vii + ii + iii + iv ® 3 [Case will be

reffered to GM]i + ii + vi + iv ® 1 [Junior teacher]

When we have decided the above threecombination giving answer choicesremain and the answer choice (a), (b) and(c), two answer choices remains and theyare answer choice (d) and answer choice(e). The answer choice (e), which saysthat the candidate is not to be selected,should be chosen when any one or moreof the given conditions is violated. Theanswer choice (d), which tells that thedata are inadequate, should be chosenwhen no information is given about anyone or more conditions.How to examine data?After step II you are required to readall the statements carefully. Just takeeach question one by one and comparethen with the given conditions. Examineesare suggested to use followingsymbols while doing this comparision:I If a basic condition is fulfilled mark

‘ü’ sign below it.II If a basic condition is violated and

it is not attached with anadditional condition then mark ‘X’sign below it.

III If a basic condition is violated butit is attached with an additionalcondition, then

(A) Mark a ‘×’ sign below it if additionalcondition is also violated.

(B) Mark a ‘ü ’ sign below it ifadditional condition is fulfilled.

IV In case of unavailability of anyinformation about any condition,a mark '?' Will be put below thatcondition.

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Analytical Decision Making88To understand point (i) to point (iv) letus see the presentation given below:

Question No.

I II/V III/VI IV

1 ü ü ü ×2 ü ü ü ü

3 ü (ü) (ü) ü

4 ü ü (×) ü

5 ü ? ü ü

Now just see the explanation of abovetable:(1) I, II, III and IV are basic conditions

while (V) and (VI) are twoadditional conditions. (V) isattached to II and (VI) is attachedto III.

(2) In question (1), I, II and III aresatisfied while VI is violated

(3) In question (2), all the basicconditions I, II, III and IV aresatisfied

STEP III(i) One by one, read the questions

very carefully and compare thefacts given with the variouscondition.

(ii) Mark the appropriate sign or ‘ü’or ‘×’ (ü) or (×)? As required

(iii) When a ‘×’ or a (×) sign is obtained,then stop examining further andwithout any hesitation select theanswer choice “not to be selected”for that particular question. Inanother words whenever you get‘×’ or (×) sign, do not take anybotheration to examine theremaining condition, select youranswer as “not to be selected andquickly move on to the nextquestion. It so happens because,if a condition as well as itsadditional condition is violated, it

does mean that one necessaryrequirement is not being fulfilled.Hence, we reach at a conclusionthat the selection is not possibleeven it other conditions arefulfilled.

STEP IVNow, this is the time to select youranswer choices on the patterngiven below:

(i) If find a ‘×’ or (×) below anycondition, go for the answer choice“not to be selected”

(ii) If you find no cross mark but thereis a question mark below anycondition, your answer choicewould be “data are inadequate”.

(iii) If you find neither any crossmark nor any question mark, thancompare the combination withthe three answer combinationsobtained in step II and select theanswer choice accordingly.After understanding the abovesteps, now we are at a positionof solving the question given inthe question format. Let us seethe solution:

Solution:(i) / (vii) (ii) (iii)/ (vi) (iv)

1 Mukesh Verma

(ü) ü ü ?

2 Karishma Tiwari

ü ü ü ü

3 Brijesh Shankar

(×) ü (ü) ü

4 Mansi Ranjan

ü ü (ü) ×

5 Subodh Saxena

ü ü (ü) ü

Question No.

Condition (V) is attached to II while theadditional condition is VI attached withthe basic condition III.

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Analytical Decision Making 89STEP WISE EXPLANATIONOF ABOVE TABLE:Step I

At the step I level, we read thequestion carefully and find outthat there are four, basic conditions(i), (ii), (iii) and (iv) and twoadditional conditions (vii) and (vi).further, it is clear that ‘(vii)’ is anexception of ‘(i)’ and ‘(vi)’ is anexception of ‘(iii)’. Now we writethe name of the candidates inextreme left and then put the basicconditions (i), (ii), (iii) and (iv) atthe top-right of the candidate inquestion 1. Next, we writeadditional condition ‘(vii)’ below‘o’ and additional condition ‘(vi)’below ‘(iii)’.

Step IIAt the 2nd level, we look at theanswer choices and prepare oneanswer combinations accordingly.This will be:i + ii + iii + iv Þ bvii + ii + iii + iv Þ ci + ii + vi + iv Þ a

Step IIIAt the step III level, we read everyquestion carefully and compare thefacts given in it with the variousconditions.Let us see the detailed analysis ofevery candidate question wise.Mukesh VermaHe is an M.Tech in computerengineering with 70% marks. Thisfulfills condition C. Hence we write‘ü’ mark below C. Next, his date ofbirth is 31st July, 1985. Here, we do

a mental calculation that on 31st

July, 2013 he turned 28th

. This isthe reason that on 1st November2013, he is more than 28 years.Therefore, (i) is violated, but theadditional condition of (i) is (vii)which is fulfilled and we write (ü)mark here. Further, Mukesh Vermais having a programmingexperience of 7 years (more than 2years). So we mark (ü) below (ii).Lastly, there is no informationabout marks of Mukesh in theinterview. Thus the sign ofquestion mark ‘?’ is put below d.Karishma TiwariKarishma is an MCA with 72%marks. This fulfills (iii), so we putthe mark ‘ü’ below (iii). Her dateof birth is 14th August, 1990, So on1st November, 2013, she is morethan 23 years. This fulfills ‘(i)’ andhence we put a (ü) mark below ‘(i)’.She is a computer teacher from last4 years. This fulfils (ii) and we put(ü) mark below (ii), lastly, she hasobtained 35 marks in the interview.This marks is more than therequired 50% (25 marks out of 50marks), therefore (iv) is also fulfilledand we put (ü) mark below (iv).

Step IVAt 4th level we select the answerchoices.

Sol. 1. No cross mark. But a questionmark is available. Hence, data isinadequate.

Sol. 2. i + ii + iii + iv Þ b [step II]So, the candidate is to be selectedas a senior teacher.

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Analytical Decision Making90

q Shortcut Approach

• For selection all basic conditionsmust be fulfilled.

• For rejection atleast oneindependent basic condition mustbe violated/basic '+' additionalcondition must be violated.

• If a basic condition is violated butan additional condition attachedwith it is fulfilled and all otherremaining basic conditions arefulfilled, then the case will bereferred to the person given in thequestions.

• Once the symbol ×/(×) is put inthe table, there is no need to checkfurther conditions as person isdeclared rejected at this stageonly.

• If for one basic condition, the datais not given while all other basicconditions are fulfilled, it meansdata is inadequate.

• If any information is not givenand answer choices don't havedata inadequate option, thencondition related to that particularinformation is supposed to beviolated.



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Chapter

18

NON-VERBAL REASONING

INTRODUCTIONThe word “series” is defined asanything that follows or forms a specificpattern or is in continuation of a givenpattern or sequence.In this type of non-verbal test, two setsof figures pose the problem. The setsare called Problem Figures and AnswerFigures. Each problem figure changesin design from the preceding one.

q Shortcut Approach· Directions – There are eight

directions as follows :

NNW

SW

NE

SES

EW

Up

RightLeft

Down· Rotational Directions –

There are two rotational directionsas follows :

Clockwisedirection (CW)

Anticlockwisedirection (ACW)

· Positions of Elements –

A

H

G

B

I

F

C

D

E

Centralelement

Top or middleelement

Up

Bottom or Downmiddle element

Upper rightelement

Upper leftelement

Middle rightelement

Middle leftelement

Lower rightelement

Lower leftelement

· Movement of Elements ThroughDistance –

QP

V

R

TU

SW

Clockwise Movement

P ® Q = 12

arm/step

P ® R = 1 arm/step

P ® S = 112 arm/step

P ® T = 2 arm/step

P ® S = 212

arm/step

P ® R = 3 arm/step

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Series92

P ® Q = 312 arm/step

QP

V

R

TU

SW

Anti Clockwise Movement

P ® W = 12

arm/step

P ® V = 1 arm/step

P ® U = 112 arm/step

P ® U = 212 arm/step

P ® V = 3 arm/step

P ® W = 312

arm/step

P ® P = 312 arm/step

· Directional Movement of Elements –

QP

V

R

TU

SW

Clockwise Movement

90°135°180°

225°270°315°360°

45°

QP

V

R

TU

SW

Anticlockwise Movement

315°

180°

360°45° 270°90° 225°

135°

TYPES OF SERIESType-I

A definite relationship between elements in given figures.

EXAMPLE 1.Study the problem figures marked (A), (B) and (C) carefully and try toestablish the relationship between them. From the answer figures markeda, b, c and d, pick out the figure which most appropriately completes theseries.Problem Figures

(A) (B) (C)

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Series 93Answer Figures

(a) (b) (c) (d)Sol. The direction of arrow which changes alternately. The dots are also changing

alternately. Hence, we are looking for a figure in which the arrow points downand the dots and positioned as in figure (b).

TYPE II. Additions of Elements :In these type of questions, each figure is obtained by either sustaining theelement of preceding figure as it is or adding a part of element or one element ormore than one element of the preceding figure in a systematic way.

EXAMPLE 2.Problem Figures

2 (A) (B) (C) (D)Answer Figures

(a) (b) ( c) (d)Sol. Two line segments are added in A to obtain B and one line segment is added in

B to obtain C. This process is repeated again to obtain D. Hence, answer figure(d) continues the series.

TYPE III. Increasing/Decreasing of Elements:

In these questions, the items in the diagrams either increase or decrease in number.


(A) (B) (C)

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Series94Answer Figures

(a) (b) (c) (d)Sol. The small circles are decreasing consecutively and the black dots are

increasing. So, figure (c) continues the series.TYPE IV Deletion of Elements :

In these type of questions, each figure is obtained by either sustainingthe element of preceding figure as it is or deleting a part of an element orone element or more than one element of the preceding figure in asystematic way.


(A) (B) (C) (D) (E)Answer Figures

(a) (b) ( c) (d)Sol. The qualitative characteristic of various elements in the diagrams change

to complete the series. So, figure (a) continues the series.TYPE V Rotation Type :

The various elements in the diagrams move in a specific manner. Theymay rotate in clockwise or anti-clockwise direction.

EXAMPLE 5.

Problem Figures

+

+ +

(A) (B) (C)

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Series 95Answer Figures

+ + +

+

(a) (b) (c) (d)Sol. The sign of plus is rotating clockwise. The pin changes direction alternately.

So, figure (d) coninues the series.

TYPE VI Replacement of Elements :

In these type of questions, each figure is obtained by either sustainingthe element of preceding figure as it is or replacing a part of element orone element or more than one element by a new element of the precedingfigure in a systematic way.


=? X

XX

?? C

**

*

*

=

? D

D2

(A) (B) (C) (D) (E)Answer figures

(a) (b) ( c) (d)

C**D

#D

#

*

CD

#D

Sol. The elements positioned at north-east (NE) corners disappear from the odd-numbered figures. The elements positioned at the south-west (SW) cornersdisappear from the even-numbered figures. Therefore * should not appear inthe answer figure. Hence (a), (b) and (d) cannot be the answers. Also newelements are introduced at the NE corners in even-numbered figures. Therefore,answer figure (c) continues the given series.



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Mirror & Water Images96

Mirror & Water Images

Chapter

19

Object Image

3. The line joining the object pointwith its image is normal to thereflecting surface.

4. The size of the image is the sameas that of the object.

I. Mirror Images of Capital Letters

ABCDEFGHIJKLM

NOPQRSTUVWXYZ

Mirror Images

INTRODUCTION

In this category, questions are based onthe criteria that a few figures are givenand you have to find out which one isthe exact image of the given figure in amirror placed in front of it. This imageformation is based on the principle of‘lateral inversion’ which implies that sizeof the image is equal to the size of theobject but both sides are interchanged.The left portion of the object is seen onthe right side and right portion of theobject is seen on the left side. Forexample, mirror image of ABC =

Note : There are ‘11’ letters in EnglishAlphabet which have identical mirrorimages: A, H, I, M, O, T, U, V, W, X, Y.

Characteristics of Reflection by planemirror1. Perpendicular distance of object

from mirror = Perpendiculardistance of image from mirror.

2. The image is laterally inverted.

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Mirror & Water Images 97

II. Mirror Images of Small Letters

abcdefghijkl

m

nopqrstuvwxyz

III. Mirror Images of Numbers

012345

678910

IV. Mirror Images of Clock:

There are certain questions inwhich the position of the hour-hand and the minute-hand of aclock as seen in a mirror are given.On the basis of the time indicatedby the mirror-image of the clockwe have to detect the actual timein the clock. In the solution ofsuch questions we use the factthat if an object A is the mirror-image of another object B then Bis the mirror-image of A.

q Shortcut ApproachWhenever you have to solve a mirrorimage question, imagine a mirror placedin front of the object and then try tofind its inverted image. The portion ofthe object that is near the mirror willnow be the portion of the image nearto the mirror in the inverted form.

EXAMPLE 1.By looking in a mirror, it appearsthat it is 6 : 30 in the clock. What isthe real time ?

Sol. As,

Time = 6 : 30

(Fig A)

Time = 5 : 30

(Fig B)Clearly, fig (A) shows the time(6 : 30) in the clock as it appears ina mirror. Then its mirror-image i.e.Fig (B) shows the actual time in theclock i.e. 5 : 30. You can solve itquickly if you remember that thesum of actual time and image timeis always 12 hours.

Water ImagesThe reflection of an object as seen inwater is called its water image. It is theinverted image obtained by turning theobject upside down.

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Mirror & Water Images98Water-images of Capital Letters

LettersWater-imageLettersWater-image

A B C D E F G H I J K L M

N O P Q R S T U V W X Y Z

Water-images of Small LettersLettersWater-imageLettersWater-image

a b c d e f g h i j k l m

n o p q r s t u v w x y z

Water-images of NumbersLettersWater-image

0 1 2 3 4 5 6 7 8 9

Note :1. The letters whose water-images are identical to the letter itself are : C, D, E, H,

I, K, O, X2. Certain words which have water-images identical to the word itself are :

KICK, KID, CHIDE, HIKE, CODE, CHICK

q Shortcut ApproachWhenever we have to analyze the water image of an object, imagine a mirror or asurface that forms an image just under the given object. The portion of the objectthat is near the water surface will be inverted but will be near the water surface inthe image as well.

EXAMPLE 2.Find the correct option for the water images below:

S T O R E

?water surface

Sol. In case of water image, the water reflection will usually be formed under theobject / word.In this case, the water image of the word will be an outcome of the waterimages of each of the letters like, the water images of S is , T is , O is ,R is and E is . Thus, the water image of the word ‘STORE’ is ‘ .’

S T O R E

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Mirror & Water Images 99



q Shortcut Approach

(i) While solving a question, try eliminating some options and solving thequestions will become easier. To eliminate options, keep in mind the patternused in the object (given diagram whose image is to be formed) as well as theposition of mirror or water such that the portion of the object near to themirror / water will produce the same portion near the mirror / water in aninverted form.

(ii) Images are images, be it water or mirror, in both the cases an inverted image ofthe alphabets / numerals / clocks / any other object are formed by inverting theobject. Inverting of the object solely depends upon the position of mirror orwater surface w.r.t. the object.

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Paper Cutting and Folding100

Paper Cutting andFolding

Chapter

20INTRODUCTIONIn this section, a sheet of paper is folded in given manner and cuts are made on it. Acut may be of verying designs. We have to analyze how this sheet of paper will lookwhen paper is unfolded.Note that when a cut is made on folded paper, the designs of the cut will appear oneach fold.

EXAMPLE 1.

Directions In the following example, figures A and B show a sequence of folding asquare sheet. Figure C shows the manner in which folded paper has been cut. Youhave to select the appropriate figure from alternatives which would appear when sheetis opened.

(A) (B) (C )

(a) (b) (c) (d)

Sol. Step I-When sheet C is unfolded once, it will appear as follows

Step II -

Clearly, the circle will appear in each of the triangular quarters of thepaper. So, figure (c) would appear when sheet is opened.

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Paper Cutting and Folding 101

EXAMPLE 2.

(a) (b) (c) (d)

(A) (B) (C)

Sol. Here, a circular cut is made on thequarter circle. Hence, this sheet,when completely unfolded, willcontain small circle on each quarterand will appear as option (d).

q Shortcut Approach· Consider a mirror placed on the

dotted line facing the portion/partwhich is to be folded and themirror image thus obtained issuperimposed on the design ofthe other side to get the foldedpattern.

· When more than one fold is madebefore punching then virtually tryto unfold each fold one by oneand predict the complete unfoldedpattern.



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Chapter

21INTRODUCTIONIn this section, an incomplete figure isgiven, in which some part is missing. Wehave to choose the segment, given inchoices, that exactly fits into the blankportion of figure so that the main figureis completed.

Note : If you observe carefully, younotice that the missing portion maybe the mirror image of any one of thequarters.

EXAMPLE 1.Select from alternatives the figure(X) that exactly fits in the mainfigure to complete its originalpattern.

?(X)

(a) (b)

(c) (d)

Sol.In this question, half shaded leafis moved clockwise. So, option (b)is right one.

q Shortcut Approach

· If answer figures contain similarfigure but in rotated forms, thenthe correct answer figure is thatfigure which can be substitutedat the missing part with leastchange in orientation.

· The correct option for the missingfigure can be given in any rotatedfrom, so student can rotate thefigures to check the correctnessof option.



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Hidden / EmbeddedFigures

Chapter

22INTRODUCTIONA figure (X) is said to be embedded in afigure Y, if figure Y contains figure (X) asits part. Thus problems on embeddedfigures contain a figure (X) followed byfour complex figures in such a way thatfig (X) is embedded in one of these. Thefigure containing the figure (X) is youranswer.

EXAMPLE 1.Directions : In each of the following ex-amples, fig (X) is embedded in any oneof the four alternative figures (a), (b), (c)or (d). Find the alternative which con-tains fig. (X) as its part.

(a) (b) (c) (d)

(X)

Sol. Clearly, fig. (X) is embedded fig. (b)as shown below :

Hence, the answer is (b)

q Shortcut Approach

· There may be some questions inwhich the question figure is notdirectly embedded in any of theanswer figure. In these type ofquestions, change the orientationof question figure to find thecorrect answer figure.

· In some questions, the questionfigure embedded in two or moreanswer figures, then the mostappropriate answer is that inwhich the question figure isembedded with least change in itsorientation.


Practice Exercises with Hints & Solutions – P-150-152Chapter Test – C-43-44Past Solved Papers

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Figure Formation and Analysis104

Figure Formation andAnalysis

Chapter

23INTRODUCTIONIn this topic, a question is one of thefollowing types :I. Formation of triangles/square/

rectangle etc. either by joining ofthree figures after choosing themfrom the given five figures or byjoining any other pieces afterselecting them from given alternatives.

II. Making up a figure from givencomponents.

III. Making up a three dimensionalfigure by paper folding.

IV. Rearrangement of the parts of givenfigure.

V. Fragmentation of key figure intosimple pieces.

TYPE-I : Formation of tr iangles/square/rectangle etc. either by joiningof three figures after choosing them fromthe given five figures or by joining anyother pieces after selecting them fromgiven alternatives.

EXAMPLE 1.A set of five figures (A), (B), (C),(D) and (E) are followed by fourcombinations as the alternatives.Select the combination of figureswhich if fitted together, will form acomplete triangle.

(A) (B) (C) (D) (E)

Sol. If figures A, B and E are fittedtogether, the resultant figure willbe a triangle.

A EB

TYPE-II : Making up a figure fromgiven components

EXAMPLE 2.

Find out which of the alternatives(a), (b), (c) and (d) can be formedfrom the pieces given in box ‘X’.

(X)

(b) (c) (a) (d)

Sol.

Figure (b) can be formed from the piecesthe given in box 'X'.

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Figure Formation and Analysis 105TYPE-III : Making up a three dimensionalfigure by paper folding. In this type, wehave to analyze when a paper foldedalong the lines, how a three dimensionalfigure look like. Sometimes, a key figureis given which is made by folding one ofthe four figures given in alternatives. Wehave to determine which figure can beused to create the key figure.

EXAMPLE 3.A figure ‘X’ is given. You have tochoose the correct figure, given inthe alternatives, when foldedalong the lines, will produce thegiven figure ‘X’.

(X)

(b) (c) (a) (d)Sol. Figure (a) will produce the given

figure 'X'TYPE-IV : Rearrangement of the partsof given figure.In this type of questions, a key figure isgiven. We have to identify the figure fromalternatives that is a rearrangement ofparts of key figure.

EXAMPLE 4.Which figure is the rearrangementof the parts of the given figure.

(X)

(b) (c) (a) (d)Sol. Figure (a) is the rearrangement of

the parts of the given figure 'X'.

TYPE-V : Fragmentation of key figureinto simple pieces.This type is opposite to TYPE-II. In thistype, a key figure is given and everyalternatives has different pieces. Wehave to select the set of pieces that canmake the given key figure.

EXAMPLE 5.Find out which of the alternativeswill exactly make up the key figure(X)

(X)

(a) (b) (c) (d) Sol. Figure (a) will exactly make up the

key figure 'X'

q Shortcut Approach· The number of elements given to

form a figure must be equal to theelements present in the answerfigure. This will help you to easilyeliminate some of the option figures.

· The size of pieces of figures inthe question figure and the sizeof pieces used to form a figure mayvary but their shapes must haveto be similar.


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Visual Reasoning106

Visual Reasoning

Chapter

24INTRODUCTIONVisual intelligence measures the abilityto process visual material and to employboth physical and mental images inthinking. As a result people with a highvisualization find it easier to comprehendinformation and communicate it toothers. Your visualization skillsdetermine how well you perceive visualpatterns and extract information forfurther use. Visualization also facilitatesthe ability to form associations betweenpieces of information something whichhelps improve long term memory.

Types of Visual Reasoning(A) Odd-Man Out Type(B) Counting of Figures

(A) ODD-MAN OUT TYPE

1. Rotation of same FigureThis is the most common type ofclassification. The similar figuresare actually the rotated forms ofthe same figure in clockwise oranti-clockwise direction. Thefigure which comes out to bedifferent from other is that figurewhich cannot be obtained byrotation of either of the otherfigures,

EXAMPLE 1.Directions : In the following question,a group of five figures is given. Out ofwhich four figures are similar to eachother in a certain way and one is differentfrom other. Find the odd figure out.

(a) (b) (c) (d) (e)Sol. After examining the above figure, it

is found that except (d) all figurescan easily be obtained by clockwiseand anti-clockwise movement oreach other.

2. Number of Elements or LinesA group of figure may be classifiedon the basis of number of elementsor the number of lines present infigures. The figures can also beclassified on even or odd numberof lines or elements present infigures. Classification can also bedone on the ratio of number of linesand elements.

EXAMPLE 2Directions : In the following question, agroup of five figures is given. Out ofwhich four figures are similar to eachother in a certain way and one is differentfrom other. Find the odd figure out.

(a) (b) (c) (d) (e)

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Visual Reasoning 107Sol. All except figure (c) contains odd

number of arrows.3. Division of Figures

This type of classification is doneon the equal or inequal division offigures or divisioin of figure insome specified ratio or parts.

EXAMPLE 3.Directions : In the following question, agroup of five figures is given. Out ofwhich four figures are similar to eachother in a certain way and one is differentfrom other. Find the odd figure out.

(a) (b) (c) (d) (e)Sol. Except figure (a) all figures are

divided into two equal parts.4. Similarity of Figures

Classification on the basis ofsimilarity of figure is done whenorientation, shape, measure ofangle or method of presentationof group is same except for the oddfigure.


(a) (b) (c) (d) (e)Sol. Let us consider the two adjacent

bent lines as a pair. Then, in eachfigure except (d) there are twostraight lines between the bent pairand the remaining bent line whenthe direction of bent is considered.

5. Relation between Elements ofFigureIn this type of classification, theelements of the figure bears acertain relationship between themin which the odd figure does notposses. This relation can be basedon shape of elements presents,inversion of elements etc.


(a) (b) (c) (d) (e)Sol. Except figure (c) in all the figures,

both the inside and outside figuresare similar but differ in size.

6. Interior-Exterior Consideration ofElementsA figure can be formed from twoor more elements, it is likely thatsome elements may lie in interiorof other elements while some maylie in the exterior of the otherelements. This consideration canbe used for classification ofelements from a group.


(a) (b) (c) (d) (e)

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Visual Reasoning108Sol. Only figure (d) does not contain

any element present in the interiorof the closed figure.

(B) COUNTING OF FIGURES TYPE

Type-1 : Counting of Straight Linesand Triangles

(a) Straight lines

A B

B

B B

A A

AA. Horizontal line

B. Vertical line

C. Slant line

q Shortcut Approach· Consider a line (AB) given

A BC· Then, on counting, it will be

counted as one line, i.e., AB andnot as a two straight lines AC andCB.

EXAMPLE 1.How many straight lines are therein the figure ?

Sol. A R B

QO

P

D CSHorizontal lines = AB + PQ + DC = 3Vertical lines = AD + RS + BC = 3Slant lines = 0\ Total lines = 3 + 3 + 0 = 6

(b) Triangle –It is a closed figure bounded bythree side.

A

B C

q Shortcut Approach· Smallest triangles are counted

first.· Now, counted those triangles

which are formed with the twotriangles and further countinggoes on in the same way.

· Largest triangle is counted in thelast.

EXAMPLE 2.How many triangles are there in thefigure ?

Sol. A

B C

O

Smallest triangle = BOC = 1Largest triangle = ABC = 1\ Total triangle = 1 + 1 = 2

Type-2 : Counting of Quadrilateralsand Polygons(a) Square

It has four equal sides, equaldiagonals, and each of the fourangles equal to 90°.

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Visual Reasoning 109

q Shortcut Approach· Count smallest squares first.· Now, count squares which are

formed with two squares andfurther counting goes on in thesame way.

· Largest square is counted in the last.

EXAMPLE 3.How many square are there in thefigure ?

Sol. A B

CD

E F

G

H

O

Smallest squares= AGOE + GBFO + EOHD + OFCH= 4Square formed with four squares= ABCD = 1\ Total squares = 4 + 1 = 5

Formula for Counting SquaresLet r be the number of rows and c bethe number of columns.Now, total number of squares= (r × c) + {(r – 1) × (c – 1)

+ (r – 2) × (c – 2) + ......The terms are continued upto the termwhich is equal to zero (0). This methodis applicable only to the figure. whereeach row and column is divided intosquares of equal sections.

(b) RectangleIt has four sides, and oppositesides are equal. It has equaldiagonals and each of the fourangles is equal to 90°.

EXAMPLE 4.How many rectangles are there inthe figure?

Sol. A

H

B

G

C

F

D

ESmallest rectangles = ABGH +BCFG + CDEF = 3Rectangles formed with two rect-angles = ACFH + BDEG = 2Largest rectangles = ADEH = 1\ Total rectangles = 3 + 2 +1 = 6

Formula for Counting ofRectangles and ParallelogramsLet r be the number of rows and c bethe number of columns.Now, totalnumber of rectangles or parallelograms= [(r + (r – 1) + (r – 2) + ..... +1]

× [c + (c – 1) + (c – 2) + ...... + 1]

The method is applicable only to thefigure, where each row and column isdivided into rectangle of equalsections.

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Visual Reasoning110Type-3 : CircleCircle is a closed figure. It has zerosides.

q Shortcut Approach

· Keep writing numbers one by oneinside the circles starting from 1i.e., for 1st circle put 1, for 2ndcircle put 2, for 3rd circle put 3and so on.

· The number which is put for thelast circle is the required numberof circles.

EXAMPLE 5.How many circles are there in thefigure ?

Sol. Here, we start counting of circlesand mark them, as 1, 2 and so onand finally we end on getting 5number of circles as shown below:

1 2 3

54



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Evaluating InferencesChapter

25

ANALYTICAL REASONING

INTRODUCTIONThis chapter makes you aware about aspecial type of question pattern whichhas become a regular trend of almost alltype of competitive examination. Aninference is a logical conclusion onevidence. A valid inference is believableand realistic. As per the pattern, apassage is given followed by someinferences (conclusions) and theexaminee is asked to decide whether agiven inference follows or not in the lightof the given passage. Let us see theformat below:What is the problem like?Problem Format/ Sample Problem:-Directions (Qs 1-5): Below is given apassage followed by several possibleinferences which can be drawn from thefacts stated in the passage. You have toexamine each inference separately in thecontext of the passage and decide uponits degree of truth or falsity.Mark answer:(a) If the inference is definitely true i.e.,

it properly follows from thestatement of facts given.

(b) If the inference is ‘probably true’though not definitely true in thelight of the facts given.

(c) If the ‘data are inadequate’ i.e. fromthe facts given you can not saywhether the inference is likely tobe true or false.

(d) If the inference is ‘probably false’though not definitely false’ in thelight of the facts given.

(e) If the inference is ‘definitely false’i.e., it cannot possibly be drawnfrom the facts given or itcontradicts the given facts.

PASSAGEIn its most ambitions bid ever to house6 crore slum dwellers and realise the visionof a slum-free India, the government isrolling out a massive plan to build 50 lakhdwelling units in five years across 400towns and cities. The programme couldfree up thousands of acres of valuablegovernment land across the country andgenerate crores worth of business for realestate developers. Proliferation of slumshas had an adverse impact on the GDPgrowth for years. Slum dwellers arecharacterised by low productivity andsusceptibility to poor health conditions.The government believes that betterhousing facilities will address socialissues and also have a multiplier effectand serve as an economic stimulus.Q 1. Development of land occupied by

slums in cities of India will not haveany effect on the common public.

Q 2. Majority of the slums in cities andtowns in India are on prime privateproperties.

Q 3. Per capita income of slum dwellersis significantly lower than that ofthose living in better housingfacilities.

Q 4. Cities and towns of developedcountries are free from slums.

Q 5. Health and sanitary conditions inslums are far below the acceptablenorms of human habitat in Indiancities and towns.

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Evaluating Inferences112Before solving the sample problem,we must see the pattern of theproblem and find out what it putsbefore the students to think.A minute look will make you clearthat here the examiner has gradedthe choices very closely. He/she has given two positive choicesinstead of one.i. Definitely trueii. Probably trueFurther, he/ she has also given twonegative choices instead of one:-i. Definitely falseii. Probably falseThis pattern requires a deeperthinking as it leaves before youfollowing areas of confusion:-1. Definitely true or probably

true2. Definitely false or probably

false3. Data inadequate or probably

true4. Data inadequate or probably

false1. Definitely true or probably true:

If the given inferences is a directconsequences of something givenin the passage, then it falls underthe category of definitely true. Butthe confusion may arise when thegiven inference is not directlystated in the passage but it appears‘almost’ definitely true to you. Butas it is not clearly stated in thepassage, you may think that even‘Probably true’ could be the answer.To get rid of this confusion, youhave to recheck your reasoning. Ifthe given inference has not beenmentioned directly in the passage,then you must have assumedsomething ‘extra’ to draw thisconclusion. Now, ask the followingquestions from yourself.

(A) Is the extra assumption anuniversal truth?

(B) Can the extra assumptionnever be false?

If you find ‘yes’ for the question(A) and ‘no never’ for thequestion (B), then accept it asdefinitely true, otherwise pick‘Probably true’.

2. Definitely false or probably falseIf the given inference does notfollow from the passage, it fallsunder the category of definitelyfalse. But confusion may arise whenthe given inference is not givendirectly in the passage and seems‘almost’ definitely false. But asrelated things are not mentionedclearly in the passage, you thinkthat ‘probably false’ may be correct.To get rid of this confusion try torecheck your reasoning. If theopposite of the inference has notbeen mentioned in the passage,then you must assume somethingextra to reach your conclusion. Justask the following questions toyourself.(A) Is this assumption an universal

truth?(B) Can this assumption never be

false?If you find ‘yes’ for question (A)and ‘no, never’ for question (B)then select your answer asdefinitely false, otherwise probablyfalse will be your correct answer.

3. Data inadequate or probably trueWhen an indirect inference isdrawn from the passage, thisconfusion may arise. As the giveninference is not explicitlymentioned, you think that data areinadequate and that sufficientinformation has not been given todraw a conclusion. However, thegiven inference appears to be in

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Evaluating Inferences 113sync with the general 'tone' of thepassage In such case you may gofor ‘Probably true’.To get r id of this confusion,recheck your general mental ability.You can declare the giveninference as probably true, if withthe help of some extra assumption,the given inference seems likely tobe true. Thus, you can some howconvince yourself that theinference is likely to be true. Onthe other hand, you can declarethat data are inadequate if nodefinite conclusion can be drawnfrom the passage even with thehelp of some extra assumption.Hence, in such case you can getconvinced that the inference islikely to be true or false.

4. Data inadequate or probably false:When the given inference is drawnindirectly from the passage, suchconfusion may arise. As it is notexplicitly said in the passage, youcome to the conclusion that dataare inadequate because sufficientinformation has not been providedto draw a definite conclusion.However, the given inferenceappears to you in contradiction withthe general ‘tone’ of the passage.Therefore, you are tempted to pickup ‘probably false’ as your answer.To get rid of this confusion recheckyour general mental ability. You candeclare an inference probably false.Only if you are able to find out areasonable assumption, combiningwhich with what is said in the givenpassage the inference appearslikely to be false.Thus, somehow, you can convinceyourself that the given inferenceis likely to be false. On the otherhand, you should pick up thechoice ‘data are inadequate’ only

if you can not find any acceptableassumption which, combined withwhat is said in the passage, maylead to some definite conclusion.In such case, you can not getconvinced whether the giveninference is likely to be true or false.Now, lets try to apply the aboverules in the passage given aboveand try to solve the sampleproblems.

Solution to sample problems:1. (c) As we have no information

about how the freed up landwill benefit the commonpublic, hence data inadequate’will be our correct answerchoice. The passage do notsuggest us any relatedassumption.

2. (e) The passage says to thecontrary getting rid of slumswould “Free up ..... valuablegovernment land”. Theinference does not followfrom the passage.

3. (b) The extra assumption thatmakes this option probablytrue is : Low productivity islikely to lead to low income.The passage does notdirectly talk about per capitaincome.

4. (b) As slums have led to a lowerGDP growth in India. Thestatement is in sync with the'tone' of the passage. Theextra assumption here can bethat as countries developthey need to deploy thingsthat improves their GDP. Soit can be probably true thatall slums vahish.

5. (a) The passage says that theslums dwellers are susceptible“to poor health conditions”.This is directly mentioned inthe passage.

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Evaluating Inferences114

q Shortcut Approach

The inference is given in

passage

Is it 100% true in context

of passage

Is it in the context of the

passage

Can it be proved 100%

true using some universally accepted

assumption

No

No

Yes Yes

Yes

DFDT(Definitely

True)(Definitely

False)

(DefinitelyFalse)

(ProbablyFalse)

(ProbablyTrue)

(Data Inadequate)

Yes|

DT(Definitely

True)

Yes

DFMay or may not

be true |

PT(Probably

True)

Negatesthe passage

|DF

(DefinitelyFalse)

Not false definitely

|PF

(ProbablyFalse)

Contradictsthe passage

Chance that it is not 100% true in the context of passage

Chance thatit is not 100% false in the passage

PF

DI

PT

Data not available to

prove the trueness

Yes No

No



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Statement &Arguments

Chapter

26INTRODUCTIONIn this chapter, we are going to studyarguments. In fact, this is the study whatwe call the basics of all logic. Do youknow what do we do in logic? In logic,we advocate certain point of view withthe help of some evidences and certainassumptions and that is calledargumentation. This is a fact that almostall segments of analytical reasoning aresomeway associated with argumentationand this is the reason why study ofargumentation is so important for theexaminees preparing for variouscompetitive examinations.Concept of ArgumentA sequence of two or more sentences(or statements)/ phrases/clauses thatincludes a conclusion (or claims), is calledan argument. This conclusion of theargument is based on one or more thanone statement and these statements maybe called premises (propositions). Apartfrom this, arguments may also have somehidden premises. which may be calledassumptions. Let us see the followingexample:Example:Mr. Sharma bought a large quantity ofsweets, he must have celebrated someoccasion.Explanation: The foregoing examplehas two parts:

Part I: “Mr. Sharma bought a largequantity of sweets.”

Part II: “He must have celebrated someoccasion.

Here, ‘Part II’ is the conclusion part ofthe given argument. How has thisconclusion (part II) been arrived at? Infact, this conclusion has come out withthe help of supporting evidence orpremise that is part I of the argument.Did you notice that in this argument partI and part II (Premise and conclusion)are connected by a hidden premisewhich is not explicitly stated. Thathidden premise is “a large quantity ofsweets is bought only on occasions”and this premise may be called anassumption. Hence, in reality the givenargument has three parts.

Part I: (Premise) Mr. Sharma bought alarge quantity of sweets.

Part II: (Assumption or hidden premise)a large quantity of sweets is bought onlyon occasions.

Part III: (Conclusion) He must havecelebrated some occasion.

Point to be noted is that part II is anassumption (a hidden premise) thatconnects part I (premise) and part III(conclusion) and hence, it is a missinglink between part I and part III of thegiven argument.

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Statement & Arguments116No doubt that above mentioned examplebrings to us the basic characteristics ofargumentation but it also leaves somequestions before us like:(i) Is the assumption or hidden premise

always present in an argument?(ii) Is the number of premise only one in

an argument?Our answer for both the questionswill be a big ‘No’. Why so? Let ussee the explanations for both thequestions given below:

(i) Explanation for question: Justconsider an argument given as “Mr.Sharma bought a large quantity ofsweets. A large quantity of sweetsis bought on occasions only. Hence,he must have celebrated anoccasion”.Here, we see that this argument hasno assumption (hidden premise)because the premise or supportingevidence (Mr. Sharma bought a largequantity of sweets) and conclusion(Hence, he must have celebrated anoccasion) are connected by anexplicit statement (A large quantityof sweets is bought on occasionsonly). Remember, an assumption is ahidden premise. It does meanassumption is a missing link in thechain of logic. Therefore, if anargument is complete in itself anddoes not have any missing link, thenit will not have any assumption. Inthe given argument, the explicitstatement (A large quantity of sweetsis bought on occasions only)connects premise or supportingevidence and conclusion to make theargument assumptionless.

(ii) Explanation for question: Justconsider the argument given as“Vandana is tall. She is slim and hasbeautiful eyes. She has long hair andcharming face as well. So, Vandanais a beautiful girl.”Here,1st premise: Vandana is tall.2nd premise: She is slim and hasbeautiful eyes.3rd premise: She has long hair andcharming face as well.Conclusion: So, Vandana is abeautiful girl.This proves that an argument canhave more than one premises.Further this explanation is also areply for question (i) as the givenargument has no missing link. Thisargument is complete in itself andhence, it is free of hidden premise orassumption.

Ways of Argumentation: So far, you musthave understood the basic concept ofargumentation and come to theconclusion that an argument is usuallymade to make strong a particular pointof view in order to convince someoneabout something.(i) Argument based on Analogy:

Analogy based arguments are oftenused to make strong a particularpoint of view. In fact analogy is aninference drawn out of aresemblance between particularthings, occasion or events (that areknown) to a further (unknown)resemblance. For example, if we finda fat-woman eating very much andmeet in another woman who is alsofat then, by analogy, we expect thatthe other fat woman would also beeating very much. We can say it inanother way that if x, y, z, q are anyentities and u, v, w are any attributes

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Statement & Arguments 117then the analogical argument may berepresented in the following form :

x, y, z, q all have the attributes ‘u and v’ x, y, z have the attribute ‘w’\ q probably has the attribute ‘w’

EXAMPLE 1. Sachin scored acentury in the 1st test against Australiaand so did Dhoni; Sachin scored morethan 150 runs in the 2nd test againstAustralia and so did Dhoni; Sachin hasscored a double century in the 3rd testagainst Australia. So, Dhoni will also hita double century in this 3rd test matchagainst Australia.

EXAMPLE 2. Australia and Englandhave both lost to India in football andhockey. So, India should defeat both thecountries in cricket.Findings:In Example 1, Sachin and Dhoniperformed very well in the 1st twomatches against Australia. In fact, itseems that Dhoni did the same thingwhat Sachin did in the 1st and 2nd test.As Sachin has played a great inningscoring a double century in the 3rd testmatch, hence on the basis of similarsituation the conclusion has been madethat Dhoni will also make a doublecentury.

We also know that performing good orbad is a matter of chance. It is also amatter of chance that two players(Sachin and Dhoni) performed equallygood in the last two test matches.Therefore, we cannot say definitely thatDhoni will make a double century becauseSachin has done so. In fact, we can saythat he may or may not hit a doublecentury. It can also be said that futureperformances can not be predicted onthe basis of past performances. Thus, it

is clear that this analogical argumentdoes not seem strong. Similary, in caseof example (2) we can say that India mayor may not defeat Australia and Englandin the game of cricket only because Indiahas defeated both the countries in twodifferent games (Football and Hockey).Hence, the argument given in example(2) also seems to be a weak argument.Final comment: Analogy basedarguments are weak arguments.

(ii) Argument based on cause: Sucharguments relate a cause with aresult. Let us see the examples givenbelow:

EXAMPLE 1. India will win the worldcup 2011 because it is the most balancedone day team in the world in present daycricket.

EXAMPLE 2. He came back home latenight. He must have gone to watch amovie.Findings: We see in the foregoingexamples that effects have been relatedwith causes. In example (1), the cause(the most balanced one day team) wellsupports the effect (India will win theworld cup) and hence, it is a goodargument. But in Example (2) it is arguedthat since the effect (coming home latenight) has taken place, the cause(watching movie) must have occurred.But the point to be noted that effect mayoccur (he may come home late night)because of the other reason as well.Hence, the argument given in the Example(2) is not a good argument or it may becalled a weak argument.

Final Comment: Arguments based oncauses may be strong or weak orfallacious.

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Statement & Arguments118(iii) Argument based on example:

Sometimes an argument is given byciting some example/ examples aspremise/ premises. Let us see thefollowing examples that will illustratethe concept:

EXAMPLE 1. We should use X brandof cold cream because X brand is usedby ‘Madhuri Dixit”, the famousbollywood actress.

EXAMPLE 2. We must like Rosesbecause Chacha Nehru loved Roses.Findings: In example (1) we havearrived at the conclusion (we should useX brand of cold cream) by using thepremise as example (X brand is used byMadhuri Dixit). In example (2) theconclusion (we must like roses) has comeout by using the premise as example(because Chacha Nehru loved it). Here,we can say in case of Example-1 thatusing certain brand by a particularactress, does not mean that X brand willbe liked by all people as likes and dislikesare the personal choices. In example (2),the case is also the same. Everyonecannot like the roses only becauseChacha Nehru loved roses.Final comment: Example basedarguments are either weak or fallacious.

Note: In Example-1 and 2, conclusion partis the start of the arguments. Sometimesyou can also see that conclusion is givenin the middle. It does mean thatconclusion part is not always in the last.But it depends on the style of writing ofdifferent writers/authors.(iv) Argument based on blind advocacy:

Such argument is like a salesman’sargument who argues only for thepurpose of selling a particular

product. He speaks of the advantagesand the benefits of his product.Hence, a salesman argument is onewhere a conclusion comes outbecause of the positive points andthe benefits that it leads to. Suchtypes of arguments are very commonin day to day life.

EXAMPLE 1. Exercise is good forhealth and students need good healthto put hard labour in their studies. Thisis the reason why every educationalinstitution must have a gym.

EXAMPLE 2. There should be a banon strikes as they disrupt the normal lifeof the common people.Findings: In example-1, the conclusionis that every educational institution musthave a gym because exercise is good forhealth and students need good health.No doubt the good health ensures goodmind but it is not practically feasible forevery educational institution to have agym. Hence, Example-1 will be a weakargument. In example-2, ban on strikes isbeing demanded and this demand isreasonable as argument has negativefeature of strike. Hence, example-2 is astrong argument.Final comment: Such arguments canbe both weak or strong.

(v) Argument based on chronology:Very often we see that a conclusionis drawn only on the basis ofchronological order of some events.Let us see the examples given below:

EXAMPLE 1. Computer was inventedlater than television. Therefore, televisionhas a technology inferior to that of acomputer.

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Statement & Arguments 119EXAMPLE 2. Song ‘B’ was released

two months earlier than song ‘C’. So theformer could not be the copy of the latter.Findings: In example-1, it is assumed thata technologically inferior object alwayscomes before the superior objects. Thismay be true most of the time but this isnot true in 100% cases. Hence, theconclusion given in example 1 isquestionable making the given argumenta weak one. In 2nd case, it is thepossibility that song ‘C’ was recordedearlier although released later than thesong ‘B’. Hence, in such a situation thepossibility of copying can not be deniedand this makes argument given inExample-2 a weak argument.Final comment: This type of argumentsare usually weak and unconvincing.By now, all the standard ways ofargumentation have been discussed indetail. We will now take a look at the keywords so that you could easily take outthe conclusion part from the givenargument. The keywords are givenbelow:

So, Hence,Therefore, ConsequentlyThus,

Apart from above given keywords, theconclusion part can also be identified bythe certain phrases given below:

As a resultIt can be inferred thatWhich means thatWhich suggests thatWhich proves thatWhich shows thatIt follows that

If you find one of these keywords/phrases before any sentence then takethat sentence as your conclusion. If the

keywords/phrases are absent, thenapply your common sense and take outthe sentences that can follow one ofthese keywords/ phrases and thatsentence will be your conclusion. After learning concept of argument wecan easily move on to the problems ofreasoning which are asked in variousexams wherein examinee is required toevaluate the forcefulness of thearguments. On the basis of a statement,arguments are given in the questionsand the candidate is required to find out:(a) Which argument is strong.(b) Which argument is weak.We know that “strong” arguments arethose which are both important anddirectly related to the question. “Weak”arguments are those which are of minorimportance and also may not be directlyrelated to the question or may be relatedto a trivial aspect of the question. To findout if a given argument is strong or notwe will move according to the solutionsteps given below:Solution stepsStep I: Do the preliminary screening

of the given arguments.Step II: Find out if the given

arguments really follow ornot.

Step III: Find out if the givenarguments are really desirable(in case of positive argument)/ harmful (in case of negativearguments)

Step IV: Find out if the argument andsuggested course of actionare properly related.

Now, we will discuss all the steps one byone.

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Statement & Arguments120Step I: Preliminary screening of thegiven arguments

At the very 1st level we test how weakan argument is. If at the very 1st level wefind the argument weak, then there is noneed to go for further steps. In manycases the weak arguments are veryclearly visible and we do not need tothink much before arriving at theconclusion that they are weak. Such typeof arguments come under the followingcategory:(i) Doubtful/Ambiguous arguments:

These arguments do not make it clearthat how they are related to a courseof action. They also do not give theclear idea about what exactly theauthor or writer wants to say.

EXAMPLE 1.Statement: One should enjoy everysecond of one’s life because everyonehas to die one day.Argument: No, because one must thinkabout fulfilling one’s ambition in life andshould not think about death as one’sgoal.Comment: Here, statement and argumentare not properly related. Statementsuggests to enjoy every second of life.Enjoying life does not mean that oneshould not follow the path of fulfillingone’s ambition. In fact a person canenjoy his/ her life in the course offulfilling his/her ambition. In fact, we cansay without enjoying work of our ownchoice, we can not fulfill our ambition.Further the given statement does notgive any indication that one should seedeath as one’s goal. Hence, in this casestatement and argument leave doubtful

and confusing impression on our mindmaking the given argument very weak.(ii) Useless/ superfluous arguments:

Such arguments do not do a deepanalysis of the given statement.They simply ‘glance’ at thestatement and put them under thecategory of weak arguments.

EXAMPLE 2.Statement: Cricket must be banned inIndia.Argument: Yes, it has no use.Comment: Here, the argument does notgo deep down into the matter makingitself a weak argument.(iii) Arguments in the form of question:

Such arguments are very weak innature as the arguments given in thequestion form are without anysubstance and have no techniqueof argumentation. In fact, in sucharguments arguers throw back thequestion.

EXAMPLE 3.Statement: Should import be banned inIndia?Argument: Yes, why not?Comment: Here, statement is given inthe form of question and arguer throwsback the question without giving anyconvincing statement in the form ofargument. Hence, the given argument isvery weak.(iv) Very simple arguments: Such

arguments are very simple in nature.They are given in small sentencesbut do not get any support by factsor established notions. Further, sucharguments are not ambiguous andthey are properly related with the

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Statement & Arguments 121statement but because of their simplenature they come under the categoryof weak arguments.

EXAMPLE 4.Statement: Enjoying life should be theprinciple of our life.Argument: No this thinking hardlyenable us to do anything.Comment: Here, the given argument isonly a simple assertion which containsno substance. Here, it will come underthe category of weak arguments.

Step II: Finding out if the givenarguments really follow or not.

If the arguments are rejected at thepreliminary step then we do not need totest them further. But, if the preliminarystep has been cleared, then we move onto step II.Case I: When the result followsAt the step II, the result will follow in thecases given below:(i) Established fact: An established fact

does mean that it must be universallyacknowledged/ scientificallyestablished. A result will follow acourse of action if it is an establishedfact that this particular result followsthis particular course of action.

EXAMPLE 1.Statement: Should drinking be avoided?Argument: Yes, it contributes to badhealth.

EXAMPLE 2.Statement: Should Tendulkar be selectedin the team even after 10 years from now?Argument: Yes, Tendulkar is one of thegreatest cricketers in the world.

EXAMPLE 3.Statement: Married people should liveseparate from their parents.

Argument: Yes, living separate will givemarried people a greater freedom.

EXAMPLE 4.Statement: Should smoking be promoted?Argument: No, smoking is injurious tohealth.Comment: In the above examples, all thegiven arguments are expected to followas they all are established facts.Therefore, all the arguments presentedcan be said to pass the test of step II.NOTE : Point to be noted that argumentsgiven under Example 1, Example 2,Example 3 & Example 4 have passedthe step II only so far but it has not yetbeen determined whether thesearguments are forceful or not (strongor not). They will be called strong onlywhen they will pass step III and step IV.(ii) Prediction on the basis of

experience: Such arguments arevery near to established facts typeof arguments. But, in reality, they arenot established facts as they are notyet so universally acknowledged asto be treated as established fact. Infact, such arguments are given onthe basis of experiences. Just see thefollowing example:

EXAMPLE 5.Statement: Captains should not havegiven their say in selection of nationalsports teams.Argument: Yes, it discourages favouritismtowards some particular players.Comment:The result or consequencesgiven in this example will be a probableresult as our experiences suggest this.Hence, this will go for further test.(iii) Logically given arguments: Such

arguments are given on the basis oflogic. It does mean that the emphasishere is on the logic and not on the

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Statement & Arguments122established fact or experience. If wesee such type of arguments we caneasily predict that such cases haveoccurred in practice. But when wethink over such situations withproper logic and reasoning then wearrive at the conclusion that suchan argument may be true. Let us seethe example given below:

EXAMPLE 6.Statement: World leaders must try forcomplete disarmament.Argument: Yes, complete disarmamentwill make a war free world.Comment: The example gives anargument that is logically convincing:The argument is probable as the logicbehind it is that if there will be armlessworld then there will be a war free world.Hence, the argument passes the step IItest and will go for further test.(iv) Notions of truth: Such arguments are

unquestionable truth because of thesimple reason of universalacceptance. It does mean that theyare the ideas or thoughts alreadyacknowledged by society. This is thereason why they are very similar toestablished facts in many ways. Thefollowing example illustrates thispoint:

EXAMPLE 7.Statement: Should marriages betweenblood relatives be promoted?Argument: No, it will promote incestwhich is a sin.Comment: No, doubt, the givenargument seems strong as it is based onprevailing notion of truth that our societydoes not allow marriages between bloodrelatives and consider such marriages as

a sin. As, the given argument is likely tobe strong it will go for next step test.Case II (When the result does not followargument will be rejected).Following are the cases when results donot follow and arguments are rejected at2nd level test in step II only.(i) Established fact: If it is an

established fact that a particularresult will not follow a particularcourse of action, then the argumentwill be rejected at step II. Let us seethe example given below:

EXAMPLE 8.Statement: Should smoking bediscouraged in the country?Argument: No, it give relaxation whenone gets tired and this way contributesto health.Comment: It is an established fact thatsmoking is injurious to health and thus,we can say that this argument is incorrectand weak enough to be rejected at step II.(ii) Prediction on the basis of

experiences: If the experiences saythat the result will not follow thenthe given argument will be rejectedat the step II. Let us see the examplegiven below:

Statement: Should cricketer A beappointed the next captain of the Indiancricket team?Argument: Yes, it will end the favouritismin selection of team as cricketer A hasmade allegations of favouritism againstthe current captain.Comment: In this example, the argumentsuggests that cricketer A should beappointed captain of the Indian cricketteam because it will end the favouritismin the team selection. This suggestionhas been given on the basis that A has

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Statement & Arguments 123made allegation of favouritism againstthe current captain. But the experiencessay that there have been so many caseswhen people did the things what theyopposed. Hence, saying one thing anddoing other is very common. This is thereason why it can not be made sure thatA will not do favouritism in team selectiononly because he has criticised the currentcaptain for this. It is clear that the givenargument is weak enough to be rejectedin step II.

Note : This is the exactly opposite topoint (ii) in step II (Case I).(iii) Argument with faulty logic: This is

exactly opposite to the point (iii) instep II (case I). Let us see thefollowing example:

Statement: Should the culprits behindthe fodder scam in Bihar be punished?Argument: No, a political vaccum willbe created if the culprits get punishment.Comment: As per the logic, punishingculprits behind the fodder scam in Biharwould please the public and improve theimage of the Bihar government. How canit create a political vaccum? This argumenthas been given with a faulty logic andhence will be rejected in step II only.(iv) Argument violating prevailing

notions of truth: Argument thatviolates unquestionable notions(Ideas that are universally acceptedand acknowledged by society) willbe rejected in step II. Let us see theexample given below:

Statement: Should marriage in bloodrelations be promoted in India?Argument: Yes, if the two mature bloodrelatives are willing to do so, then theycan not be prohibited from doing it.

Comment: In our society, it is widelyaccepted truth (or universally acceptedtruth) that the marriages between bloodrelatives are considered to be a sin as itpromotes incest. The given argumentviolates this prevailing notion of truth andis weak enough to be rejected in step II.(v) Arguments based on examples/

analogies: Very often it is seen thatan example or a precedent is madethe basis of an argument. But pointto be noted that analogy or examplebased arguments come under thecategory of bad arguments. It mustbe cleared that just becausesomeone did something in the past,the same can not be said aspursuable. Let us see the examplegiven below:

Statement: Should everyone beoptimistic in Life?Argument: Yes, Indira Gandhi wasoptimistic and this is the reason why shebecame the prime minister of India.Comment: Here, the example of IndiraGandhi is given that makes the argumentvery weak. Thus, such type of argumentsare rejected in step II.(vi) Arguments based on individual

perceptions (or assumptions): Insome cases it is seen that anassumption or view of the author isthe substance of an argument. Sucharguments neither have proper logicnor substance of established fact.These arguments are called badarguments and they can be rejectedin step II.

Statement: Should India be declared aHindu Rashtra?Argument: No, it will lead to chaos.Comment: What message author givesthrough the argument is view of the

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Statement & Arguments124author. In fact, declaring India a HinduRashtra may or may not lead to the resultgiven in the argument. It means thatassertion made by argument may or maynot follow in actual practice and if theauthor has a rigid stand on this assertion,it is his/ her individual perception orassumption which makes the argumentweak enough to be rejected in step II.Step III: Given arguments are reallydesirable/ harmful

In step II, we come to the conclusionthat Examples 1-7, have passed the 2ndlevel test and qualified for the step III(3rd level test). Hence, we will take theexamples to be qualified for step III oneby one:

EXAMPLE 1. Here, the argument ispositive and therefore, we have to checkthe desirability. As, it is a established factthat drinking contributes to bad healthand thus it is desirable to avoid it. It isclear row that Example 1 passed the 3rdlevel test.

EXAMPLE 2. No doubt that at presentTendulkar is one of the greatestcricketers in the world. He will also remainin the list of great ones in the history ofthe game of cricket. But it is also a truththat he has spent more than 20 years inthis game and is a retired cricketer. Thisis the reason that after 10 years he willdefinitely not be in team as his selectionis impossible. Hence, despite being anestablished fact the argument is notdesirable and is rejected in step III.(Example 2 is a weak argument)

EXAMPLE 3. Here, it is true that livingseparately from parents gives marriedpeople more freedom but at the same timegetting freedom at cost of separation

from parents is undesirable. Further,separating from parents does meanavoiding duty of taking care of parents.Hence, argument given in example 3 isnot desirable and is weak enough to berejected in step III.

EXAMPLE 4. As smoking is injuriousto health, its promotion is harmful. Thisreason makes the argument strongenough to pass the step III test.

EXAMPLE 5. It is true that favouritismtakes place on the part of captains attimes, but that does not mean that theyshould not be given their say whileselecting team. In fact, captains areexpected to bring positive and desiredresult if given their say in team selection.Further, giving their say in team selectionmakes the captains more responsible forthe bad performance of the team and thisinspires the captain to draw best out ofthe players in the team. Hence, the resultis not desirable and the given argumentproves to be weak enough to be rejectedin step III.

EXAMPLE 6. If it is possible to makeworld free of wars through completedisarmament, it is well and good. But,complete disarmament does not assurethat there would be no antisocialelements like murderers, looters, terroristsand the likes. To tackle these kind of anti-social elements, police and differentsecurity forces are needed. How dopolice and other security forces functionwithout arms? No, doubt, it is impossiblefor such security providing bodies towork without arms. Hence, the argumentgiven in Example 6 is weak and will berejected in step III.

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Statement & Arguments 125EXAMPLE 7. Marriages in blood

relatives promote incest which is a sinand hence harmful for the establishednorm of society. On the basis of thislogic, argument given in Example 7 isstrong enough to pass the 3rd level teststep III.Now, we have,Examples qualified for step IV test:Example-1, 4 and 7. Rejected examples instep III: Example- 2, 3, 5 and 6.

Note : How to decide a positiveargument which is really desirable or anegative argument which is reallyharmful, is only the matter of commonsense. Just apply your common sense,think over the argument, try to go byproper logic and general norms ofsociety.

Step IV: Finding proper relationbetween argument and suggestedcourse of action.

What does proper relation betweenstatement and argument mean? In fact, itdoes mean that argument must bepinpointed on the main issue involvedand it should not focus on any irrelevant,insignificant or minor issues. Now, wemove on to step IV or final test. AsExample-1, 4 and 7 have qualified for thistest, let us check the three examples oneby one:

EXAMPLE 1. Drinking and bad healthare properly and directly related. Hence,the given argument “Yes, it contributesto bad health” is a strong argument andthis is the final conclusion.

EXAMPLE 2. Smoking and bad health(injurious to health) are directly andproperly related. Hence, the given

argument “No smoking is injurious tohealth” is a strong argument and this isthe final conclusion.

EXAMPLE 3. Marriages in bloodrelatives and promotion of incest isdirectly and properly related. Hence, thegiven argument “No, it will promoteincest which is a sin” is a strongargument and this is the final conclusion.

Now, we have come to the end ofthis chapter. For the understanding ofstudents, below is given a questionformat the for the examination. Thequestion format has been made with theExample 4 given in this chapter.Question format:Direction: Each question given belowis followed by two arguments numberedI and II. You have to decide which one ofthe arguments is a ‘strong’ argument andwhich is a 'weak' argument.Give answer (a) If only argument I isstrong.

(b) If only argument II is strong.(c) If either I or II is strong.(d) If neither I nor II is strong.(e) If both I and II strong.

Statement: Should smoking bepromoted?

Argument: I: No, smoking is injuriousto health.

II: Yes, why not?Solution:I will follow (the reason already givensee Example 4)II will not follow as it is a question backtype of argument and such type ofarguments are very weak.Hence, option (A) is the correct answer.

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Statement & Arguments126

q Shortcut Approach

Step I: Preliminary Screening of argument

Step II: The argument follows the statement

Step III: The argument is desirable (for positive statements) / harmful (for negative statements)

Step IV: The argument is properly related to the statement.

Strong Argument

Passes

Passes

Passes

Passes

Fails

Fails

Fails

Fails

Weak Argument

Weak Argument

Weak Argument

Weak Argument

—

—

—

—



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Statement &Assumptions

Chapter

27INTRODUCTIONAssumptions are essential part ofanalytical reasoning. This is the reasonwhy in various competitive examinations,examinees are asked to identifyassumptions. In this chapter, we will seehow to identify assumptions. Before wego ahead, we must have a look at acommon format of the problem as it willgive you a clear idea of the questions tobe asked in the examination.

PROBLEM FORMAT(SAMPLE PROBLEM)Directions: In every question givenbelow a statement (or a passage) isfollowed by two assumptions number I& II. An assumption is somethingsupposed or taken for granted. You haveto consider the statement and thefollowing assumptions and then decidewhich of the assumptions is implicit inthe statement.Mark answer:(a) If only assumption I is implicit.(b) If only assumption II is implicit.(c) If either assumption I or

assumption II is implicit.(d) If neither of the assumption is

implicit(e) If both the assumptions are

implicit.

Statement: “A” television — the largestselling name with the largest range” —an advertisement.Assumptions:I. There is a demand for televisions in

the market.II. ‘A’ television is the only one with

wide variations.The given statement in the problemformat is an advertisement. This isthe one form of statement. But thestatement may be in different formslike it can be in the form of a passage;in the form of a single line; in theform of a notice; in the form of anappeal; in any other different forms.

WHAT DOES ANASSUMPTION MEAN?Assumption is the hidden part of anargument. It does mean that anassumption is something which isassumed, supposed and taken forgranted. In fact, when a person sayssomething, he does not put everythinginto words and leaves some part unsaidas why does he ? so?He does so because he takes this unsaidpart for granted. In other words he thinksthis unsaid part will be understoodwithout saying and hence there is noneed to put this (unsaid part) into words.It does mean this unsaid part is hiddenin the given statement and this hiddenpart is called assumption. Let us

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Statement & Assumptions128understand it in another way. Justremember your childhood days whenyou used to solve the given arithmeticproblem without leaving any single step.But what you do today? Today yourapproach is totally different. Today youleave easier steps as you assume thatthe person who see your solution, isvery much aware of these elementaryoperations. Therefore, this is an exampleof assumption.To get the concept of assumption moreclearly just suppose a thrilling one dayinternational cricket match is going onbetween India and Australia. TheAustralian team has scored 300 runs butwhile chasing the score India has made280 runs in 48 overs and now, thesituation is India has to score 21 runs towin the match in remaining two overs.As Yuvraj Singh is batting, you tell yourfriend - “No need to worry as Yuvraj is abig hitter. India will definitely win thematch”. What do you find in thisstatement. In fact this statement has twoparts:-(i) No need to worry as Yuvraj is a big

hitter.(ii) India will win the match.Now, this is the time to think over thesetwo parts. How do you relate them?Obviously, by assuming that a big hittermay score 21 runs in the remaining twoovers. Therefore, this is another exampleof assumption. The above statement canbe written in three parts as follows:-(i) No need to worry as Yuvraj is a big

hitter.(ii) A big hitter may score 21 runs in 2

overs (Hidden part/Assumption)(iii) So, India will win the match.Let’s get more ideas about assumptionwith some simple examples given below:-

EXAMPLE 1.Statement: Of all the mobile setsmanufactured in India 'M' brand has thelargest sale.Assumption: The sale of all the mobilesets manufactured in India is known.Comment: The given assumption isvalid. Here the statement makes a claimthat of all the mobile sets manufacturedin India, 'M' brand has the largest sale.In fact, without knowing sale figures maybe rough data of all mobile brandsmanufactured in India, no such claimabout M brand could be made. Hence, itmust have been implicitly assumed in thegiven statement that sale figure of allbrands is known.

EXAMPLE 2.Statement: Virat is in great form andtherefore, India is going to beat NewZealand in upcoming test series.Assumption:I. Virat will give a good performance in

upcoming series against NewZealand.

II. Virat will score a triple century in theupcoming series against NewZealand.

Comment: Assumption I is valid as thestatement says that Virat is in great formand therefore, India is going to beat NewZealand in the upcoming test series. Itdoes mean that it is assumed in thestatement that Virat will perform well inthe upcoming test series against NewZealand and on the basis of that goodperformance India will beat New Zealand.But II is invalid because if Virat is in greatform, that does not mean he will surelyhit a triple century. He may or may notdo so. Hence, assumption II is not hiddenin the statement.

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Statement & Assumptions 129EXAMPLE 3.

Statement: The next meeting of thegoverning body of the society X will beheld after one year.Assumption: Institute X will remain infunction after one year.Comment: The given assumption is validas we know that the common practice isto hold meetings of only those bodiesthat are functional. Hence, it does meanthat the announcer must be assumingthat the society will remain functionalafter one year.

EXAMPLE 4.Statement: The student is too clever tofail in the examination.Assumption: Very clever students do notfail in the examination.Comment: This is a valid assumption. Asper the given statement the student willnot fail (This is an effect) as he / she isvery clever (This is a cause). Clearly, ithas been assumed in the statement thatvery clever students do not fail.

HOW DOES A SINGLEWORD OR PHRASE MAKE ADIFFERENCE?

A. Definitive Words Cases:Just consider the words like ‘all’,‘only’, ‘best’, ‘strongest’, ‘certainly’,‘definitely’, etc. These are somewords that put a greater degree ofemphasis or more weight on thesentence than some others. In fact,these words impart a kind ofexclusiveness to the sentence andthereby reduce the scope / range ofthe sentence. In fact, some kind ofcertainty is associated with all thesewords. Let us consider the followingexamples:

EXAMPLE 5.Statement: The crisis of onion hasworsened and the government shouldmake every effort to boost import of onion.Assumption:I. Import is the best solution to avert

the onion crisis.II. Import is a reasonably good solution

to the onion crisis.III. Import is the only solution to

overcome the onion crisis.IV. The onion crisis will definitely be

averted by boosting import of onion.V. The onion crisis will probably be

averted by boosting import of onion.Comment: In the above mentionedexample, the assumption II and V arevalid. But I, III and IV are not valid. Thereason is that there is use of definitivewords (best, only and definitely) in caseof I, III and IV. The given statementmentions a fact that crisis of onion hasworsened and then makes a suggestionthat imports of onion should be boosted.In fact the statement assumes that importshould help to overcome onion crisis orthat import is a good/ reasonably goodsolution to the onion crisis. But, there isno hint that import is the only solution/best solution/a definitely effectivesolution.Therefore, the example given aboveillustrates how a definitive word may givea different ‘tone’ to a sentence.

B. Cases of Conjunctions:The words like ‘because’,‘therefore’, ‘in spite of’, ‘despite’,‘so’, ‘after’, ‘even’, ‘although’ ‘as’,‘as a result of’ are some significantconjunctions. When a statement hastwo clauses and the clauses areconnected by a conjunction, then

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Statement & Assumptions130the nature of conjunction helps indetecting the assumption that theauthor suggests in his statement.Suppose ‘x’ is one clause of asentence that mention an event (orfact/suggestion) and ‘y’ is theanother clause of the same sentencewhich mentions another event (orfact/suggestion), than dependingupon the conjunction, we canconclude the following assumption.

(i) x because/ as a result of y Þ It isassumed that ‘y’ leads to x.

EXAMPLE 6.Statement: You will find improvement inyour English after taking classes ininstitute M.Valid Assumption: An institute mayhelp in improving English.(ii) x therefore/ hence y Þ It is

assumed that ‘x’ leads to ‘y’.EXAMPLE 7.

Statement: Sachin Tendulkar has becomethe 1st man to score 50th test century,therefore all Indians must be feeling veryproud on his achievement.Valid Assumption: An achievement by afellow countryman makes other citizensproud.(iii) x even after/ despite/ in spite of y Þ

It is assumed that usually x does notoccurs when y occurs.

EXAMPLE 8.Statement: There was a theft in the citymall last night inspite of the maximumsecurity arrangement made by the police.Valid Assumption: Maximum securityarrangement is usually sufficient toprevent theft.(iv) Not ‘x’ even after/ in spite of/ despite

‘y’ Þ It is assumed that usually xoccurs when y does.

EXAMPLE 9.Statement: There was no outbreak of anyepidemic even after the continuousdeposition of rain water for six days.Valid Assumption: Deposition of rainwater usually leads to epidemic.C. Cases of Connotive Phrases:

Sometimes words used by theauthor are slightly indirect orunconventional. This is the reasonyou may miss the thing which theauthor wants to say. Such indirector unconventional words are calledconnotative or connotive phrases.For example “It is true that ....” canbe put / written as:

(i) It can be claimed with reasonabledegree of truth that...

(ii) It would be correct to say that...(iii) Even the most sceptic of men

would agree that....Similarly, “It is false” is put / written bythe author as :

(i) It is baseless to say that ...(ii) It would be highly misleading

to say that....(iii) Nothing could be farther from

truth than...

Note: The role of connotative phrases isvery limited in the questions askedbecause they are given so that they donot escape your eyes whenever onecome across them.

Conditions for Invalidity of Assumptions:(a) Restatement

If the given assumption is arestatement of the given statement,then the given statement will beinvalid. In fact, in such case, samething is put in different words.

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Statement & Assumptions 131EXAMPLE 10.

Statement: Of all the computer brands,manufactured in India, brand M has thelargest sale.Invalid Assumption: No other brand ofcomputer has as high a sale as brand M.(b) Long-drawn Conclusion: If an

assumption makes too far fetchedlogic or long drawn conclusion, thenit will be considered as invalidassumption.

EXAMPLE 11.Statement: All teaching should be donein religious spirit as religious instructionleads to a curiosity for knowledge.Invalid Assumption: Curious persons aregood persons.(c) Observation : It is slightly different

from the restatement case. In suchcase, two of the trio (Subject, verb,predicate) are changed into negativethat changes the appearance of the

sentence without changing itsmeaning.

EXAMPLE 12.Statement: Beauty is lovable.Invalid Assumptions :I. Ugliness is not lovableII. Beauty is not hateable(d) Conversion : When you study the

chapter of syllogism, you see thatstatements are converted to getimmediate inference. In fact, thereare three standard cases ofconversion:(i) All M are N, converted into

Some N are M.(ii) Some M are N, converted into

Some N are M.(iii) No M are N, converted into No

N are MPoints to be noted that givenassumptions will be invalid if they areconversions of the given statements.

q Shortcut Approach



Assumption will be implicit if

· it is in context of passge· it is not directly mentioned

· it is a mandatory factor condition forthe statement to be correct.

Note : The assumption must follow allthe above rules for it to be implicit.

Assumption will not be implicit if

· not in context of statement or passage· it is directly mentioned in the

statement· it is not an accepted fact or cannot be

truly inferred· there is use of definitive words· it is a restatement or a long-drawn

conclusion or negative rephrasing ora converted syllogism form.

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Statement & Conclusions132

Statement &Conclusions

Chapter

28INTRODUCTIONIn this type of questions, a statement isgiven followed by two conclusions. Wehave to find out which of theseconclusions definitely follows from thegiven statement.

WHAT IS A ‘CONCLUSION’?‘Conclusion’ means a fact that can betruly inferred from the contents of a givensentence. Conclusion is the art ofjudging or deciding, based on reasoning.DIRECTIONS (for Examples 1 to 3) : Ineach of the following questions, astatement is given followed by twoconclusions I and II. Give answer :(a) if only conclusion I follows;(b) if only conclusion II follows;(c) if either I or II follows;(d) if neither I nor II follows;(e) if both I and II follows;

EXAMPLE 1.Statement : The oceans are a storehouseof practically every mineral includinguranium. But like most other minerals, itis found in extremely low concentration– about three gms per 1000 tonnes ofwater.Conclusions :I. The oceans are a cheap source of

uranium.II. The oceans harbour radiation hazards.Sol. (d) I can not be concluded as most

of the minerals are available insimilar concentration levels inoceans. II is out of context ofthe sentence.

EXAMPLE 2.Statement : Today, out of the worldpopulation of several thousand million,the majority of men have to live undergovernment which refuses them personalliberty and the right to dissent.Conclusions :I. People are indifferent to personal

liberty and the right to dissent.II. People desire personal liberty and

the right to dissent.Sol. (b) It is mentioned in the

statement that most peopleare forced to live undergovernments which refusethem personal liberty and rightto dissent. This means thatthey are not indifferent tothese rights but have a desirefor them. So, only II follows.

EXAMPLE 3.Statement : It has been decided by theGovernment to withdraw 33% of thesubsidy on cooking gas from thebeginning of next month—a spokesmanof the Government.Conclusions :I. People no more desire or need such

subsidy from government as theycan afford increased price of thecooking gas.

II. The price of the cooking gas willincrease at least by 33% from the nextmonth.

Sol. (d) I does not follow because agovt’s policy is not determinedmerely by people’s needs.

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Statement & Conclusions 133II does not follow. Let thepresent price be x\ Price if subsidy is removed

= x

1.49x0.67

=

Hence increase in price will bearound 49%

DIRECTIONS (for Examples 4 to 5) : Ineach of the following questions, astatement is given followed by twoconclusions I and II. Give answer :(a) if only conclusion I follows;(b) if only conclusion II follows;(c) if either I or II follows;(d) if both I and II follow.(e) if neithter I nor II follows;

EXAMPLE 4.Statement : Interest rate will be fixed onthe basis of our bank’s rate prevailingon the date of deposit and refixed everyquarter thereafter.Conclusions:I. It is left to the depositors to guard

their interest.II. The bank’s interest rates are subject

to change on a day-to-day basisdepending on market position.

Sol. (b) I does not follow because thestatement is silent about thedepositors. II follows from thephrase “bank’s rate prevailingon the date of deposit” whichmeans the rates are subject today-to-day changes.

EXAMPLE 5.Statement : The government of countryX has recently announced severalconcessions and offered attractivepackage tours for foreign visitors.Conclusions :I. Now, more number of foreign

tourists will visit the country.

II. The government of country X seemsto be serious in attracting tourists.

Sol. (e) Clearly, the government hastaken the step to attract moretourists. So, both I and II follow.

q Shortcut ApproachFor a adhere conclusion to follow astatement must to the following4 GOLDEN RULES.1. The conclusion must be in context

of the statement. If out of contextthan it does not follow.

2. The conclusion must support thecontents of the statement. If itnegates than it does not follow.

3. The conclusion must be trulyinferred. If there is some doubt thatit may or may not be correct or trulyinferred, than it does not follow.

4. The conclusion must not repeat orrephrase the statement. If so, it doesnot follow.

Now let us apply these rules to the 5examples solved above.Ex. 1 I. Rule 2 applies as it negates the

statement.II. Rule 1 applies as it is out of

context.Ex. 2 I. Rule 2 applies as it negates the

statement.II. Fulfils all the conditions in Rule

1-4.Ex. 3 I. Rule 1, 2 & 4 follow but 3 does

not as there can be variousreasons to withdraw subsidy.

II. Rule 1, 2 & 4 follow but 3 doesnot as the price increase isactually 49%

Ex. 4 I. Rule I applies as it is out ofcontext.

II. Follows all the 4 rules perfectly.Ex. 5 Both I & II follow all the 4 rules

and hence follow the statement.


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Courses of Action134

INTRODUCTIONIn many competitive examinationsquestions related to courses of actionare frequently asked.The basic reason behind asking suchquestions is to test your ability to judgea problem correctly in order to determinethe root of the given problem and thenfinding out a proper course of action forthat particular problem.What is the format of the problem?Directions: In the question given belowis given a statement followed by twosuggested courses of action number Iand II. A course of action is a step oradministrative decision to be taken forimprovement, follow up, or further actionin regard to the problem, policy etc. Onthe basis of the information given in thestatement. Read the situation carefullyand then decide which of the givencourses of action follow/ follows.Mark answers:(a) If only I follows(b) If only II follows(c) If either I or II follows(d) If neither I nor II follows(e) If both I & II follow.Statement: The sale of a particularproduct ‘A’ has gone down considerably,causing great concern to company ‘X’.Courses of action :I. Company ‘X’ should mark a proper

study of the rival products in themarket.

II. The price of product ‘A’ should bereduced.

NOTE : In the examinations more thantwo courses of actions may also be given.

Types of Problems(1) Problems based on problem and

solution relationship.(2) Problems based on fact &

improvement relationship.1. Problems based on problem

and solution relationshipThis is a case when the givenstatement talks of a problem and thesuggested course of action talks ofa solution. It is very easy to find outwhen a suggested course of actionis acceptable and when it is not. Infact, the suggested course of actionwill be acceptable if:

(a) it solves/ reduces or minimises thegiven problem

(b) it gives a practical and wise solution.Now, what to do ? Just see the givenproblem with a serious eye; think overthat; apply your day to day experiences;apply your common sense and use yourgeneral knowledge to judge whether asuggested course of action solves orreduces or minimises the problem givenin the statement. After this step, the nextstep is checking the practicality. Here,you have to check if the solutionsuggested by the given course of actionis wise enough and applicable inpractical way in day to day life.

Courses of ActionChapter

29

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Courses of Action 135Infact (a) is the 1st step test and afterpassing the step I test, the given courseof action will have to pass step II (whichis (b)). If the given course of actionpasses both the tests [step I and step II]only then it will be called a correct action. Step I testTo pass the step I test a suggestedcourse of action must be(i) based on an established fact or(ii) based on logical prediction or(iii) based on experiences(iv) based on prevailing notions of truthLet us discuss all the conditionsmentioned above:-(i) Action based on established

fact: -In some of the cases an action takenis an established fact whichsuggests that the given problem canbe reduced or solved by thisparticular solution. It does mean thatthe solution suggested by the givencourse of action is universallyacknowledged to the given problem.Let us see the examples given below:

EXAMPLE 1.Statement: Southern part of India hasbeen coming rapidly into the grip ofmalaria.Courses of action:I. The Southern Indian population

must be instructed not to come outof their houses. [wrong action]

II. Anti-mosquito liquids should besprayed in the southern part ofIndia. [correct action]

EXAMPLE 2.Statement: A child was caught whilestealing money of a respectable personof society.

Courses of action:I. The child should be sent to child

welfare society. (correct action)II. The child should be put in jail and

severly beaten (wrong action)Comment: In example I, I is rejected as itis an irrelevant action. It does not makeit clear how instructing population fornot coming out of their houses will solveor reduce the problem of spreadingmalaria. But II is a proper course of actionas it is an established biological fact thatmalaria can be prevented by usingsafeguards against mosquitoes. This isthe reason that II will go for further test(step II test) proving itself a proper courseof action in 1st level test (step I test).In example 2, II is rejected on the basisthat it is totally illogical to beat a childand put into jail as a child is not matureenough to decide what is right and whatis wrong. Further, it is an established fact(socially established fact) that childcriminals must not be treated aspunishable wrong doer but they shouldbe made to mend their ways and on thebasis of this I is the correct course ofaction. Hence, I will qualify for the 2ndround test ( Step II test)

(ii) Action based on logicalprediction :In such type of cases, solutionsprovided for the given problems areneither an established fact nor theycan be considered as proper actionon the basis of our past experiences.Hence, in such cases examinees arerequired to apply certain logic andreasoning to find out if the givencourse of action solves or reducesor minimises the problem. Let us seethe example given below:

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Courses of Action136EXAMPLE 3.

Statement: Jammu & Kashmir isexperiencing, again, the rise of terrorismand it is obvious that Pakistan isencouraging it.Course of action: India must go to theinternational bodies with all the proof ofPakistani involvement in Jammu &Kashmir and demand that Pakistan mustbe declared a terrorist nation. [ correctaction]Comment : Here, the given course ofaction is the correct one at step I test. Infact, it is a matter of simple logic ofdiplomacy that in case of disturbancescreated by a hostile nation within ourcountry, we put this issue beforeinternational bodies so that the hostilenation stands at disadvantage. Thus Ex.3 will qualify for the next step test (stepII or practicality test).(iii) Action based on experiences: In

certain cases, while deciding if agiven course of action solves orreduces or minimises the givenproblem, our experiences work. Infact, in such cases the given problemmay be a relatively new one. It willnot be totally new but it will not bevery old either. This is the reasonthat the solution can not be said asan established fact. However, basedon our past experiences, in the similarkind of situation, we can reach theconclusion that the given problemcan be solved/ reduced/ minimisedby this particular action. Let us seethe example given below:

EXAMPLE 4.Statement: Several foreign powershaving expansionist thinking are threatto India.

Course of action: Efforts should be madethat the Indians remain united for anyeventuality. [correct action]Comment: Our past experiences say thatwe (India) became a sufferer several timesbecause of the foreign powers and atthat time we lacked our unity. In anotherwords, India has fallen victim to foreignpowers only when our country (India)has not remained united. Hence, on thebasis of our past experience, we canconclude that the given course of actionsolves or reduces the problem makingits entry for 2nd level (step II) test.(iv) Action based on prevailing notions

of truth: In such type of casessolutions provided for the givenproblem is as per the social norms.In other words, the given course ofaction suggests a solution that isprevailing notion of truth. In fact,they are the ideas that are universallyaccepted and acknowledged by thesociety and hence in many ways theyare similar to established fact. Let ussee the following examples:

EXAMPLE 5.Statement: Mr Sharma got angry and beathis son mercilesely.Course of action : Mr.Sharma should becaned publicly [ wrong action]

EXAMPLE 6.Statement : Most of manufacturingcompanies in India are running in losses.Course of action: Prospects ofprivatisation of these companies mustbe explored. [correct action]Comment: In example 5, the givensolution is against the societal worm aspublic beating is not considered a goodpunishment. In other words, it isprevailing notion of truth that public

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Courses of Action 137beating is not good. Hence, on the basisof this the given solution is rejected andwill not go for 2nd level test (step II test).In example 6, the given course of actionsuggests privatisation for loss makingmanufacturing companies and nodoubts, it is a prevailing notion of truththat privatisation can reduce or minimisetheir losses. There is also a chance thatprivatisation can convert a loss makingcompany into a profitable one. Hence,we conclude the given solution iscorrect one and will qualify for furthertest (2nd level test or step II test). Now,we can move on to step II test. Step II (Test of Practicality)

This is the 2nd part of test. In the 1stpart we just found out whether asuggested action really solves/ reduces/minimises the given problem. But animportant part also remains to be checkedand that is the test of practicality. Pointto be noted that a given course of actionmay solve/ reduce/ minimise a particularproblem but if it is not practicallypossible, it will be consider useless. Thisis the reason why this point too, needssound checking. For this you have tokeep the following things in your mind:A. The problem and solution must be

well matched and must be inproportion. In other words, ifsolutions are too simple for toosevere problems, they will beuseless. Conversly, we can say thattoo severe solutions are not goodsolutions for too simple problems.

B. Even after passing the step I test,the given solution is creating a newproblem, then the given solutionwill not be a good solution and willfail in practicality test.

EXAMPLES FOR (A)

EXAMPLE 7.Statement : Lack of discipline is a goodreason for low productivity in India.Course of action : Government must takestep to make military traing compulsoryfor all Indian citizens. [ wrong action]

EXAMPLE 8.Statement: As per the report of ‘WHO’(World Health Organisation) the lifeexpactancy of an average Indian iscontinuously declining.Course of action : A serious effort mustbe made to prevent children from makingnoises. [wrong action]Comment: In Example 7, the given courseof action is not a good solution for thegiven problem. No, doubt that militarytraining wold be a solution for lack ofdiscipline but is it a practical solution?Your answer will be a big ‘No’ (why?). Inreality, at the 1st step test the givencourse of action may seem true as itsolves the given problem but when itcomes to the 2nd level test, it becomesclear that it is too severe solution for arelatively small problem. Hence, on thisbasis the given course of action isrejected finally.

In example 8, the given course ofaction suggests that problem ofdeclining life expectancy can be solvedif children are prevented from makingnoises. At one stage the given course ofaction reduces the problem to someextent as it suggests that less noise willincrease the chances of low bloodpressure and this will result in lessdeaths. But when we think analytically,we come to the conclusion that theproblem is very serious and the givensolution is very simple for it. Hence on

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Courses of Action138this basis the given course of actionwould be declared a wrong one andwould be rejected finally.

EXAMPLE FOR (B)

EXAMPLE 9.Statement: In recent years, people havedeveloped a tendency of tax evasion andthis is the reason it has increased at analarming level.Course of action : Government mustmake law to abolish taxes. [ wrong action]Comment: Here, the given problem isabout tax evasion. Tax evasion doesmean showing less income to pay lesstax. Why tax evasion is a problem?Because tax evasion generates blackmoney. The given course of actionsuggests the abolition of taxes whichconnot be a good solution as taxes aretaken to provide people certain indirectservices like the facilities of roads, parks,police etc. Suppose if taxes are notcharged, how and where from money willcome to provide such indirect servicesto community. No doubts, the taxabolition will create a new problem.Hence on this basis the given course ofaction will be rejected finally as it failsthe 2nd level test (step II test) ofpracticality.Now after understanding what is apractical solution, we can test thecourses of action that have passed thestep I test and given under examples 1,2, 3, 4 and 6.Step II test of Example 1 ( Course ofaction II):IInd course of action given under example1 is “Anti mosquito liquids should besprayed in the southern part of India".In step II, we need to check if it is apractical solution for the given problem.

In the past we have also seen that suchsteps have been taken. Not in the pastonly even today whenever it seems thatmosquito born diseases are imminent,the anti-mosquito liquids are sprayed.Such step is taken only because it ispractical. Here, the IInd course of actiongiven under example 1 passes both thetest to be finally declared as proper andcorrect solution.Step II test of Example 2 [Course ofaction I]:Ist course of action given under example2 is “child should be sent to child welfaresociety”. In step II, we need to check if itis a practical solution. In so many caseswe have seen that when a child does acrime like stealing and some other moreserious crime, then they are put undersuch atmosphere that they canunderstand the seriousness of theircrime and try to mend their ways. Forsuch children, child welfare societies andsome other such kind of organisationsare very helpful. Hence, this course ofaction passes its final test to be declareda correct course of action.Step II test of Example 3 :The course of action given underexample 3 is “India must go to theinternational bodies with all the proof ofPakistani involvement in Jammu &Kashmir and demand that Pakistan mustbe declared a terrorist nation” and this isa very practical solution. As we haveseen in certain circumstances in past thatIndia has put such type of demand fromUNO and even from some other nationson individual basis. No doubts, that onsuch demands India has got support tosome extent. Hence it is a very practicalsolution and this given course of actionpasses it practicality test to be declareda proper and correct course of action.

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Courses of Action 139Step II test of Example 4 :The given course of action “effortsshould be made that the Indians remainunited for any eventualities” is a practicalone as we have shown this type of unityin the past. For example, in the freedomstruggle we were united. How this unitytook place? Only because this waspractically possible. Hence, this givencourse of action, too, passed thepractically test to be declared finally aproper and correct course of action.Step II test of Example 6:The given course of action “Prospectsof privatisation of these (loss making)companies must be explored is not acorrect solution at the end at the 2ndlevel test (Practicality test) because thecourse of action and the given statementare not properly linked. The statementdoes not make it clear that it talks onlyabout public sector manufacturingconcerns as even a private sectormanufacturing company may be a lossmaking company. Hence the statementand given course of action createsconfusion. Therefore, the given courseof action is rejected at 2nd level test.

2. Problem based on fact andimprovement relationshipThis is the 2nd type of problemrelated to course of action. But pointto be noted is that this does notrequire any new skill. The solvingmethod is exactly the same as youhave solved the 1st type of problemthat is problem solution based. Infact you have to solve this type ofproblem in two steps:

(i) Find out whether the suggestedcourse of action will help inimprovement of the situation.

(ii) Find out whether the two areproperly balanced.In fact problem given under example7 is such type of problem.Now we have come to the end ofthis chapter and this is the time tosolve the problem given under 'whatis the format of the problem'? Let ussolve it:

Statement : The sale of a particularproduct ‘A’ has gone down considerably,causing great concern to company ‘X’.

Courses of action : I. Company should make a proper

study of rival products in themarket.

II. The price of product ‘A’ should bereduced.

Solution. Option (a) is the correct optionas only I follows.Reason /Explanation: If the sale of ‘A’has gone down, then there must be somesolved reasons. The company X mustknow this reason. As I suggest the similarsolution, it follows. But II does not follow.The company should first know if pricewas a factor behind the drop in sale.Without knowing this, reducing pricemay turn out to be a wrong and harmfulaction.

Note : If you see 'an either choice' in theanswer options avoid it. It will be a wronganswer. Either choice can be in the formlike “Either of I or II (or III or I etc.)follows”.

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Courses of Action140

q Shortcut Approach

Study the Statement

Problem Solution Type

Fact Improvement Type

Solves/minimises/reducesthe problem

Does it help in improvingthe situation ?

Check if it is a balanced or proportionate solution

Check if it is a balancedsolution?

Does it creates new problems ?

Yes Yes

Yes Yes

Yes

No No

No No

No

Rejected

Rejected

Rejected

RejectedRejected

Accepted

Accepted



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Critical ReasoningChapter

30INTRODUCTIONCritical Reasoning (CR) is ability toreason clearly to evaluate and judgearguments. You are using this skill a lotduring your everyday life while readingnewspapers or watching movies. Whenyou think that the movie is pushing thelimit of the Reasonable or the newssounds less reasonable than the moviethat was pushing the limit, you are usingyour Critical Reasoning skills to producethese conclusions. The argument youmeet can be anything from a classicalargument to an advertisement or a dialog.Critical Reasoning questions will ask you

to manipulate the argument to weaken/strengthen it, find the conclusion,assumption, explanation, do an inferenceor supplement a statement, etc.Whatever it is that you have to do, youwill need 2 things to succeed: know thebasic structure of arguments and clearlyunderstand the argument.In general, most of them, argumentsconsist of evidence, usually 2 pieces, aconclusion - the main point of anargument, and an assumption - thebridge between the evidence andconclusion. The majority of thearguments you encounter on the test willbe 3 step arguments:

Evidence 1 + Evidence 2 = Conclusion.

E 1 E 2 C+ =Assumption

EXAMPLE 1. Last week Mike wasdetained for shoplifting at a groceriesstore near his house, but he has been aChristian for 10 years, therefore, thepolice must have been wrong accusinghim in stealing.

Note : There are two pieces of evidence:‘Mike was accused of stealing’ and that‘he is a Christian’. The conclusion isthat ‘the police are wrong’. Therefore,our huge assumption here is that ‘aChristian could not have stolenanything.’

EXAMPLE 2. There are a lot ofmosquitoes outside today, please do notturn on the light in the room because alot of them will fly in.

Note : Here the evidences are ‘there area lot of mosquitoes outside today’ and‘do not turn on the light’. Theconclusion is that ‘Many will fly in’ andthe assumption is ‘mosquitoes willapproach the light.’There is no set scheme for structure inCR, but since the majority of thearguments are only a few sentences long,

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Critical Reasoning142the conclusion usually comes in the firstor the last sentence. However, some ofthe arguments encountered will not havea conclusion at all or will have just animplied one.

Strategy to Crack CriticalReasoning QuestionsThis strategy is not the easiest way todo CR (the easiest would be read-and-answer), but it lets you get the mostquestions right spending less time percorrect answer.1. Read the questions first; this is

needed so that you would knowwhat to look for and what to do: findan assumption, strengthen/weaken,infer something or else; do not worryabout the details in the question,read for keywords, such asstrengthen, deny, or explain. [Usesymbols for convenience, e.g. + forstrengthen or – for weaken].

2. Read the passage very attentivelybecause in contrast to ReadingComprehension, there is very littletext here and mostly everything isimportant; try to read only once.Reread if required.As you read, look for the problem inthe passage (evaluate howconvincing it is)

3. Paraphrase (reword) the passage. Itis a very important step becausewhen you do a paraphrase, youcheck whether you understood thepassage and at the same time youextract the skeleton of the argument,making it easier to identify theconclusion and the assumption. Veryoften, the paraphrase of the passagewill be pretty close to the conclusion.It is not surprising, since theconclusion is the main point andevidence just supports it.) Your

paraphrase should be as close to thetext and as simple as possible so thatyou would understand it easily andat the same time could fully trust it.Do not make it too general nor toodetail oriented. When you do aparaphrase, do it in three steps:Evidence1, Evidence2, andConclusion; put “therefore” wordbefore you start your conclusion,this will help you to set it off.

4. Read the question again (now withmore understanding of what is beingasked; reading the question 2 times,it will also help you to make sure youranswer exactly what is stated andthat you understand the question.)

5. Answer before reading the answerchoices. There are two reasons forthis :(i) if you can think of the correct

answer or at least the generaldirection that the answer choiceneeds to be, you will identify itamong the wrong choices muchfaster, thus spend less timereading the answers, whichusually take 30 seconds tocover.

(ii) Often students are seduced bythe author’s wording. One readsa few words that were used inthe passage and the brainidentifies this choice with thepassage, thus making it seemmore right that it needs to be.The more problems you practicewith, the more chance is you willguess the right answer evenbefore reading it.

6. Go through the answers, first timescan them for YOUR answer choice(usually you will guess correctly in60-70% of cases), if you did not findit, reread them more attentively.

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Critical Reasoning 1437. Draw a grid to eliminate the wrong

answers easier. Use “ü” for a sureanswer, “û” for a definitely wronganswer choice, and “?” for ananswer that may be right orquestionable. This will help toconcentrate only on a few answerchoices and will prevent you fromreading same answers several timesif you get confused or keep havingtroubles locating the right answer.

TYPES OF CRITICALREASONING QUESTIONSCritical reasoning questions will ask youto:1. Identify the inference / Must be true

question2. Identify the assumption.3. Strengthen an argument.4. Weaken an argument.5. Select the best conclusion/Main Point6. Identify the paradox7. Evaluation/ Reasoning8. Identify a parallel argument/Structure.1. Identify the Inference / Must

be True QuestionThese type of questions areextremely common. An Inferencemeans the same thing as “must betrue”. Conclusions differ frominferences in that conclusions arethe result of premises and inferencesare something that must be true. Thefollowing are the typical Inference(Must be true) based Questions:• If the statements above are true,

which of the following must alsobe true?

• Which of the following is[implied, must be true, implicit,most reasonably drawn] in thepassage above?

• Which of the following inferencesis best supported by thestatement made above?

q Shortcut ApproachHow to tackle “Identify the inference /Must be true questions”:• Read the stimulus and look for the

argument.• Note that Must Be True questions

may not contain an argument. Theymay just be a series of facts.Nevertheless, try to find theargument.

• Avoid choices which containabsolute statements - never, always,none, only etc. Although these wordsmight appear in some correct choice,you should be very sure about them.

• Some of the options can be eliminatedas they go beyond the scope of thepassage. Note that an inference canbe based on only some of theinformation provided and not thecomplete passage.

EXAMPLE 1. Stimulus ArgumentIncreases in funding for police patrolsoften lower the rate of crimes ofopportunity such as petty theft andvandalism by providing visualdeterrence in high-crime neighborhoods.Levels of funding for police patrols insome communities are increased whenfederal matching grants are madeavailable.Question : Which of the following canbe correctly inferred from the statementsabove?Options :(a) Areas with little vandalism can never

benefit from visual deterrence.

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Critical Reasoning144(b) Communities that do not increase

their police patrols are at higher riskfor crimes of opportunity late atnight.

(c) Federal matching grants for policepatrols lower the rate of crimes ofopportunity in some communities.

(d) Only federal matching grants arenecessary to reduce crime in mostneighborhoods.

(e) None of theseSol.(c) is a summary of the information

provided; it is the logical end of achain of reasoning started in thestimulus argument. The sequence ofevents goes like this :Increased funding ® Increasedvisual deterrence ® Lower crimeThe last statement could be mappedas follows:Federal grants ® Increased patrolfunds(c) makes the chain complete bycorrectly stating that federal grantscan lead to lower crime in somecommunities. Now the logical chainbecomes:Federal grants ® Increasedfunding ® Increased visualdeterrence ® Lower crimeThe other answer choices may notbe correctly inferred because theygo beyond the scope of theargument. They may be objectively,factually correct, or they may bestatements that you would tend toagree with. However, you are limitedto the argument presented whenchoosing a correct answer.

2. Identify the AssumptionAn assumption is an unstatedpremise that supports the author’sconclusion. It’s the connectionbetween the stated premises and theconclusion., which together formsthe passage. An assumption issomething that the author ’sconclusion depends upon.Assumption questions are extremelycommon and have types that looklike this:• Which of the following most

accurately states a hiddenassumption that the author mustmake in order to advance theargument above?

• Which of the following is anassumption that, if true, wouldsupport the conclusion in thepassage above?

q Shortcut Approach

How to approach “Identify theassumption Questions”• Look for gaps between the premises

and the conclusion. Ask yourselfwhy the conclusion is true. Beforeyou progress to the answer choices,try to get feel of what assumption isnecessary to fill that gap between thepremises.

• Beware of extreme language in theanswer choices of assumptionquestions. Assumptions usually arenot extreme. “Extreme” answerchoices usually contain phrasessuch as always, never, or totally.

EXAMPLE 2. Stimulus ArgumentTraditionally, decision making bydoctors that is carefully, deductivelyreasoned has been considered preferable

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Critical Reasoning 145to intuitive decision making. However, arecent study found that senior surgeonsused intuition significantly more than didmost residents or mid-level doctors. Thisconfirms the alternative view thatintuition is actually more effective thancareful, methodical reasoning.Question : The conclusion above is basedon which of the following assumptions?Options :(a) Senior surgeons are more effective

at decision making than are mid-leveldoctors.

(b) Senior surgeons have the ability touse either intuitive reasoning ordeductive, methodical reasoning inmaking decisions.

(c) The decisions that are made by mid-level and entry-level doctors can bemade as easily by using methodicalreasoning as by using intuitivereasoning.

(d) Senior surgeons use intuitivereasoning in making the majority oftheir decisions.

(e) None of theseSol.(a) The correct answer is (a), which

provides a missing link in theauthor’s reasoning by making aconnection from the evidence: thatintuition is used more by seniorsurgeons than other, less-exper ienced doctors, and theconclusion: that, therefore, intuitionis more effective. None of the otherchoices helps bridge this gap in thechain of reasoning. Although someof the other statements may be true,they are not responsive to thequestion. In fact, they mostly focus

on irrelevant factors such asappropriateness, ease of application,ability, etc.

3. Strengthen an ArgumentAssumptions connect premises toconclusions. An argument isstrengthened by strengthening theassumptions. Here are someexamples of Strengthen questiontypes :• The conclusion would be more

properly drawn if it were madeclear that...

• Which of the following, if true,would most strengthen theconclusion drawn in the passageabove?

q Shortcut ApproachHow to approach “Strengthen anargument”• Once you have identified the argument

of the passage, i.e. the evidence(s) +conclusion, try putting in each optionwith the argument. Check if theassumption(s) you have drawn is (are)strengthened if you accept the contentof the option as true.

EXAMPLE 3. Stimulus ArgumentThree years after the Bhakra Nangal Damwas built, none of the six fish speciesnative to the area was still reproducingadequately in the river below the dam.Because the dam reduced the averagetemperature range of the water fromapproximately 40° to approximately 10°,biologists have hypothesized that sharpincreases in water temperature must beinvolved in signaling the affectedspecies to begin their reproductionactivities.

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Critical Reasoning146Question :Which of the following statements, iftrue, would most strengthen thescientists’ hypothesis?Options :(a) The native fish species were still able

to reproduce in nearby streamswhere the annual temperature rangeremains approximately 40°.

(b) Before the dam was built, the riverannually overflowed its banks,creating temporary backwaters thatwere used as breeding areas for thelocal fish population.

(c) The lowest temperature everrecorded in the river prior to damconstruction was 30°; whereas thelowest recorded river temperatureafter construction was completedhas been 40°.

(d) Non-native fish species, introducedafter the dam was completed, havebegun competing with the nativespecies for food.

(e) None of theseSol.(a) most strengthens the conclusion

that the scientists reached. It doesso by showing that there is a controlgroup. In other words, a similarpopulation, not subjected to thesame change as the population nearthe dam, did not experience the sametype of result. Here the basicassumption about the conclusionthat scientists reached is that‘because of the reduction of averagetemperature range of the water, thereproduction of the native fishspecies has reduced drastically’.Option (a) clearly strengthens theassumption.

4. Weaken an ArgumentAssumptions connect premises toconclusions. An argument isweakened by weakening theassumptions. Here are someexamples of Weaken question types:• Which of the following, if true,

would weaken the conclusiondrawn in the passage above?

• The argument as it is presentedin the passage above would bemost strengthened if which of thefollowing were true?

q Shortcut ApproachHow to approach “Weaken anargument”• Once you have identified the

argument of the passage, i.e. theevidence(s) + conclusion, try puttingin each option with the argument.Check if the assumption(s) you havedrawn is (are) weakened if you acceptthe content of the option as true.

EXAMPLE 4. Stimulus ArgumentA drug that is very effective in treatingsome forms of cancer can, at present, beobtained only from the bark of theRaynhu, a tree that is quite rare in thewild. It takes the bark of approximately5,000 trees to make one pound of thedrug. It follows, then, that continuedproduction of the drug must inevitablylead to the raynhu’s extinction.Question :Which of the following, if true, mostseriously weakens the above conclusion?Options :(a) The drug made from Raynhu bark is

dispensed to doctors from a centralauthority.

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Critical Reasoning 147(b) The drug made from the Raynhu

bark is expensive to produce.(c) The Raynhu generally grows in

largely inaccessible places.(d) The Raynhu can be propagated from

cuttings and cultivated by farmers.(e) None of theseSol.(d) provides an alternate source of the

Raynhu bark. Even though the treeis rare in the wild, the argument issilent on the availability ofcultivated trees. The author of theargument must be assuming thatthere are no Raynhu trees other thanthose in the wild, in order to makethe leap from the stated evidence tothe conclusion that the Raynhu isheaded for extinction. The option (d)weakens the assupmtion - ‘there arelimited raynhu trees’ - by saying thatthere are other ways as well for thepropogation of Raynhu. The otheranswer choices all containinformation that is irrelevant. Notethat the correct choice does notmake the conclusion of the argumentimpossible. In fact, it is possible thatthere may be domesticated Raynhutrees and the species could stillbecome extinct. Answer choice (d)is correct because it makes theconclusion about extinction lesslikely to be true.

5. Conclusion / Main PointQuestionIn Main Point / Conlcusionquestions, you have to identify theconclusion of an argument. You aretrying to find the author’s point andshould approach this question in a

similar way to the readingcomprehension main pointquestions. They come in severaldifferent formats:• The main point of the passage is

that...• Which of the following statements

about... is best supported by thestatements above?

• Which of the following beststates the author’s conclusion inthe passage above?

• Which of the followingconclusions can be most properlydrawn from the data above?The conclusion of arguments inMain Point questions is usuallynot directly stated. To find theconclusion, identify the premisesand then identify the conclusiondrawn from the premises. MainPoint questions differ from theother Critical Reasoningquestions in that the argument inthe stimulus is usually valid. (Inmost other Critical Reasoningquestions the reasoning isflawed.) Conclusion questionsrequire you to choose the answerthat is a summary of the argument.

q Shortcut ApproachHow to approach “Main PointQuestions”:• Main Point answers must be within

the scope of the passage.• Your opinions or information outside

of the passage are always outside ofthe scope.

• Some of the options given can be outof the scope of the passage.

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Critical Reasoning148• Knock out answers with extreme

wording. Main Point answerstypically do not use only, always,never, best or any strong words thatleave little room.

EXAMPLE 5. Stimulus ArgumentPeople should be held accountable fortheir own behaviour, and if holdingpeople accountable for their ownbehaviour entails capital punishment,then so be it. However, no person shouldbe held accountable for behaviour overwhich he or she had no control.Question : Which of the following is themost logical conclusion of the argumentabove?Options :(a) People should not be held account-

able for the behaviour of otherpeople.

(b) People have control over their ownbehaviour.

(c) People cannot control the behaviourof other people.

(d) People have control over behaviourthat is subject to capital punishment.

(e) None of theseSol.(b) The correct response is (b). The

argument includes the following twopremises:Premise 1: People are accountablefor their own behaviour.Premise 2: People are notaccountable for behaviour theycannot control.Here’s the logical conclusion basedon these two premises:Conclusion: People can control theirown behaviour.

(a) would require that people neverhave control over the behaviourof other people. Yet the argumentdoes not provide this premise.

(b) would require that peopleshould not be held accountablefor the behaviour of otherpeople. Yet the argument doesnot provide this premise.

(d) is not inferable. The argumentallows for the possibility that aperson might not have controlover another person’s behaviourwhich is subject to capitalpunishment.

(e) None of these6. Identify the Paradox

These questions present you with aparadox, a seeming contradiction ordiscrepancy in the argument, andask you to resolve it or explain howthat contradiction could exist. Inother words, there are two facts thatare both true, and yet they appear tobe in direct conflict with one another.Here are some examples of the waysin which these questions are worded:• Which of the following, if true,

would help to resolve theapparent paradox presentedabove?

• Which of the following, if true,contributes most to anexplanation of the apparentdiscrepancy described above?

q Shortcut ApproachHow to approach “Identify the paradoxquestions”• Read the argument and find the

apparent paradox, discrepancy, orcontradiction.

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Critical Reasoning 149• State the apparent paradox,

discrepancy, or contradiction in yourown words.

• Use process of elimination. The bestanswer will explain how both sidesof the paradox, discrepancy, orcontradiction can be true. Eliminateanswers that are out of scope.

EXAMPLE 6. Stimulus ArgumentTown Y is populated almost exclusivelyby retired people and has almost nofamilies with small children. Yet Town Yis home to a thriving business specializingin the rental of furniture for infants andsmall children.Question : Which of the following, if true,best reconciles the seeming discrepancydescribed above?Options :(a) The business specializing in the

rental of children’s furniture buys itsfurniture from distributors outside ofTown Y.

(b) The few children who do reside inTown Y all know each other and oftenstay over night at each other’shouses.

(c) Many residents of Town Y who movefrequently prefer to rent theirfurniture rather than buy it outright.

(d) Many residents of Town Y mustprovide for the needs of visitinggrandchildren several weeks a year.

(e) None of theseSol.(d) The correct answer (d), explains why

a town of mostly retired residentsmight need to rent children’s

furniture. The other answer choicesall contain irrelevant information.This further illustrates the fact that,on all question types, if youeliminate the irrelevant choices, theremaining choice will most likely becorrect.

7. Evaluation/ ReasoningBased QuestionsReasoning questions ask you todescribe how the argument wasmade, not necessarily what it says.These questions are closely relatedto assumption, weakening, andstrengthening questions. Thecorrect answer identifies a questionthat must be answered or informationthat must be gathered to determinehow strong the stimulus argumentis. The information will be related toan assumption that the author ismaking. Another type of questionthat you will encounter asks you toidentify a flaw in the stimulusargument. The question tells youthat there is a problem with the logicof the argument. You just have tochoose the answer that describes theflaw. Here are some examples of theways in which these questions areworded:• How does the author make his

point?• A major flaw in the argument

above is that it...• A’s response has which of the

following relationships to B’sargument?

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Critical Reasoning150

q Shortcut ApproachHow to approach Reasoning Questions• Read the argument and find the

conclusion.• State the reasoning in your own

words.• Check whether the reasoning given

in the various options fall in line withthe reasoning described above.

EXAMPLE 7. Stimulus ArgumentSome observers have taken the positionthat the recently elected judge is biasedagainst men in divorce cases that involvechild custody. But the statistics revealthat in 40% of such cases, the recentlyelected judge awards custody to thefathers. Most other judges awardcustody to fathers in only 20%–30%oftheir cases. This record demonstrates thatthe recently elected judge has notdiscriminated against men in cases ofchild custody.Question : The argument above is flawedin that it ignores the possibility thatOptions :(a) A large number of the recently

elected judge’s cases involve childcustody disputes.

(b) The recently elected judge isprejudiced against men in divorcecases that do not involve childcustody issues.

(c) The majority of the child custodycases that have reached the recentlyelected judge’s court have beenappealed from a lower court.

(d) The evidence shows that menshould have won custody in morethan 40% of the recently elected

judge’s cases involving divorcingfathers.

(e) None of theseSol.(d) The correct answer (d), points out a

flaw in the argument. Specifically, itpoints out that the author of theargument was comparing therecently elected judge to otherjudges, not to the evidencepresented in the recently electedjudge’s cases. In other words, theauthor of the argument made anunwarranted assumption that therecently elected judge did not ruleagainst many men in custody battleswhere the evidence clearly favoredthe men. As with strengthening andweakening questions, the correctanswer in flaw questions ofteninvolves unwarranted assumptions.

EXAMPLE 8. Stimulus ArgumentAlthough dentures produced through anew computer-aided design process willcost more than twice as much as ordinarydentures, they should still be costeffective. Not only will fitting time andX-ray expense be reduced, but the newdentures should fit better, diminishingthe need for frequent refitting visits tothe dentist’s office.Question : Which of the following mustbe studied in order to evaluate theargument presented above?Options :(a) The amount of time a patient spends

in the fitting process versus theamount of money spent on X-rays

(b) The amount by which the cost ofproducing dentures has declinedwith the introduction of the newtechnique for producing them

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Critical Reasoning 151(c) The degree to which the use of the

new dentures is likely to reduce theneed for refitting visits whencompared to the use of ordinarydentures

(d) The amount by which the newdentures will drop in cost as theproduction procedures becomestandardized and applicable on alarger scale

(e) None of theseSol.(c) The correct answer (c), highlights an

assumption in the stimulusargument. It shows that the authormust be assuming that the reductionin refitting with the new denturescompared to ordinary dentures issignificant in order to conclude thatthat difference will help offset aninitial outlay that is twice as much.In other words, if you answer thequestion posed by answer choice (c)with “not much,” the argument isweakened. If you answer it with “atremendous amount,” the argumentis strengthened. The other answerchoices are all irrelevant because nomatter what the answers are, there isno impact on the relationshipbetween the evidence presented inthe stimulus argument and itsconclusion.

8. Identify a Parallel Argument/ Structure.The last type of Critical Reasoningquestion is the parallel structurequestion. In this type of question,you must choose the answer thathas the same structure as thestimulus argument. In other words,

you have to find the argument thatis analogous to the given argumentin that it includes the samerelationship between the evidencepresented and the conclusion. Hereare some examples of the ways inwhich these questions are worded:• Which of the following is most

like the argument above in itslogical structure?

• Which of the following is aparallel argument to the abovegiven argument?

EXAMPLE 9. Stimulus ArgumentIt is true that it is against internationallaw to provide aid to certain countriesthat are building nuclear programs. But,if Russian companies do not provide aid,companies in other countries will.Question : Which of the following is mostlike the argument above in its logicalstructure?Options :(a) It is true that it is against United

States policy to negotiate withkidnappers. But if the United Stateswants to prevent loss of life, it mustnegotiate in some cases.

(b) It is true that it is illegal to selldiamonds that originate in certaincountries. But there is a longtradition in Russia of stockpilingdiamonds.

(c) It is true that it is illegal for anattorney to participate in atransaction in which there is anapparent conflict of interest. But, ifthe facts are examined carefully, itwill clearly be seen that there is noactual conflict of interest in thedefendant’s case.

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Critical Reasoning152(d) It is true that it is against the law to

steal cars. But someone elsecertainly would have stolen that carif the defendant had not done sofirst.

(e) None of theseSol.(d) The correct answer (d), has the same

structure as the stimulus argument.If you just replace “aid to developingnuclear powers” with “car theft,” and“Russian companies” with the“defendant,” it is essentially thesame argument. Sometimes theparallel structure is easier to see ifyou use symbols to represent the

terms of the argument: It is true thatX is illegal. But, if Y doesn’t do it,others will. Here X is stealing carsand Y is the defendant.

q Shortcut ApproachHow to crack Parallel ArgumentQuestion?• Read the argument and find the

conclusion.• Try to establish a reasoning structure

between the premise and thecondusion.

• Read out the options and look outfor one having the similar reasoningstructure.



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