Contents of IBPS PO Study Kit - Bank Exam Portal...English Grammar and Comprehension pas sages take...

Contents of IBPS PO Study Kit

REASONING · Alphabet Test· Logical Sequence of Words · Classification Test · Analogy · Series Completion · Coding-decoding · Blood Relation · Direction Sense Test · Alpha-numeric Sequence Test · Number, Ranking and Time Sequence Test · Mathematical Operations · Puzzle Test · Logical Venn Diagram · Syllogism · Input Output · True and False · Statement and Arguments

(Non- Verbal) · Series · Analogy · Coding-decoding

MATHEMATICAL APTITUDE · Number System · Decimal Fractions · HCF and LCM · Average · Ratio and Proportion · Problem on Ages · Percentage · Profit and Loss · Ratio · Time and Work · Time and Distance· Alligation or Mixture · Probability · Simple and compound interest · Area · Data Interpretation

GENERAL AWARENESS · English Language · Comprehension · Common Error · One-Word Substitution

· Synonyms and Antonyms · Idioms and Phrases · Sentence Correction · Sentence Arrangements · Fill in the Blanks · Analogy

Computer & Marketing · Computer Knowledge · Marketing Aptitude

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COMPREHENSION

Comprehension

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Comprehension is the act of understanding.If you do not understand a thing, it is no usewasting time upon it. At times you may comeacross a man immaculately dressed, properlybespectacled, and seriously reading a bookconsidered to be a classic; but ask him what hegot in the book and he hardly has an answer.Such a man has understood nothing of what hehas read. For him, the hook is merely a statussymbol. It may serve as a momentary illusionto others that he is an educated man. But themoment he comes to conversation, the balloonof hypocrisy is pinpricked. Reason: he hasunderstood nothing of wiat he has read.

In other words, reading withoutunderstanding is even worse than tastingwithout digesting. Whenever an edible or abeverage comes in contact with the tongue, atleast the taste-buds are gratified. You feel happywhen sugar tastes sweet. It is only later thatindigestion causes stomach troubles. In readingwithout understanding you do not get even thismomentary gratification. At best, you create animpression which is no more than an illusion,as we saw in the first paragraph.

All this I have written to drive home thefact that reading without understanding is acomplete waste of time. Understanding is what

one should aim at. It is a habit which should beformed early in life. The earlier, the better. Oncethis becomes a habit, life becomes easy at everystep.

Why is comprehension judged incompetitions?

Wherever you go, a person with a bettercomprehension is always valued. Once apprisedwith a situation, his decisions will be based ona clear picture. On the other hand, one whocannot comprehend well, in spite of his or herdecision-making ability, can never take the rightdecision.

Most of the selectors are also looking forcandidates who are unbiased. When you aregiven a passage, you are not supposed to answerthe questions based on preconceived notions. Theanswers have to he based on what is given inthe passage. Success at comprehension showsan un-preoccupied mind.

When you go to an interview, yourcomprehension may be judged by narrating anincident and then asking you what you makeout of certain aspects of the incident. At thewritten level, the same thing is done by givinga passage before your eyes. There is anotheraspect of the personality which comprehension

Comprehension

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English Grammar and Comprehension

pas sages take care of - the ability to understandthe things in a given time. Time limit plays animportant role in answering questions based onthe comprchen sion passages.

How to tackle the comprehension testIf the student has developed an approach

of his own to answering the comprehensionquestions and the approach is effective, he orshe should stick to that approach. However, thismethod of one s own should be thoroughlychecked bearing in mind the time duration.

But for those of you who feel uneasy themoment a comprehension passage comes intosight, here are some tips which may also becalled speed enhancing techniques.

1. It is a good idea to take a cursory glanceat the questions given. In an age of cut-throat competition, you cannot afford thecopybook style of reading and re-readingthe passage until you have thoroughlyunderstood it and then come down toquestions. No, be pragmatic. It you take alook at the questions before reading thepassage, you know what aspects of thepassage to concentrate on.Caution: Avoid reading the answer-choices before you have read the passage.Doing so will only serve in generatingconfusion in your mind. This is so becausethe answer-choices are meant to confuseyou.

2. Now read the passage carefully. Whilereading find out the i ain point and thearguments that have been given in itsfavour. If you have got these correct, youhave well begun and it is more than halfdone.

3. Examine the attitude of the writer. This

is one of the pet questions of those settingcomprehension tests.

4. Often the questions pertain to synonymor antonym of a word as used in thepassage. The important point here is asused in the passage. You should not gofor the meaning blindly.

5. Here is in a nutshell what is generallylooked for in the questions:(i) main idea of the passage:

Whenever a passage is written, it isto propagate an idea. This idea formsthe nucleus around which words andsentences are constructed. Get to theroot of this idea.

(ii) attitude of the writer: This is againimportant because the same sentencemay carry a different meaning iflooked at in isolation. But when usedin a given context, it takes themeaning dependent on the attitude ofthe writer, which is nothing but theoverall feeling that you get afterhaving read the passage.

(iii) what the writer says and what hedoes not: It is very important tocategorically see what the writer saysand what he does not. This will bepossible if we do not operate withunnecessary assumptions.

(iv) implied meaning of the passage :Often you may come across passageswhich carry meaning beyond theliteral one. You should have an insightsharp enough to penetrate the literallayer.

(v) title of the passage: If you arcfamiliar with the main idea and the




Comprehension

way it has been put in, this issomething not difficult.If you bear in mind the above points,you may comprehend the passageeven in one reading. But if you are notsure of the answers after the firstreading and time allows, you shouldnot hesitate in going for a secondreading.

6. This suggestion is of course a homeworkand has to do with cultivation in dueprocess. But if you cultivate it, it is goingto be of immense help in the examinationhall. The suggestion is: develop yourvocabulary and sentenceconstruction. Then you do not have togrope in the dark or loiter while readingthe passage.

The trend of the day is short sentences. Butwe still encounter sentences which prove to bediscomfitingly long. Fortunately, however, thesesentences are not as long as you would find inearlier authors - George Eliot s sentences oftenran for almost one long paragraph. Still, thesentences today are long at times. And thelonger they are, the more baffling they becomefor the begin ners. The editorials of certainnewspapers and articles by certain academicsput off a not-too-well-versed reader.

This chapter is an attempt to make youmaster long sentences. For, after all, longsentences are nothing but a combination of shortones. All you need know is how to split them. Inthe beginning, the exorcise (done preferablywith a pencil) might appear cumbersome. Butonce you have practised this with about ahundred passages, your mind will automaticallybegin to split sentences. As soon as you reach

this stage, put the pencil in your drawer. Andspeed won t be a problem thereafter.

Key splittersHow do we split a sentence? Here are some

major clues:(i) The structure of the sentence: We

must first divide the sentence into its mainparts: Subject + verb + object (if the verb istransitive) + comple ment. For example: (1) Thestudents of each class in the school in which Istudied /(2) elected /(3) the naughtiest boy oftheir class 1(4) the monitor. The sentence abovehas been split into its major parts: (1) - subject,(2) - verb, (3) - object, and (4) - complement. Theparts may be sub-divided if the meaning is stillnot clear.

Note: The verb is the most important partof the sentence. If you identify the verb, splittingthe rest of the sentence becomes very easy.

At times, you may have a long sentenceconnected by one small word is (or any otherform of be or any other verb of incompletepredication). In such sentences of the form Ais B , identify the parts A and B, understandeach of them separately by sub-dividing theseparts, and then try to connect the whole in yourmind.

For example: What transpired at themeeting amidst such uproarious scenes / is / nota matter of such significance as to be includedin the history text-books.

(ii) Punctuation marks: A punctuationmark (or ; or: or) denotes a pause. Such pausesare very helpful in splitting a sentence.

For example: There was a prediction fromabove: /Ayodhya, / the son of Raja,/ will bebanished.





(iii) Conjunctions: Words such as and,but, that, while, yet etc. should be looked for. Ifthe words form a conjunction pair (such as notonly... but also ..., either... or...), we should tryto find out their connection.

(iv) Prepositions: We have seen thatprepositions show relationships. If you split thesentence at these points, the relationshipbetween different parts of the sentence will thusbecome clear. So look for words such as from,to, of, on, in, for, by etc.

(v) Adjective (or participle) after anoun: It is convenient to split a sentence whereyou find an adjective following a noun.

For example: (1) This question has asolution / (2) difficult to be arrived at. Part (2)here tells us what kind of solution. The keyadjective is difficult which follows noun solution.

Since present and past participles alsofunction as adjectives, you may apply it to themas well.

For example: We were taken aback by thenotice / issued by the Principal.

A man crosses a train / running in theopposite direction.

(vi) Infinitive: We have seen how verbsare the key splitters. Now, an infinitive also ismuch the same as a verb. So it is a convenientsplitting point.

For example: School education helps us /to come to terms with the social aspects of life.

(vii) Relative words: Words such asrelative pronouns and relative adverbs alsoperform the function of joining sentences orparts of a sentence.

And the basic rule is : We split where wejoin. So look for words such as who, which,where that etc.

For example: This book has been writtenfor readers / who find English difficult andtherefore lag behind / where others come outwith flying colours.

(viii) Phrases: Phrases are words thatform a group. We must be able to identify sucha group as a whole. For example: with a view to,by and large etc. The situation at the KSCAstadium was / by and large / the same as that atWankhede.

Comprehension questions on an unseenpassage are meant to test the student s grasp ofa passage given to him. He is required to read apassage and answer a few questions based onit. The following points should be carefully notedwhile attempting this question:

1. Read the passage carefully and try to geta general idea of the subject it deals with.

2. Read the passage again, this time morethoroughly, taking a mental note of thevarious points discussed.

3. Now take each question in turn and makesure of its import. Read the passage againand make out the answer.

4. Having answered all the questions, re-read the passage and make sure that youhave answered the questions correctlyand that your answers are brief and to thepoint and they do not overlap.

5. Your answers should be, as far as possible,in your own words.

6. Don t give your comments on the opinionsexpressed in the passage unless commeinsarc asked for. Remember that your job issimply to comprehend the passage and notto quarrel with the ideas it contains.

7. Don t explain or elaborate any point withillustrations of your own. Keep yourselfquite close to the passage.





Passage 1At the time Jane Austen s novels were

published - between 1811 and 1818 -Englishliterature was not part of any academiccurriculum. In addition, fiction was understrenuous attack. Certain religious and politicalgroups felt novels had the power to make so-called immoral characters so interesting thatyoung readers would identify with them; thesegroups also considered novels to be of littlepractical use. Even Coleridge, certainly noliterary reactionary, spoke for many when heasserted that novel-reading occasions thedestructi in of the mind s powers.

These. attitudes towards novels helpexplain why Austen received the attention fromearly nineteenth-century literary critics. (In anycase, a novelist published anonymously, asAusten was, would not be likely to receive much

Solved Examples

Practice Exercises Multiple Choice

Direction for Questions: Each of the passages given below is followed by a set of questionschoose the best answer to each question.

critical attention.) The literary response thatwas accorded to her, however, was often asincisive as twentieth-century criticism. In hisattack in 1816 on novelistic portrayals outsideof ordinary experience, for example, Scott madean insightful remark about the merits ofAusten s fiction. Her novels, wrote Scott,present to the reader an accurate and exact

picture of ordinary everyday people and places,reminiscent of seventeenth-century Flemishpainting. Scott did not use the word realism,but he undoubtedly used a standard of realisticprobability in judging novels. The critic Whatelydid not use the word realism either, but heexpressed agreement with Scott s evaluation,and went on to suggest the possibilities for moralinstruction in what we have called Austen srealistic method. Her characters, wroteWhately, are persuasive agents for moral truthsince they are ordinary persons so clearly




Comprehension

evoked that we feel an interest in their fate asif it were our own. Moral instruction, explainedWhately, is more likely to be effective whenconveyed through recognisably human andinteresting characters than when imparted bya sermonising nar rator. Whately especiallypraised Austen s ability to create characters whomingle goodness and villainy, weakness and

virtue, as in life they are always mingled.Whately concluded his remarks by comparingAusten s art of char acterisation to Dickens ,stating his preference for Austen s.

Yet the response of nineteenth-centuryliterary critics to Austen was not always solaudatory, and often anticipated thereservations of twentieth century critics. Anexample of such a response was Lewescomplaint in 1859 that Austen s range ofsubjects and characters was too narrow.Praising her verisimilitude, Lewes added thatnonetheless her focus was too often upon onlythe unlofty and the commonplace. (Twentieth-century Marxists, on the other hand, were tocomplain about what they saw as her exclusiveemphasis on a lofty upper-middle class.) In anycase, having been rescued by some literarycritics from neglect and indeed graduallylionised by them, Austen steadily reached, bythe mid-nineteenth century, the enviablepinnacle of being con sidered controversial.

1. The primary purpose of the passage is to(a) demonstrate the nineteenth-century

preference for realistic novels ratherthan romantic ones.

(b) explain why Jane Austen s novels werenot included in any academiccurriculum in the early nineteenthcentury.

(c) urge a reassessment of Jane Austen s

novels by twentieth-century literarycritics.

(d) describe some of the responses ofnineteenth-century critics to JaneAusten s novels as well as to fiction ingeneral.

(e) argue that realistic characterportrayal is the novelist s mostdifficult task as well as the aspect of anovel most likely to elicit criticalresponse.

2. The passage supplies information foranswering which of the followingquestions?(a) Was Whately aware of Scott s remarks

about Jane Austen s novels?(b) Who is an example of a twentieth-

century Marxist critic?(c) Who is an example of a twentieth-

century critic who admired JaneAusten s novels?

(d) What is the author s judgement ofDickens?

(e) Did Jane Austen express her opinionof those nineteenth-century criticswho admired her novels?

3. The author mentions that Englishliterature was not part of any academiccurriculum in the early nineteenthcentury in order to(a) emphasise the need for Jane Austen

to create ordinary, everydaycharacters in her novels.

(b) give support to those religious andpolitical groups that had attackedfiction.

(c) give one reason why Jane Austen snovels received little critical attentionin the early nineteenth century.





(d) suggest the superiority of an informaland unsystematised approach to thestudy of literature.

(e) contrast nineteenth-century attitudestowards English literature with thosetowards classical literature.

4. The passage supplies information tosuggest that the religious and politicalgroups (mentioned in the third sentence)and What ly might have agreed that anovel(a) has little practical use.(b) has the ability to influence the moral

values of its readers.(c) is of most interest to readers when

representing ordinary humancharacters.

(d) should not he read by young readers.(e) needs the sermonising of a narrator in

order to impart moral truths.5. The author quotes Coleridge in order to

(a) refute the literary opinions of certainreligious and political groups.

(b) make a case for the inferiority of novelsto poetry.

(c) give an example of a writer who wasnot a literary reactionary.

(d) illustrate the early nineteenth-centurybelief that fiction was especiallyappealing to young readers.

(e) indicate how widespread was theattack on novels in the earlynineteenth century.

6. The passage suggests that twentieth-century Marxists would have admiredJane Austen s novels more if the novels,as the Marxists understood them, had (a) described the values of upper-middle

class society.

(b) avoided moral instruction andsermonising.

(c) depicted ordinary society in a moreflattering light.

(d) portrayed characters from more thanone class of society.

(e) anticipated some of the controversialsocial problems of the twentiethcentury.

7. It can be inferred from the passage thatWhately found Dickens characters to be(a) especially interesting to young

readers.(b) ordinary persons in recognisably

human situations.(c) less liable than Jane Austen s

characters to have a realistic mixtureof moral qualities.

(d) more often villainous and weak thanvirtuous and good.

(e) less susceptible than Jane Austen scharacters to the moral judgments ofa sermonising narrator.

8. According to the passage, the lack ofcritical attention paid to Jane Austen canbe explained by all of the followingnineteenth-century attitudes towards thenovel EXCEPT the(a) assurance felt by many people that

novels weakened the mind(b) certainty shared by many political

commentators that the range of novelswas too narrow

(c) lack of interest shown by some criticsin novels that were publishedanonymously

(d) fear exhibited by some religious andpolitical groups that novels had the




Comprehension

power to portray immoral charactersattractively

(e) belief held by some religious andpolitical groups that novels had nopractical value

9. The author would most likely agree thatwhich of the following is the best measureof a writer s literary success?(a) Inclusion of the writer s work in an

academic curriculum(b) Publication of the writer s work in the

writer s own name(c) Existence of debate among critics

about the writer s work(d) Praise of the writer s work by religious

and political groups(e) Ability of the writer s work to appeal

to ordinary people

Passage 2(This passage was written in 1978.)Recent years have brought minority-owned

businesses in the United States unprecedentedopportunities-as well as new and significantrisks. Civil rights activists have long arguedthat one of the principal reasons why Blacks,Hispanics, and other minority groups havedifficulty establishing themselves in businessis that they lack access to the sizable orders andsubcontracts that are generated by largecompanies. Now Congress, in apparentagreement, has required by law that businessesawarded federal contracts of more than $500,000 do their best to find minoritysubcontractors and record their efforts to do soon forms filed with the government. Indeed,some federal and local agencies have gone sofar as to set specific percentage goals forapportioning parts of public workers contracts

to minority enterprises. Corporate responseappears to have been substantial. According tofigures collected in 1977, the total of corporatecontracts with minority busi nesses rose from$ 77 million in 1972 to $ 1.1 billion in 1977. Theprojected total of corporate contracts withminority businesses for the early 1980s isestimated to he over $ 3 billion per year with noletup anticipated in the next decade.

Promising as it is for minority businesses,this increased patronage poses dangers forthem, too. First, minority firms risk expandingtoo fast and overextending themselvesfinancially, since most are small concerns and,unlike large businesses, they often need to makesubstantial investments in new plants, staff,equipment, and the like in order to perform worksubcontracted to them. If, thereafter, theirsubcontracts are for some reason reduced, suchfirms can face potentially crippling fixedexpenses. The world of corporate purchas ingcan be frustrating for small entrepreneurs whoget requests for elaborate formal estimates andbids. Both consume valuable time and resources,and a small company s efforts must soon resultin orders, or both the morale and the financialhealth of the business will suffer.

A second risk is that White-ownedcompanies may seek to cash in on the increasingapportionments through formation of jointventures with minority-owned concerns. Ofcourse, in many instances there arc legitimatereasons for joint ventures; clearly, White andminority enterprises can team up to acquirebusiness that neither could acquire alone. Butcivil rights groups and minority business ownershave complained to Congress about minoritiesbeing set up as fronts with White backing,rather than being accepted as full partners in





legitimate joint ventures. Third, a minorityenterprise that secures the business of one largecorporate customer often runs the danger ofbecoming - and remaining - dependent. Even inthe best of circumstances, fierce competitionfrom larger, more established companies makesit difficult for small concerns to broaden theircustomer bases; when such firms have nearlyguaranteed orders from a single corporatebenefactor, they may truly have to struggleagainst complacen cy arising from their currentsuccess.

1. The primary purpose of the passage is to(a) present a commonplace idea and its

inaccuracies.(b) describe a situation and its potential

drawbacks.(c) propose a temporary solution to a

problem.(d) analyse a frequent source of

disagreement.(e) explore the implications of a finding.

2. The passage supplies information thatwould answer which of the followingquestions?(a) What federal agencies have set

percentage goals for the use ofminority owned businesses in publicworks contracts?

(b) To which government agencies mustbusinesses awarded federal con tractsreport their efforts to find minoritysubcontractors?

(c) How widespread is the use of minority-owned concerns as fronts by Whitebackers seeking to obtainsubcontracts ?

(d) How many more minority-ownedbusinesses were there in 1977 than in1972?

(e) What is one set of conditions underwhich a small business might finditself financially overextended?

3. According to the passage, civil rightsactivists maintain that one disadvantageunder which minority-owned businesseshave traditionally had to labour is thatthey have(a) been especially vulnerable to

governmental mismanagement of theeconomy.

(b) been denied bank loans at ratescomparable to those afforded by largercompetitors.

(c) not had sufficient opportunity tosecure business created by largecor porations.

(d) not been able to advertise in thosemedia that reach large numbers ofpotential customers.

(e) not had adequate representation in thecentres of government power.

4. The passage suggests that the failure of alarge business to have its bids forsubcontracts result quickly in ordersmight cause it to(a) experience frustration but not serious

financial harm.(b) face potentially crippling fixed

expenses.(c) have to record its efforts on forms filed

with the government.(d) increase its spending with minority

subcontractors.(e) revise its procedure for making bids

for federal contracts and subcontracts.




Comprehension

5. The author implies that a minority-ownedconcern that does the greater part of itsbusiness with one large corporatecustomer should(a) avoid competition with larger, more

established concerns by not expanding.(b) concentrate on securing even more

business from that corporation.(c) try to expand its customer base to

avoid becoming dependent on thecorporation.

(d) pass on some of the work to be donefor the corporation to other minority-owned concerns.

(e) use its influence with the corporationto promote subcontracting with otherminority concerns.

6. It can be inferred from the passage that,compared with the requirements of law,the percentage goals set by some federaland local agencies (last sentence of para1) are(a) more popular with large corporations.(b) more specific.(c) less controversial.(d) less expensive to enforce.(e) easier to comply with.

7. Which of the following, if true, would mostweaken the author s assertion that, in the1970s corporate response to federalrequirements (para2) was substantial?(a) Corporate contracts with minority-

owned businesses totalled $ 2 billionin 1979.

(b) Between 1970 and 1972, corporatecontracts with minority-ownedbusi nesses declined by 25 per cent.

(c) The figures collected in 1977 under-

represented the extent of corporatecontracts with minority-ownedbusinesses.

(d) The estimate of corporate spendingwith minority-owned businesses in1980 is approximately $ 10 million toohigh.

(e) The $ 1.1billion represented the samepercentage of total corporate spending in1977 as did $ 77 million in 1972.

8. The passage most likely appeared in(a) a business magazine(b) an encyclopaedia of Black history upto

1945(c) a dictionary of financial terms(d) a yearbook of business statistics(e) an accounting textbook

9. The author would most likely agree withwhich of the following statements aboutcorporate response to working withminority subcontractors?(a) Annoyed by the proliferation of front

organisations, corporations are likelyto reduce their efforts to work withminority-owned subcontrac tors in thenear future.

(b) Although corporations showedconsiderable interest in working withminority businesses in the 1970s, theiraversion to government paper workmade them reluctant to pursue manygovernment contracts.

(c) The significant response ofcorporations in the 1970s is likely tobe sustained and conceivably beincreased throughout the 1980s.

(d) Although corporations are eager tocooperate with minority owned





businesses, a shortage of capital in the1970s made substantial responseimpossible.

(e) The enormous corporate response hasall but eliminated the dangers ofoverexpansion that used to plaguesmall minority-owned businesses.




Comprehension

Answers and explanationsPassage 1

1. (d); The passage, in fact, traces the historyof Jane Austen criticism, though it isconfined mainly to the nineteenthcentury. In this course, criticism of fictionin general is also talked about.

2. (a); Whately was aware of Scott s remarks,otherwise how could he expressagreement with Scott s evaluation ?

Beware of (4)! The judgement aboutDickens is Whately s, not the author s.

3. (c); The first sentence of the passagedescribes one of the attitudes towardsnovels which help explain why Austenreceived little attention ....

4. (b); Both Whately as well as the groupsshared the opinion stated in (2): thatnovels can influence moral behaviour.However, they disagree about the valuesof such influence.

5. (e); When Coleridge, who was not areactionary, could thus attack novels, wecan well imagine how others, who werereactionaries or who were influenced bythem, might have attacked novels.

6. (d); The Marxists were against herexclusive emphasis on a lofty upper-middle class. (3) is rejected because beingagainst exclusive emphasis on one doesnot mean pampering the other.

7. (c); See the last two sentences of thesecond paragraph.

8. (b); (1), (4) and (5) are mentioned in thefirst paragraph as factors resulting inlack of critical attention . (3) is also stated

as such a factor: see the sentence withinbrackets in the second paragraph. (2) is,in fact, the result of critical attention.

9. (c); The last sentence of the passage saysthat being considered controversial (thatis, existence of debate) is the enviablepinnacle (highest point everyone wishesto reach).

Passage 21. (b); The first two paragraphs describe a

situation: increased patronage forminority businesses. The next threeparagraphs describe its potentialdrawbacks.

2. (e) ; See the first part of the th irdparagraph.

3. (c); See the second sentence of the firstparagraph.

4. (a); The substantial investments thatsmall concems have to make is unlikelarge businesses . So while small concernscan face potentially crippling fixed

expenses , large firms will be spared suchfinancial harm.

5. (c); See the last paragraph. The danger:is of becoming dependention the




English Grammar and Comprehensioncorporation because it becomes difficultfor the minority-owned concerns tobroaden their customer bases So theauthor s suggestion is to counter thisdrawback: struggle againstcomplacency .

6. (b); The law is vague: it talks in terms ofdo their best . Some federal and local

agencies , on the other hand, have setspecific percentage goals .

7. (e); That the response was substantialrests on the fact that contracts rose from$ 77 million in 1972 to $11 billion in 1977. (5) suggests that the two amounts

represented the same percentage of totalcorporate spending in their respectiveyears. So, in actual terms there was nogrowth; there was no proportional gain.

8. (a); (3) can be easily ruled out. (2) isrejected because of time lag (1978 and1945). (1) is preferred to (4) and (5)because there is not too much emphasison statistics; the passage rather makesinteresting reading.

9. (c); The last line of the second paragraphtells us that no letup is anticipated inthe next decade (that is, the 1980s, sincethe passage was written in 1978).




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17Computer Knowledge




Computer Knowledge

11. To identification particular location in storagearea one have a1. Address 2. Password3. Logic 4. Mouse5. None of these

12. A local storage register in the CPU whichcontains the address of the next instruction tobe executed is referred as1. Key register 2. Address register3. Password 4. All of the above5. None of these

13. A sequence of precise and unambiguousinstructions for solving a problem in a finitenumber of operations is referred as1. Address 2. Algorithm3. Advice 4. All of the above5. None of these

14. A character set that contains letters, digits, andother special characters such as $, @, + % etc.is referred as1. Numeric 2. Alphanumeric3. Alphabetic 4. All of the above5. None of these

15. One of the components of central ProcessingUnit (CPU) of the computer that performsmathematical and logical operations is1. ALU (Arithmetic Logic Unit)2. Address register 3. Analog4. All of the above 5. None of these

16. A standard intended to connect relativelylow speed devices such as keyboards, mouse,modems and printers is1. Access bus 2. Access time3. Connector 4. All of the above5. None of these

17. The concept that one can disconnect peripheralsand plug them in without letting computer shutdown or reconfigure the system is referred as1. Hot plugging 2. Cold plugging3. Access bus 4. All of the above5. None of these

18. The time interval between the instant at whichdata is called from a storage device and the rustdelivery begins in1. Access time 2. Delivery time3. Service time 4. All of the above5. None of these

19. The automatic execution of lower-priority(background) computer programs whenhigher priority (foreground) programs are notusing the system resources is referred as1. Background processing2. Foreground processing3. Null processing4. All of the above 5. None of these

20. A form of access to a computer or network withspecified user name and password is referred as1. Account 2. Address3. Algorithm 4. All of the above5. None of these

ANSWERS1. (1) 2. (4) 3. (2) 4. (1) 5. (1) 6. (1) 7. (2) 8. (1) 9. (3) 10. (1)

11. (1) 12. (2) 13. (2) 14. (2) 15. (1) 16. (1) 17. (1) 18. (1) 19. (1) 20. (1)




SAMPLE MATERIAL

OF OUR STUDY KIT

MARKETING APTUTUDE

Computer Knowledge

1. Bancassurance is a relationship between Bankand1. Education 2. Insurance Company3. Employee 4. Customer5. All of these

2. BIM stands for1. Bank Insurance Model2. Book In Management3. Bank In Money4. Bank Investment Model5. All of these

3. Effective Communication is1. Good Vocabulary2. A sine qua non for marketing3. Not required of demand exceeds supply4. All of these5. None of these

4. Which is not a part of 7 ps of marketing?1. Price 2. Policy3. Product 4. People5. Process

5. Market Plan can be for1. A brand 2. A product3. Product line 4. All of these5. None of these

6. Solid marketing strategy is the fundation of a1. Sales 2. Budget3. Well written marketing plan4. Market 5. All of these

7. Which is/are promotional content?1. SalesPromotion2. Branding 3. Direct Marketing4 Advertising 5 All of these

8. Marketing strategy means1. To introduce in sales promotion scheme2. Population 3. Perseverance4. Demands 5. Networth

9. Customisation means1. Making Few change according to client

requirement to an already existing product2. Test 3. Production4. Costing 5. All of these

10. Marketing should be resorted1. Only among rich person2. Depends on income3. Only in crowded areas4. Depends on the product5. Only among the poor

11. Marketing is1. A one off affair2. A day to day function3. A collective process4. A one man show 5. None of these

12. Marketing Strategies means1. Plan for effective marketing2. Report 3. Loss4. Risk 5. Profit

13. Qualities needed by a good marketing staff are1. Politeness 2. Perseverance3. Pushy 4. Aggressiveness5. Only 1. and 2.

14. Marketing is required in banks due to1. Globalisation2. Government dictates3. Increase in population4 Computerisation 5 None of these

17Marketing Aptutude




Computer Knowledge

ANSWERS

1. (2) 2. (1) 3. (2) 4. (3) 5. (4) 6. (3) 7. (3) 8. (1) 9. (1) 10. (4)11. (3) 12. (1) 13. (5) 14. (1) 15. (3) 16. (3) 17. (1) 18. (4) 19. (2) 20. (2)

15. HNI means1. Honest Neutral Individual2. Honest Marketing Staff3. High Networth Individual4. High Income Individual5. None of these

16. Which is/are conventional media that are I6reaching the rural audience effectively?1. Bullock Cart 2. Television3. Horse Cart 4. Radio5. All of these

17. Rural markets and rural marketing involve anumber of strategies, which iclude1. Client and location specific promotion2. Partnership for sustainability3. Bundling of inputs4. Joint or cooperative promotion5. All of these

18. Which is/are Features of Rural Market ?1. Irregular income 2. Low income3. Population is Predominantly, illiterate4. Lack of monthly income5. All of these

19. Which is/are reasons for improvement ofbusiness in rural area?1. Infrastructure Facilities2. Literacy level3. Socio-economic changes4. Increase in Income5. All of these

20. Who is the target of Rural Marketing ?1. Doctors 2. Rural Consumers3. Students4. Chartered Accountant5. All of these




SAMPLE MATERIAL

OF OUR STUDY KIT

DATA INTERPRETATION

&

DATA SUFFICIENCY

Quantities can be compared by the height or length of a bar in a bar graph. A bar graph can have eithervertical or horizontal bars. You can compare different quantities or the same quantity at different times.

DISABILITY BENEFICIARIES REPORTED AS REHABILITATED

(Number, as percent of all rehabilitated clients of statevocational rehabilitation agencie, years 1985-2001)

20

15

10

5

0Year 1985-95 1996 1997 1998 1999 2000 2001

Q. Between 1997 and 2001, the lowest number of disability beneficiaries were reported as rehabilitated in theyear(a) 1997 (b) 1998(c) 1999 (d) 2000

The answer is (A) since the lowest bar is the bar for 1997.ExampleDirections: Given here is a multiple bar diagram depicting the changes in the students strength of acollege in four faculties from 1990 91 to 1992 93. Study the diagram and answer the questions.

1. In which faculty was there a regular decrease in students strength?(a) Arts (b) Science(c) Commerce (d) Law

Bar Charts




2. The percentage of students in Science faculty in 1990 91 was(a) 26.9 (b) 27.8(c) 29.6 (d) 30.2

3. The total students strength in 1991 92 was how many times that of Commerce students in the same year?(a) 3 (b) 4(c) 5 (d) 6

4. What was the percent increase in Science students from the year 1990 91 to 1992 93?

(1) 50 (b)2

663

(3) 75 (d) 150

0

100

200

300

400

500

600

1990-91 1991-92 1992-93

Year ¾®

Arts

Science

Commerce

Law

Solution:1. (a)2. (c) Number of students in all faculties taken together in 1990 91

= 600 + 400 + 200 + 150 = 1350Number of students in science faculty = 400

\ Required percentage400

100 29.6%1350

= ´ =

3. (d) Total students strength in 1991 92= 550 + 500 + 250 + 200 = 1500

Students strength in commerce in 1991 92 = 250

\ Required solution = =1500 6 times250

4. (a) Students strength in Science in 1990 91 = 400Students strength in Science in 1992 93 = 600

Increase = 600 400 = 200

Percent Increase = ´ =

200100 50%

400




Directions: The bar graph given here shows thenumber of job-seekers of a state in various yearsat different stages of education.

Study the graph carefully and answer thequestions based on it.

4000

3000

2000

1000

MatriculatesSenior SecondaryGraduates

1400

850

325

16251850

2300

1000

375

1050

525

1250

700

1800

725

2200

800

3300

4000

1. In which year was the number of Graduate job-seekers the same as that of Senior Secondary job-seekers?(a) 1973 (b) 1974 (c) 1975 (d) 1976

2. In comparison to the year 1973, how many morejob-seekers in all, were there in the year 1977?(a) 700 (b) 1700 (c) 2375 (d) 2150

3. In which year, was the number of Matriculate job-seekers maximum?(a) 1973 (b) 1975 (c) 1972 (d) 1977

4. The number of job-seekers, having theirqualification as Senior Secondary, in the year 1974was :(a) 525 (b) 800 (c) 1050 (d) 1875

EXERCISE ANSWERS

1. (b) 2. (c) 3. (d) 4. (b)

EXPLANATIONS

1. Number of Graduate job-seekers in 1974 = 525Number of Senior secondary job-seekers in 1974= 1050 525 = 525

2. Number of job-seekers:In Year 1973 = 1625In Year 1977 = 4000

Difference = 4000 1625 = 23753. Number of Matriculate job-seekers:

In Year 1976 = 3300 1800 = 1500In Year 1977 = 4000 2200 = 1800

4. Required number of job-seekers having theirqualification as Senior Secondary= 1850 1050 = 800




Line graphs are used to show how a quantity changes continuously. Very often the quantity is measured astime changes. If the line goes up, the quantity is increasing; if the line goes down, the quantity is decreasing; ifthe line is horizontal, the quantity is not changing. To measure the height of a point on the graph, use your noteboard as a straight edge.

TRENDS IN INDUSTRIAL INVESTMENT, LABOUR PRODUCTIVITY,EMPLOYMENT AND OUTPUT, 1980 TO 2007

(Index numbers, 1980 = 100)

17001600150014001300120011001000900800700600300200100

0

400

300

200

100

0 1980 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007

Note: The lefthand scale in roubles only to theconstant- price value of industrial investment

Million roubles

InvestmentOutput

ProductivityEmployment

Q. The ratio of productivity in 2007 to productivity in 1980 was about(a) 1 : 4 (b) 1 : 3(c) 3 : 1 (d) 4 : 1

In 2007 productivity had an index number of 400, and the index numbers are based on 1980 = 100. So theratio is 400 : 100 = 4 : 1. Therefore, the answer is (d).

Line Graphs




Directions: Study the following graphs carefullyand answer the questions given below:

Number of candidates appeared (In thousands) andPercentage of candidates qualified in a Competitiveexamination over the years

No. of Candidates appeared (In Thousands)

0

5

10

15

20

25

30

35

40

1997 1998 1999 2000 2001 2002 2003 2004

Years

Percentage of Candidates Qualified

0

5

10

15

20

25

30

35

40

45

1997 1998 1999 2000 2001 2002 2003 2004

Years

1. What was the ratio between the number ofcandidates appeared in 1997 and the number ofcandidates qualified in 2004?(a) 14 : 5 (b) 5 : 14(c) 3 : 7 (d) Data inadequate

2. In which of the following years was the numberof candidates qualified the lowest among the givenyears?(a) 1997 (b) 2002 (c) 2001 (d) 1998

3. What was the percentage drop in the number ofcandidates appeared from the year 2002 to 2003?

(a) 2663

(b) 30

(c) 70 (d) None of these 4. How many candidates qualified in the year 2002?

(a) 6750 (b) 13500(c) 9900(d) Cannot be determined

5. The number of candidates qualified in 1999 waswhat percentage of the number of candidatesappeared in 1998?(a) 685 (b) 70(c) 32.5 (d) 67.5

ANSWERS

1. (b) 2. (a) 3. (d) 4. (a) 5. (d)

EXERCISE




You can compare several categories by a graph of the cumulative type. These are usually bar or line graphswhere the height of the bar or line is divided up proportionately among different quantities.

Q. In 1986, roughly what percent of the federal prisoners received from the courts were guilty in other offenses?(a) 10 (b) 15(c) 25 (d) 30

The total number of prisoners in 1986 was about 20,000, and guilty in other offences was about 5,000.

Since = =

5,000 1 25%,20, 000 4

the correct answer is (c).

In DI section of the question paper, the intention should be to attempt all questions as skipping them wouldamount to losing precious scoring opportunities. There are two approaches to arrive at the solution. One is to workon the data to arrive at the correct answer. The other one is the Elimination method which requires workingbackwards by eliminating the wrong choices. Though the elimation method is more time consuming, it may still bepreferred where direct solution involves enormous calculation of data.

At times, examiners pose rather difficult data sets at the beginning of the sections. These are intended to beSPEED BRAKERS which take away much of precious time. Therefore, as a rule, scan the whole section quicklybefore actually attempting the questions and start with easier part of the section.

In some exams, data are presented in more than one table or graph. The objective is to test not only quantitativeskills but also relational and analytical ability. Recently, in some exams the questions in this section are being

Mix Diagrams




framed in caselet (paragraph) form, beginning with probability and reasoning questions. It is left to the reader tostudy the case, call out requisite data and arrange it in a suitable form for meaningful interpretation. It is best toarrange data with rough sketch to hasten comprehension.

EXERCISEDirections: Study the pie-chart given to answerthese questions.

Composition of Exports and Imports (per cent)Exports (1998 1999)

A Agriculture and Allied ProductsB Ores and MineralsC Manufactured GoodsD Crude and Petroleum ProductsE Capital Goods

Imports (1998 1999)

A Food and Allied ProductsB FuelC FertilisersD Paper Board Manuf.and NewsprintE OthersF Other Bulk ItemsG Others

1. India s trade balance during the year 1998 99was:

(a) favourable (b) unfavourable(c) neutral (d) none of these

2. Maximum export contribution has been due to :(a) agriculture and allied products(b) ores and minerals(c) crude and petroleum products(d) manufactured goods.

3. The import of capital goods and other bulk itemsincurred more than of total import expenditure(a) 50% (b) 60%(c) 35% (d) 70%

4. The imports exceeded by about millions.(a) US$ 8000 (b) US$ 8200(c) US$ 8199.4 (d) US$ 8400

5. The export of agriculture and allied products wasto the tune of US$ :(a) 5700 millions (b) 6700 millions(c) 4700 millions (d) 1730 millions

ANSWERS

1. (b) 2. (d) 3. (a) 4. (c) 5. (a)




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SAMPLE MATERIAL

OF OUR STUDY KIT

MATHEMATICAL APTITUDE

IntroductionIt is the rule that is used to determine the mean value of the mixture when the prices of the individual items

being mixed together and the proportion in which they are being mixed are given. Here, the value of the mixtureis always higher than the lowest value and lower than the higher value of the items being mixed.

According to the Rule of Alligation

Quantity of cheaperQuantity of dearer =

Price of dearer Mean priceMean price Price of cheaper

-

-

It can be also expressed as,

Cost price of 1 unitquantity of cheaper (x)

Mean price (m)

Cost price of 1 unitquantity of cheaper (x)

(y m) (m x)

\ (Cheaper quantity : Dearer quantity) = (y m) : (m x)Where, mean price (m) is the cost price of a unit quantity of the mixture.Also, if a container contains x units of liquid from which y units are taken out and replaced by water. After n

operations, the quantity of pure liquid is 1nyx

xé ùæ öê ú-ç ÷ê úè øë û

unit.

Example 1: How many kilograms of rice costing ̀ 18 per kg must be mixed with 30 kg of rice costing ̀ 14 perkg, so that the resultant mixture cost ̀ 15 per kg.

Solution. Applying the rule of alligation, we have

( 14)` ( 18)`

18 - 15 = 3 15 - 14 = 1

Mean price( 15)`

Alligation or Mixure




\Quantity of cheaper riceQuantity of dearer rice =

31

If cheaper rice is 3 kg, dearer rice is 1 kg.

If cheaper rice is 30 kg, dearer rice = 30 1

3´æ ö

ç ÷è ø

kg = 10 kg

EXERCISE1. How many kg of tea worth ` 29 per kg must be

blended with 25 kg of tea worth ` 32 per kg sothat by selling the blended variety at ` 33 per kgthere should be 10% gain?(a) 45 kg (b) 33 kg(c) 25 kg (d) 50 kg

2. Two groups of students, whose average ages are20 yr and 30 yr, combine to form a third groupwhose average age is 23 yr. What is the ratio ofthe number the first group to the number ofstudents in the second group?(a) 5 : 2 (b) 2 : 5(c) 7 : 3 (d) None of these

3. John stole some whisky from a bottle his fatherhad kept away in the cupboard. This bottle ofwhisky contained 50% alcohol. John replacedwhat he had drunk by another brand of whiskywhich contained only 25% alcohol. The whisky inthe bottle now has only 35% alcohol. How muchof the bottle did John steal?(a) 3/5 (b) 2/5(c) 4/5 (d) 2/3

ANSWERS

1. (d) 2. (c) 3. (*)

EXPLANATIONS

1. SP of blended variety = ` 33 per kg

CP of blended variety = 10033110

´ = ` 30 per kg

By the rule of alligation,

29 32

30

2 1

So, tea worth ` 29 per kg and tea worth ` 32 perkg should be priced in 2 : 1.\ If there is 25 kg of tea worth ` 32 per kg.Then, there must be 50 kg of tea worth ` 29 perkg.

2. By the rule of alligation,

20 30

23

7 3

\ Required ratio = 7 : 3.3. By the alligation rule,

Whisky containing Whisky containing50% alcohol50% alcohol

Whisky containing25% alcohol

Whisky containing

36% alcohol

10 15

Whisky with 50% alcoholWhisky with 25% alcohol =

10 215 3

=




Wo rkWork to be done is generally considered as one unit. It may be digging a trench constructing or painting a

wall, filling up or emptying a tank, reservoir or a cistern.

General rules to be followed in the problems on Time and Work1. If Acan do a piece of work in n days, then work done by Ain 1 day is 1/n. ie,if a person can do some work in

12 days, he does 1/ 12th of the work in one day.2. If A s 1 day s work = 1/n, then A can finish the whole work in n days. ie, if a person s one day work is 1/10,

then he can finish the whole work in 10 days.3. If A is thrice as good a workman as B, then ratio of work done by A and B = 3 : 1. ie, if a man works three

times as fast as a woman does, then when the work is complete, 3 parts of the work has been done by theman and 1 part by the woman.

4. If A is thrice as good a workman as B, then ratio of time taken by A and B = 1 : 3. ie, if the womantakes 15 days to complete the work, then the man takes 5 days to complete the same work.

5. If two persons A and B can individually do some work in a and b days respectively, then A and B togethercan complete the same work in ab (a + b) days.

6. The fundamental rules on variation also apply in Time and Work.(i) Work and men are directly proportional to each other ie, if the work increases, the no. of men required

to do it, also increases, if the work is to be completed in the same number of days.(ii) Men and days are inversely proportional, ie, if the number of men increases, the number of days

required to complete the same work decreases and vice versa.(iii) Work and days are directly proportional, ie, if the work increases, the number of days required also

increases, if the work is to be completed with the same number of men and vice versa.Example 1: Ravi can do a job 10 days. Determine his one day job.Solution. Ravi s 10 days work = 1

Ravi s 1 day work =110

Time and Work




EXERCISE65. A tap can fill a cistern in 12 h. After half the tank

is filled, 2 more similar taps are opened. What isthe total time taken to fill the tank complete by?(a) 9 h (b) 6 h (c) 8 h (d) 4 h

66. An electric pump can fill a reservoir in 36 h.Because of a leak in the reservoir it took 45 h tofill the reservoir. When the reservoir is full, howmuch time will the leak take to empty it?(a) 180 h (b) 175 h(c) 185 h (d) 170 h

67. A cistern has three pipes A, B and C. The pipes Aand B can fill it in 5 h and 6 h respectively and Ccan empty it in 3 h. If the pipes are opened inorder at 3 pm, 4 pm and 5 pin respectively at whattime will the tank be filled?(a) 6 am (b) 5 am(c) 4 am (d) 7 am

ANSWERS

1. (a) 2. (a) 3. (b)

EXPLANATIONS

1.12 of the tank can be filled by the tap in 5 h.

Part filled by one tap in 1 h = 1

12

Part filled by three taps in 1 h = 14

\ 12 tank can be filled by the three pipe =

1 24

´

= 2 hTotal time taken to fill the tank completely = 6 + 2= 8 h

2. Work done by the leak in 1 h = 1 136 45

æ ö-ç ÷

è ø

= 1

180\ Leak will empty the reservoir in 180 h.

3. By 5 pm, the water filled by two pipes = 2 h workdone by pipe A + 1 h work done by pipe B

=1 12 15 6

´ + ´ =2 15 6

+ =1730

After 5 pm all the three pipes are working andthe work done by all the three pipes in 1 h =1 1 15 6 3

+ - =130

After 5 pm only 1330 of the tank is to be filled time

taken in filling 1330 of the tank =

133030

´ = 13 h

\ 13 h after 5 pm= 6 am




Relation between Time, Speed and DistanceDistance covered, time and speed are related by

Time = Distance

Speed ...(i)

Speed = Distance

Time ...(ii)

Distance = Speed Time ...(iii)Distance is measured in metres, kilometres and miles.Time in hours, minutes and seconds.Speed in km/h, miles/h and m/s.

1. To convert speed of an object from km/h to m/s multiply the speed by 5

18 .

2. To convert speed of an object from m/s to km/h, multiply the speed by 185 .

Average SpeedIt is the ratio of total distance covered to total time of journey.

\ Average speed = Total distance coveredTotal time of journey

General Rules for Solving Time & Distance ProblemsRule 1

If a certain distance is covered with a speed of x km/h and another equal distance with a speed of y km/h,then the average speed for the whole journey is the harmonic mean of the two speeds.

Average speed =2 km/h1 1

x y

æ öç ÷ç ÷ç ÷+ç ÷è ø

= 2 km/hxyx y

æ öç ÷

+è ø

Time and Distance




EXERCISE1. A passenger train running at the speed of 80 km/

h leaves the railway station 6 h after a goods trainleaves and overtakes it in 4 h. The speed of thegoods train is(a) 32 km/h (b) 40 km/h(c) 50 km/h (d) 60 km/h

2. Two persons A and B are at two places P and Qrespectively. A walks at v km/h and B is 2 km/hfaster than A, starting simultaneously from wherethey stand. If they walk towards each other, theymeet in 72 min. If they walk in the same direction,the faster overtakes the slower in 6 h. Find theirrespective speeds (in km/h).(a) 3 and 5(b) 4 and 6(c) 2 and 4 (d) 3 and 5

ANSWERS

1. (a) 3. (b)

EXPLANATIONS

1. Let the speed of the goods trains = x km/hDistance travelled by the goods train in 6 h = 6x

Now, Time =Distance

Relative Speed

\ 4 =6

80x

x-

Þ 320 4x = 6xÞ 10x = 320Þ x = 32 km/h

2. Let d kilometre be the distance between A and B.When A and B walk toward each other, then

( 2)d

v v+ + =7260

and if they walk in the same direction

( 2)d

v v+ - = 6

Þ 2d

= 6 Þ d = 12 km

\ 2 2d

v +=

7260 \ v = 4 km/h

Hence, the speed are 4 km/h and (4 + 2) = 6 km/h




InterestIt is the sum which is paid by the borrower to the lender for using the money for a specific time period. The

money borrowed is called the Principal. The rate at which the interest is calculated on the principal is calledRate of Interest. The time for which the money is borrowed is Time and the total sum of principal and interestis called the Amount.

Simple InterestIf P = Principal, R = Rate per cent per annum T = Number of years, SI = Simple Interest and A = Amount.Then,

(i) SI = 100P T R´ ´

(ii) P = 100 SI

R T´

´(iii) R =

100 SIP T

´

´

(iv) T = 100 SI

P R´

´(v) A = P + SI = P + 100

P T R´ ´= 1

100RTP æ ö

+ç ÷è ø

Here, the interest is calculated on the original principal ie, the principal to calculate the interest remainsconstant throughout the time period. The interest earned on the principal is not taken into account for the purposeof calculating interest for later years.

Example 1: Find the SI on ` 7200 at 8% per annum for 10 months.

Solution. Here, P = ` 7200, R = 8% per annum and T = 10 yr12 =

5 yr6 .

SI = 100P T R´ ´æ ö

ç ÷è ø

= ` 5 17200 86 100

æ ö´ ´ ´ç ÷

è ø= ` 480

Example 2: A sum is lent at 10% per annum. Simple interest will get doubled in how many years?Solution. Sum will be doubled when SI = P

Therefore, SI = P = 100PRT

Þ RT = 100 Þ T = 100R =

10010 = 10 year

Simple Interest




EXERCISE1. The least number of years in which the simple

interest on ̀ 2200 at 16 %3

simple interest will be

a whole number of rupees, is(a) 4 yr (b) 3 yr(c) 6 yr (d) 5 yr

2. ` 2000 is invested at 10% per annum simpleinterest. If the interest is added to the principalevery 10 yr, the amount will become ̀ 4600 after(a) 12 yr (b) 11 yr(c) 12 yr (d) 11 yr

3. A bicycle is sold for ` 2200 cash or ` 1500 cashdown payment and ` 770 to be paid after 4months. What is the rate of interest charged inthe instalment scheme?(a) 10% (b) 20%(c) 30% (d) 40%

ANSWERS

1. (b) 2. (d) 3. (c)

EXPLANATIONS

Money invested is in the ratio= 5000 : (8000 5000) = 5000 : 3000 = 5 : 3

1. SI = 19 122003 100

næ ö´ ´ ´ç ÷

è ø, where n is the number

of years = 418

3n

For SI to be a whole number the least value of nshould be 3.Hence, the least number of years is 3 year.

2. SI for 10 year = ` 2000 10 10

100´ ´æ ö

ç ÷è ø

= ` 2000

Principal after 10 year becomes= ` (2000 + 2000) = ` 4000

SI on it = ` (4600 4000) = ` 600

Time =100 6004000 10

´

´=

32 year

= 112 year

Total time =110 12

æ ö+ç ÷

è øyear

= 1112 year

3. Cash price = ` 2200Cash down payment = ` 1500Balance = ` 2200 ` 1500 = ` 700Interest = ` 770 ` 700 = ` 70

Here P = ` 700, SI = ` 70, T = 4

12 = 13 year

\ R = 100 SI

P T´

´=

100 7017003

´

´ = 10 3 = 30%




A Civil Servant should be well-versed in basics of Algebra. In the Civil Services Aptitude Test Paper 2, inBasic Numeracy, certainly there will be asked some questions based on equations and their roots.

PO L YN OM I AL SPolynomial

An expression in term of some variable(s) is called a polynomial.For examplef(x) = 2x 5 is a polynomial in variable xg(y) = 5y2 3y + 4 is a polynomial in variable y

Note that the expressions like 2 32

1 43 , ,5 ,7 6

x x xxx x

- -- +

etc. are not polynomials. Thus, a rational x integral

function of x is said to be a polynomial, if the powers of x in the terms of the polynomial are neither fractions nornegative. Thus, an expression of the form

f(x) = an xn + an 1xn 1 + + alx + a0 is called a polynomial in variable x where n be a positive integer and a0, al,...,an be constants (real numbers).

Degree of a PolynomialThe exponent of the highest degree term in a polynomial is known as its degree.For example

f(x) = 342

x - is a polynomial in the variable x of degree 1.

p(u) = 3u3 + u2 + 5u 6 is a polynomial in the variable u of degree 3.q(t) = 5 is a polynomial of degree zero and is called a constant polynomial.

Linear PolynomialA polynomial of degree one is called a linear polynomials. In general f(x) = ax + b, where a ¹ 0 is a linear

polynomial.

Basic Algebra




EXERCISE1. For what range of values of a will the inequality

215 1?aa

- >

(a)1 150.4,3 2

a a< < > (b)1 2and 3 5

a a< - >

(c)1 20,3 5

a a- < < > (d)13

x <

2. If one of the roots of the quadratic equation a2 +ba + 24 = 0 is 1.5, then what is the value of b?(a) 17.5 (b) 12.7(c) 15.25 (d) 14.5

ANSWERS

1. (b) 2. (a)

EXPLANATIONS

1.215aa

- > 1Þ 15a2 2 > aÞ 15a2 a 2 > 0Þ 15a2 6a + 5a 2 > 0Þ 3a (5a 2) + 1 (5a 2) > 0Þ (5a 2) (3a + 1) > 0

\ a > 25 and a <

13

-

2. 1.5 is the root of quadratic equationa2 + ba + 24 = 0

\ (1.5)2 + 1.5 b + 24 = 02.25 + 1.5 b + 24 = 0

1.56 = 26.25b = 17.5




SetsA set is a collection of well defined objects.The objects of the sets are called elements.

(i) Sets are usually denoted by capital letters A, B, C,..., X, Y, Z.(ii) The elements of the sets are denoted by small letters like a, b, c,..., x, y, z etc.

Representation of SetsSets are usually described into two ways.

(i) Tabular form or roster form, in this form, all the elements of the set are separated by commas and enclosedbetween the bracket { }.

For example(a) The set of vowels of English Alphabet as

A = {a, e, i, o, u)(b) The set of numbers on a clock face is written as

B = (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}(ii) Set builder from: We define a set by stating properties which its elements must satisfy. For example the

set of all even integers. Then, we use the letters usually x, and we writeA = {x | x is an even integer}

This is to be read as A is a set of numbers x such that x is an even integer. The vertical line | to be read assuch that some times we use x in place of vertical line.

A = {x : x is an even integer}eg, C = {1,w, w2} = {x | x3 1 = 0}

If an object x is an element of a set A, we write x Î A which is read as x belong to A and if an object x is nota member of A we write x Ï A and read as x does not belong to A .

Some Important Terms(i) Empty or Null set The set which contains no elements is called the empty set or the null set. The empty

set is written as f.Thus, f = { } as there is no element in the empty set.For example; the set of odd numbers divisible by 2 is the null set.

Set Theory,Venn Diagrams,

Functions & Relations




EXERCISE1. Given the following Venn diagram, determine

(P È Q) (P Ç R).

1 2 3

4 5

6

7

P

R

Q

(a) {1, 2, 3} (b) {4, 5, 6, 7}(c) {1, 2, 3, 4} (d) {1, 2, 3, 4, 5, 6}

2. In a class of 40 students, 12 enrolled for bothEconomics and Industrial Psychology. 22 enrolledfor Industrial Psychology. If the students of theclass enrolled for at least one of the two subjects,then how many students enrolled for onlyEconomics and not Industrial Psychology ?(a) 12 (b) 18(c) 22 (d) 20

ANSWERS

1. (a) 2. (b) 3. (b) 4. (d)

EXPLANATIONS

1. It is clear from the given Venn diagramP È Q = {1, 2, 3, 4, 5, 6}

and P Ç R = {4, 5, 6}\ (P È Q) (P Ç R)= {1, 2, 3}

2. Economics Industrial 12 Psychology

Economics 18

12Industrial

Psychology10

Students enrolled in only economics = 18.




StatisticsThe branch of Mathematics which deals with collection, classification and interpretation of data is called

statistics.When used in the singular sense, statistics refers to the subject as a whole of science of statistical methods

embodying the theory and techniques. When it is used in the plural sense, statistics refers to the data itself (ie,numerical facts collected in a systematic manner with some definite purpose in view, in any field of enquiry).

The Frequency Table or the Frequency DistributionIf the data is classified in a convenient way and presented in a table it is called frequency table or frequency

distribution.Frequency: When the data is presented in a frequency table, the number of observations that fall in any

particular class is called the frequency of that class.Class Limit: The starting and end values of each class are called lower limit and upper limit of that class

respectively.Class-interval: The difference between the upper and lower boundary of a class is called the class-interval

or size of the class . It can also be defined as the difference between the lower or upper limits or boundaries of twoconsecutive classes.

Class Boundaries: The average of the upper limit of a class and the lower limit of the succeeding class iscalled the upper boundary of that class. The upper boundary of a class becomes the lower boundary of the nextclass.

Range: The difference between the highest and the lowest observation of a data is called its range.Histogram: Pertaining to a frequency distribution, if the true limits of the classes are taken on the x-axis

and the corresponding frequencies on the y-axis and adjacent rectangles are drawn, the diagram is calledhistogram .

Frequency Polygon and Frequency Curve: If the points pertaining to the mid values of the classes of afrequency distribution and the corresponding frequencies are plotted on a graph sheet and these points are joinedby straight lines, the figure formed is called frequency polygon. If these points are joined by a smooth curve thefigure formed is called frequency curve.

Cumulative Frequency Curves: If the points pertaining to the boundaries of the classes of a frequencydistribution and the corresponding cumulative frequencies are plotted on a graph sheet and they are joined by asmooth curve, the figure formed is called cumulative frequency curve.

Statistics




CSAT SMART PRACTICEDirections (Q. Nos. 1-5) Consider the table givenbelow

Class-interval Number of Cumulative(Age in years) employees frequency frequency

25-29 5 530-34 15 2035-39 22 4240-44 19 6145-49 9 70

From the above table find the following.1. Class size is

(a) 4.5 (b) 5(c) 4 (d) None of these

2. Mid value of class 40-44 is(a) 42.5 (b) 42(c) 43 (d) None of these

ANSWERS

1. (b) 2. (b) 3. (c) 4. (d) 5. (a)

EXPLANATIONS

1. Class size of 25-29 ie, 24.5- 29.5 is = (29.5 24.5)= 5

2. Mid value of the class interval 40-44 means midvalue of the class interval 39.5- 44.5 ie,

39.5 44.5 422+æ ö

=ç ÷è ø




Arithmetic Progression (AP)An arithmetic progression is a sequence in which terms increase or decrease by a constant number called the

common difference.(i) The sequence 2, 6, 10, 14, 18, 22 is an arithmetic progression whose first term is 2 and common difference

4.

(ii) The sequence 5 72, ,3, ,42 2 is an arithmetic progression whose first term is 2 and common

difference .An arithmetic progression is represented by a,(a + d), (a + 2d), (a + 3d) a + (n 1)dHere, a = first term

d = common differencen = number of terms in the progression

The general term of an arithmetic progression is given by Tn = a + (n - 1) d.

The sum of n terms of an arithmetic progression is given by S, = 2n

[2a + (n 1) d] or Sn = 2 [a + l]

where l is the last term of arithmetic progression.If three numbers are in arithmetic progression, the middle number is called the arithmetic mean of theother two terms.

If a, b, c are in arithmetic progression, then b = 2a c+

where b is the arithmetic mean.

Similarly, if n terms al, a2, a3 an are in AP, then the arithmetic mean of these n terms is given by

AM = 1 2 3 .na a a an

+ + +¼+

If the same quantity is added or multiplied to each term of an AP, then the resulting series is also an AP.If three terms are in AP, then they can be taken as (a d), a, (a + d).If four terms are in AP, then they can be taken as (a 3d), (a d), (a + d), (a + 3d).If five terms are in AP, then they can be taken as (a 2d), (a d), a, (a + d), (a + 2d).

Sequences & Series




EXERCISE60. If 4, 6, a are in AP. 4, 6, b are in GP and 4, 6, c

are in HP, determine the value of 3a + 2b c.(a) 35 (b) 30(c) 12 (d) 27.6

61. In a geometric progression, the sum of the firstand the last term is 66 and the product of thesecond and the last second term is 128. Determinethe first term of the series.(a) 64 (b) 64 or 2(c) 2 or 32 (d) 32

62. Ashok is employed in a firm which promises topay him a salary of ̀ 3000 per month for the firstyear and an increment of `1000 in his monthlysalary every succeeding year. How much does heearn from the firm in 20 yr?(a) ` 2500000 (b) ` 3000000(c) ` 3200000 (d) ` 4400000

ANSWERS

1. (b) 2. (b) 3. (b)

EXPLANATIONS

1. 4, 6 a in AP12 = 4 + a or a = 84, 6, b are in GP36 = 4b or b = 94, 6, c are in HP ie, 1/4, 1/6, 1/c are in AP

2/6 = (1/4) + (1/c)c = 12

3a + 2b c = 3 8 + 2 9 12 = 30

2. Let a be the first term and r be the common ratioof the GP.From the given problem

a + arn 1 = 66 ...(i)Also, ar arn 2 = 128Þ a2rn 1 = 128 ...(ii)From Eq. (ii), again, a . arn 1 = 128

ar n 1 = 128/aSubstituting this in Eq. (i),

a + 128/a = 66a2 66a + 128 = 0

a = 2[( 4 ] / 2b b ac a- ± -




A Civil Servant should be well-versed in basics of Number System. In the Civil Services Aptitude Test Paper2, in Basic Numeracy, certainly there will be asked some questions based on types of, and operations on numbers.

In Indian system, numbers are expressed by means of symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, called digits. Here, 0is called insignificant digit whereas 1, 2, 3, 4, 5, 6, 7, 8, 9 are called significant digits. We can express a number intwo ways.

Notation: Representing a number in figures is known as notation as 350.Numeration: Representing a number in words is known as numeration as Five hundred and forty five .

Place Value (Indian)

Crore Lakh Thousand UnitTen Crore Crore Ten Lakhs Lakh Ten Thousands Thousand Hundred Tens One

100000000 10000000 1000000 100000 10000 1000 100 10 1108 107 106 105 104 103 102 101 100

Place Value (International)

Million Thousand UnitHundred Ten Millions One Million Hundred Ten Thousand Hundred Tens OneMillions Thousands Thousands

100000000 10000000 1000000 100000 10000 1000 100 10 1108 102 106 105 104 103 102 101 100

EXERCISE

Number System

1. Which of the following is a multiple of 88 ?(a) 1392578 (b) 138204(c) 1436280 (d) 143616

2. Which of the following fractions is less than 7/8and greater than 1/3 ?(a) 1/4 (b) 23/24(c) 11/12 (d) 17/24

3. If the numbers : 169 248 416 974 612 325 and

517 are arranged in descending order based onthe sum of the digits of each of these numbers,the middle number will be(a) 248 (b) 517(c) 612 (d) 974

4. Which of the following is true, if a = 3/4, b = 4/5and c = 5/6?




(a) a < c < b (b) a < b < c(c) c < a < b (d) b < a < c

5. In the array 48392874362754869364, thenumber of instances where an even number isfollowed by two odd numbers is(a) 1 (b) 2(c) 3 (d) 4

6. How many integers from 1 to 100 exist such thateach is divisible by 5 and also has 5 as a digit ?(a) 10 (b) 11(c) 12 (d) 20

7. If x is an even integer, which of the following isan odd integer ?(a) 3x + 2 (b) 7x(c) 8x + 5 (d) x3

8. When the integer n is divided by 6, the remainderis 3. Which of the following is not a multiple of 6?(a) n 3 (b) n + 3(c) 2n (d) 3n.

ANSWER

1. (d) 2. (d) 3. (b) 4. (b) 5. (c)6. (b) 7. (c) 8. (d)

EXPLANATIONS

1. Only 143616 is a multiple of both 11 and 8 so it isa multiple of 88.

2.78 = 0.875, 3 = 0.333, 1 = 0.25,

2324 = 0.958

7 10.875, 0.333,8 3= =

1 230.25, 0.9584 24= =

11 170.916, 0.70812 24

= =

Clearly, 0.708 lies between 0.333 and 0.875.\ Required fraction is 17/24.

3. 1 + 6 + 9 = 16 ... (ii)2 + 4 + 8 = 14 ...(iii)4 + 1 + 6 = 11 ...(v)9 + 7 + 4 = 20 ...(vi)6 + 1 + 2 = 9 ...(vii)3 + 2 + 5 = 10 ...(vi)5 + 1 + 7 = 13 ...(iv)

\ The middle number will be 517.

4. a = 3 0.754=

b = 4 0.8005=

c = 5 0.8336=

\ a < b < c5. In the array 48392874362754869364; 8, 2 and 6

ie, three number of required instances.6. These numbers are following

5, 15, 25, 35, 45, 50, 55, 65, 75, 85, 95So, total 11 such type of numbers.

7. If x is an even integer, then clearly 8x will also bean even integer.So, 8x + 5 will be an odd integer.

8. If n is divided by 6 and the remainder is 3, then n 3 and n + 3 are divisible by 6.

2n is also divisible by 6.But, 3n is not divisible by 6.




A fraction is a part of the whole (object, thing, region). It forms the part of basic aptitude of a person to haveand idea of the parts of a population, group or territory. Civil servants must have a feel of fractional thinking. eg,5

12 , here 12 is the number of equal part into which the whole has been divided, is called denominator and 5 is

the number of equal parts which have been taken out, is called numerator.

Example1: Name the numerator of 37 and denominator of

5 .13

Solution: Numerator of 37 is 3.

Denominator of 5

13 is 13.

Lowest Term of a FractionDividing the numerator and denominator by the highest common element (or number) in them, we get the

fraction in its lowest form.

eg, To find the fraction 6

14 in lowest form Since 2 is highest common element in numerator 6 and denominator

14 so dividing them by 2, we get 3 .7 Which is the lowest form of

6 .14

Equivalent FractionsIf numerator and denominator of any fraction are multiplied by the same number then all resulting fractions

are called equivalent fractions.

eg, 1 2 3 4, , ,2 4 6 8 all are equivalent fractions but

12 is the lowest form.

Fractions




Example 2: Find the equivalent fractions of 25 having numerator 6.

Solution: We know that 2 3 = 6. This means we need to multiply both the numerator and denominator by3 to get the equivalent fraction.

Hence, required equivalent fraction ´= = =

´

2 2 3 65 5 3 15

EXERCISE1. 1.4 is equal to which of the following?

(a)1410 (b)

149

(c)1490 (d)

139

2. HCF of 3, 2.7 and 0.09 is(a) 3 (b) 0.03(c) 9 (d) 0.09

3. LCM of 0.54, 1.8 and 7.2 is(a) 21.6 (b) 2.16(c) 216 (d) 0.216

4. 0.009 ? = 0.01(a) 9 (b) 0.9(c) 0.09 (d) 0.0009

5.1

0.04 = ?

(a) 0.025 (b) 0.25(c) 2.5 (d) 25

6. HCF of 0.4, 0.9, 0.5 is(a) 0.1 (b) 0.4(c) 0.2 (d) 0.01

7. LCM of 0.25, 0.5, 0.3 is(a) 0.1 (b) 0.15(c) 1.5 (d) 10

8. Ascending order of 10 12 5 11, , and13 17 6 21 , is

(a)10 12 5 11, , ,13 17 6 21 (b)

11 12 10 5, , ,21 17 13 6

(c)5 10 11 12, , ,6 13 21 17 (d)

5 10 12 11, , ,6 13 17 21

9. Descending order of 15 11 13 1, , ,16 20 25 3 , is

(a)15 11 13 1, , ,16 20 25 3 (b)

1 13 11 15, , ,3 25 20 16

(c)1 11 13 15, , ,3 20 25 16 (d)

15 13 11 1, , ,16 25 20 3

ANSWERS

1. (d) 2. (b) 3. (a) 4. (b) 5. (d)6. (a) 7. (c) 8. (b) 9. (a)

EXPLANATIONS

1. 1.4 = 1 + 0.4 = +419 =

139

2. HCF of 3, 2.7 and 0.09or 3.00, 2.70 and 0.09First we find the HCF of 300, 270 and 9 which is3\ HCF of 3, 2.7 and 0.09 is = 0.3

3. Given numbers are 0.54, 1.8 and 7.2 or 0.54, 1.80and 7.20Without the decimal points, numbers are 54, 180and 720LCM of 54, 180 and 720 = 2160\ LCM of given numbers = 21.60 or 21.6

4. Let0.009

x = 0.1

Þ0.0090.01 =

0.91 = 0.9

5.1

0.04 = ´

´

1 1000.04 100 =

1004 = 25

6. Q HCF of 4, 9 and 5 = 1




\ HCF of 0.4, 0.9 and 0.5 = 0.17. Given numbers are 0.25, 0.5 are and 0.3 or 0.25,

0.50 and 0.30Now, LCM of 25, 50 and 30 = 150\ LCM of 0.25, 50 and 30 = 1.50 = 1.5

8.1013 = 0.76,

1217 = 0.70,

56 = 0.82,

1121 = 0.52

\ ascending order is 11 12 10 5, , ,21 17 13 6

9.1516 = 0.93,

1120 = 0.55,

1325 = 0.52,

13 = 0.34

\ descending order is 15 11 13 1, , ,16 20 25 3




In our day-to-day life, we get plenty of data in form of powers of numbers. To have a feeling of what theymeasure we need to have an exact idea of indices and surds. There may be some kit items in CSAT, specificallydesigned to test proficiency of candidates in indices and surds.

IndicesIn the expression xn, n is called the exponent or index and x is called the base and xn is read as x to the power

of n or x raised to the power n .eg,1. 36 = 3 3 3 3 3 3 = 729

43 = 4 4 4 = 64The expression (xm)n is read as x raised to the power m whole raised to the power n .2. (24)3 = (16)3 = 212

The expression nmx is read as x raised to the power m power n .

3. 342 = 264

Hence, (xm)n ¹ nmx

Laws of Indices

1. am an = am + n 2.m

naa

= am n (a ¹ 0)

3. (am)n = amn 4. (ab)m = am bm

5. æ öç ÷è ø

mab =

m

mab

(b ¹ 0) 6. a0 = 1 if (a ¹ 0)

7. a n = 1na

if (a ¹ 0) 8.1na = n a is called the nth root of a.

9. mna = n ma is called the nth root of am.

Indices and Surds




10. When the bases of two numbers are equal, then their powers are also equal.eg, If 3n = 32, then, n = 2.

11. When the powers of two numbers are equal, then their bases are equal.eg, If a3 = 43, then a = 4.Where a is a positive real number and n is a rational number.

EXERCISE1. Which of the following is the greatest?

(a) 333333 (b) 333333

(c) 333333 (d) 333333

2. If 2

22 2xæ ö=ç ÷

è ø, then x is equal to

(a) 4 (b) 2(c) 1 (d) 2

3.323 8

3 75 5 ?

5´

=

(a) 5 (b) 25 (c) 3 5 (d) 1

4.2 1)

25 (2 ) 10 (2 ?

10

k k

k

- -

+

´ + ´=

(a)1

8 (5 )k´(b)

116 (5 )k´

(c)1

32 (5 )k´(d)

14 (5 )k´

5.44

4 ?ab ba ab

-æ ö-

=ç ÷ç ÷-è ø

(a)2

2ab

(b)ab

- (c)ab (d)

ab

6. If 3x+1 + 32x+1 = 270, then x is equal to(a) 1 (b) 2(c) 0 (d) 4

7. Determine a possible value of x from the equation5x 2 23x/x+1 = 4.(a) 0 (b) 4(c) 2 (d) 3

8. The least value of 3x + 3 x is(a) 2 (b) 1(c) 0 (d) 2/3

9. Given t = 3 32 4 2+ + , determine the value of t3 6t2 + 6t 2.

(a) 0 (b) 1(c) 2 (d) 2

0. If a = 5 and b = 6, find the value of (a b)b a +(b a)a b.(a) 1 (b) 1(c) 0 (d) 2

11. In Republic Day Parade, 6440 NCC cadets wereasked to stand in rows to form a perfect square. Itwas fond that 40 NCC cadets were left out. Whatwas the number of NCC cadets in each row?(a) 40 (b) 80(c) 64 (d) 60

ANSWERS

1. (d) 2. (c) 3. (a) 4. (b) 5. (d)6. (b) 7. (c) 8. (a) 9. (a) 10. (c)

11. (b)

EXPLANATIONS

1. 333333 is the greatest number.

2.2

22æ öç ÷è ø

= 2x Þ 2 22

´ = 2x

Þ 22 = 2x Þ 2 = 2x

Þ x = 1

3. 323 8

3 75 5

5´

= 23 8/3

7/35 5

5´

= 2 8 73 3 35+ - = 5

4.2 1

25 (2 ) 10 (2 )

10

k k

k

- -

+

´ + ´=

5 2 1

2 22 [5 2 10 2 ]

2 5k k

- -

+ +

´ + ´

´

= 225 / 4

4 5k+´=

116 5k´




5.44

4ab ba ab

-æ ö-ç ÷ç ÷-è ø

=41/4 1/4 1/4

1/4 1/4 1/4[[ ]

b a ba a b

-é ù-ê ú

-ê úë û=

41/4

1/4ba

-é ùê úê úë û

=ab

6. 1 2 13 3x x+ ++ = 270Let 3x = t

3t + 3t2 = 270t2 + 10t 90 = 0

(t + 10) (t 9) = 0t = 9 = 3x

32 = 3x

x = 27. 5x 2 23x/(x + 1) = 4

5x 2 23x/(x + 1) = 50 22

Equation the indicates of equal bases,x 2 = 0 and 3x/(x + 1) = 2From both these questionsx = 2

8. Let 3x + 3 x = aLet 3x = K

Then, a = K + 1/K = (K2 +1)/Kie, K2 Ka + 1 = 0

For this to have real roots, the discriminant shouldbe greater than or equal to 0.ie, a2 4 ³ 0or a ³/2/2a ³ 2or a < 2

(not possible)Least value = 2.

9. t = 3 32 4 2+ +

t 2 = 3 34 2+

= 22/3 + 21/3 = 21/3 (1 + 21/3)(t 2)3 = [21/3 (1 + 21/3)]3 = 2(1 + 21/3)3

= 2[1 + 2 + 3 21/3 (1 + 21/3)]0. a = 5 and b = 6

(a b)b a + (b a)a b

= ( 5 + 6) 6 + 5 + ( 6 + 5) 5 + 6

= (1) 1 + ( 1)1 = 1 1 = 011. Remaining NCC cadets = 6440 40 = 6400

So, NCC cadets in each row = 6400 = 80




In compound interest, the interest is added to the principal at the end of each period and the amount thusobtained becomes the principal for the next period. The process is repeated till the end of the specified time.

If P = PrincipalR = Rate per cent per unit time

Time = n yearsA = Amount; CI = Compound Interest

When the interest is compounded annually

Amount after n years = A = 1100

nRP æ ö+ç ÷

è ø

Compound Interest = 1100

nRP Pæ ö+ -ç ÷

è ø= 1 1

100

nRPé ùæ öê ú+ -ç ÷ê úè øë û

Important Formulae1. If the rate of interest differs from year to year ie, R1 in the first year, R2 in the second year, R3 in the third

year. Then, A = 31 21 1 1100 100 100

RR RP æ öæ öæ ö+ + +ç ÷ç ÷ç ÷

è øè øè ø

2. When the principa changes every year, we say that the interest is compounded annually. Then,

A = 1100

nRP æ ö+ç ÷

è ø

3. When the principal changes as per every six months, we say that the interest is compounded half yearly orsemi-annually. Then,

A =

2

21100

nRPæ öç ÷

+ç ÷ç ÷ç ÷è ø

Compound Interest




EXERCISE1. What annual payment (in rupees) will be

discharge a debt of ` 7620 due in 3 yr at 216 %3

per annum compound interest?(a) ` 2540 (b) ` 3260(c) ` 3380 (d) ` 3430

2. A man borrows ` 12500 from a bank at 20%compound interest. At the end of every year hepays ` 2000 as part repayment. How much (inrupees) does he still owe to the bank after threesuch instalments?(a) 15600 (b) 12864(c) 13780 (d) 14320

3. A sum of ` 390200 is to be paid back in threeequal annual instalments. How much is eachinstalment, if the rate of interest charged is 4%per annum compounded annually?(a) ` 140608 (b) ` 120560(c) ` 10000 (d) ` 18000

4. A sum of ` 2400 deposited at CI, doubled after 5yr. After 20 yr it will become(a) ` 24000 (b) ` 38400(c) ` 19200 (d) Can t be determined

ANSWERS

1. (d) 2. (d) 3. (a) 4. (b)

EXPLANATIONS

1. Let that annual payment be x.7620 =

2 3

100 100 1002 2 2100 16 100 16 100 163 3 3

x

é ùæ ö æ ö æ öê úç ÷ ç ÷ ç ÷ê ú+ +ç ÷ ç ÷ ç ÷ê úç ÷ ç ÷ ç ÷+ + +ç ÷ ç ÷ ç ÷ê úè ø è ø è øë û

Þ 7620 =6 36 2167 49 343

x é ù+ +ê ú

ë û

Þ 7620 =294 252 216

343x + +é ùê úë û

Þ x =7620 343

762´

= ` 3430

2. Remaining amount after 1 year

= 12012500 2000100

´ -

= ` 13000Remaining amount after 2 year

= 12013000 2000100

´ -

= ` 13600Remaining amount after 3 year

= 12013600 2000100

´ -

= ` 143203. Let each instalment be ̀ x

The amount to be paid in instalments = ̀ 390200The total value of all the three instalments is

2 325 25 2526 26 26

x xé ùæ ö æ ö æ öê ú+ +ç ÷ ç ÷ ç ÷ê úè ø è ø è øë û

and this must be equal to ` 390200

\ 25 25 625126 26 676

x é ù´ + +ê ú

ë û = 390200

Þ x = ` 140608

4. 2P = 5

1100RP æ ö

+ç ÷è ø

Þ 24 P =20

1100RP æ ö

+ç ÷è ø

Þ The amount becomes 24 times = 16 times andrequired amount = ` 2400 16 = ` 38400




AreaThe area of a plane figure is the measure of the surface enclosed by its boundary. The area of a triangle or a

polygon is the measure of the surface enclosed by its sides.

1. Triangle

Area of the triangle = 1 Base Height2

æ ö´ ´ç ÷

è ø=

12

bh

Area of the triangle, D = ( )( )( )s s a s b s c- - -

Where s = 1 ( )2

a b c+ +

Perimeter of the triangle = a + b + c or 2sRadius of incircle of a triangle = D/s

2. Right-Angles Triangle

Area = 12

bh

Hypotenuse, d = 2 2b h+ (Pythagoras theorem)Perimeter = b + d + h

3. Isosceles Right-Angled Triangle

Area =1 ( )2

a a´ =2

2a

Hypotenuse, d = 2 2a a+ = 2a

Perimeter = 2a + 2a

A

B C

a

b

c h

A

B C

h d

b

Area of Plane Figures




EXERCISE

1. What is the area of the region enclosed by thearea below?

12

10

20

(a) 116 (b) 144(c) 176 (d) 179

2. The length and breadth of a rectangular hall are40 m and 30 m respectively. What is the distancebetween two opposite corners of the hall?(a) 20 m (b) 35 m(c) 50 m (d) 40 m

3. The sides of a triangle are in the ratio 1 1 1: :2 3 4

and its perimeter is 104 cm. The length of thelongest side (in cm) is(a) 26 (b) 32(c) 48 (d) 52

4. A rectangular field has dimensions 25 m by 15m. Two mutually perpendicular passage, 2 mwidth have been left in its central part and grasshas been grown in rest of the field. The areas (insq metres) under the grass is(a) 295 (b) 299(c) 300 (d) 375

ANSWERS

1. (c) 2. (c) 3. (c) 4. (b)

EXPLANATIONS

1. Area of ABCD + Area of CEFG

12 mA

D

C

E F

G

10

8

B12 8

= 12 10 + 7 8 = 1762. Distance between two corners of hall

= 2 2(Length) (Breadth)+

= 2 2(40) (30)+ = 1600 900+ = 50 m

3. Let the sides of triangle are 1 1 1, and2 3 4

x x x

\1 1 12 3 4

x x x+ + = 104

6 4 312

x x x+ += 104 \ x =

104 1213´

= 96

\ Longest side = 2x

=962 = 48 cm

4. Area under the grass

15 m

25 m

= 25 15 (25 2 + 15 2 2 2)= 375 (50 + 30 4) = 299 sq m




PointA point is defined by its position. It has no length, width or thickness. A straight line joining two points is the

shortest distance between them. Three or more points are said to be collinear, if there is a line which contains allof them.

LineA line is defined by its length and has no breadth. It has length units. (metre, foot, centimetre kilometre, etc.).A line contains infinite points. Through a given point, there pass infinite lines. One and only one straight line

passes through two distinct points. Three or more lines are said to be concurrent, if they pass, through one pointand that point is called the point of concurrence. Two lines are said to be intersecting lines, if they have acommon point.

AngleWhen two straight lines meet at a point, they are said to form an angle. Angles generally are measured in

degrees. There are 180 in a straight line and a full circle constitutes 360 .1. Two angles are said to be complementary, if their sum is 90 . Complement of x is (90 x).

A

B

C

O

In the adjoining figure, Ð AOC + Ð BOC = 90 .\ Ð AOC and Ð BOC are complementary to each other.

2. Two angles are said to be supplementary, if their sum is 180 . Supplement of x is (180 x).

A B

C

O

180 Oq

Ð AOC + Ð BOC = 180 .\ Ð AOC and Ð BOC are supplementary to each other.

Concepts of Geometry




EXERCISE1. How many sides has a regular polygon whose

interior angle is 11 times its exterior angle ?(a) 21 (b) 24 (c) 18 (d) 26

2. Two angles of a regular polygon are 100 eachand each of the remaining angles is 130 . Findthe number of sides of the polygon.(a) 5 (b) 6 (c) 4 (d) 7

3. The ratio of the measure of an interior angle of aregular nonagon to the measure of each of itsexterior angles is :(a) 3 : 5 (b) 2 : 7(c) 1 : 4 (d) 4 : 7

4. In the given figure, find x

A B

C

D E

F

2x 3x

x+20 x

3xx

(a) 72 (b) 76(c) 70 (d) 74

5. ABCD is a rhombus, ÐC = 80 . Find Ð ABC(a) 90 (b) 120(c) 100 (d) 70

ANSWERS

1. (b) 2. (b) 3. (b) 4. (c) 5. (c)

EXPLANATIONS

1. Measure of each interior angle of n sides

= (2 4)90n

n- °

Measure of each exterior angle of n sides = 360

n°

\(2 4)90n

n- °

= 36011

n°

´

Þ 2n 4 = 11 360

90´ °

= 44

Þ 2n = 48 n = 242. Let the number of sides of a polygon be n.

Sum of interior angles = (2n 4) 90Þ 130(n 2) + 100 + 100 = (2n 4) 90Þ 130n 260 + 200 = 180n 360Þ 50n = 300Þ n = 6Hence, the number of sides of the polygon is 6.

3. Each exterior angle of a regular nonagon

= 360

9°

= 40

Each interior angle of a regular nonagon

= (2 9 4) 909

´ - ´ ° = 140

Required ratio = 40 : 140 = 2 : 74. ABCDEF is a hexagon. Sum of the interior angles

of a hexagon = (2 6 4) 90 = 720Þ (x + 20) + x + 3x + 2x + 2x + x = 720Þ 10x + 20 = 720Þ 10x = 700Þ x = 70

5. As ABCD is a rhombus.ÐA = ÐC = 80

[In a rhombus opposite angles are equal]A D

B C80o

ÐA + ÐB+ ÐC + ÐD = 360[Sum of the angles in a quadrilateral is 360 ]

(ÐA + ÐC) + (ÐB + ÐD) = 360(80 + 80) + 2 ÐB = 360[ÐB = ÐD opposite angles in a rhombus are equal]Þ 2ÐB = 360 160 = 200Þ ÐB = 100




Coordinate Geometry is also called Analytical Geometry. It is that branch of geometry in which we use twonumbers called coordinates to indicate the position of a point in a plane.

Cartesian Coordinate SystemThe horizontal line x is called the x-axis and the vertical line y oy is called the y-axis and together they are

called the coordinate axes. The point of intersection of these two axes is called the origin. Let P be any point in aplane. From P draw perpendiculars to the coordinate axes meeting the x-axis in M and y-axis in N. Here, OM(x)is the x-coordinate or absicssa of a point P. Similarly, ON(y) is the y-coordinate or ordinate of point P.

y

x

y

x

3N P(2,3)

1 2MO

21

y

x

This position of the point P in the plane with respect to the coordinate axes is represented by the ordered pair(x, y) and this system is called the cartesian coordinate system.

The coordinates of the origin O are (0, 0). Also, x ox and y oy divide the plane into four regions called quadrants.1. xoy is quadrant I. Here, x-coordinate is positive and y-coordinate is positive. (+,+)2. x oy is quadrant II. Here, x-coordinate is negative and y-coordinate is positive. ( , +)3. x oy is quadrant III. Here, x-coordinate is negative and y-coordinate is negative. ( , )4. xoy is quadrant IV. Here, x-coordinate is positive and y-coordinate is negative. (+, )

eg,(1,5) lies in first quadrant( 2,3) lies in second quadrant( 2, 4) lies in third quadrant(4, 2) lies in fourth quadrantThe coordinate of origin is (0, 0).The ordinate of every point on x-axis is 0.The ordinate of every point on y-axis is 0.

y

x x

y

II ( ,+)

I (+, +)

O

III ( , )

IV (+, )

Coordinate Geometry




EXERCISE1. The image of the origin with respect of the straight

line 4x + 3y 25 = 0 is(a) (2, 3) (b) (8, 6)(c) ( 8,6) (d) (6, 8)

2. If x + y + =0 and lx 5y 5 = 0 represent thesame line, then l + is equal to(a) 1 (b) 0(c) 4 (d) 1

3. If the points (x, 2), ( 3, 4) and (7, 1) are collinear,then the value of x is(a) 1 (b) 0(c) 2 (d) 2

4. When the graph of a linear equation is plotted, italways comes to be(a) curve (b) straight line(c) circle (d) parabola

5. Look at the following figure. What is the area ofsquare ABCD?

y

3 B(1,5)

4

C(5,2)

O

D(2,-2)

XA(-2,1)

y

(a) 20 (b) 25(c) 30 (d) 35

ANSWERS

1. (b) 2. (c) 3. (a) 4. (b) 5. (b)

EXPLANATION

1. Let equation of perpendicular line AC is3x 4y + l = 0It passes through (0, 0)\ l = 0it 3x 4y = 0The point of intersections of AC and DE isB (4, 3).Let C(x1, y1) be the image point of A. Then, B isthe mid point of AC.

\ 4 = 10 ,2x+

3 = 102

y+

Þ x1 = 8, y1 = 6Hence, required point is (8, 6).

2. Since, lines x + y + m = 0 and l x 5y 5 = 0represents the same line.

\1l

=15-

= 5m

-

Þ m = 1 Þ l + m = 5 + 1 = 43. Since, the given points are collinear.

\

2 13 4 1

7 1 1

x-

-= 0

Þ x (4 + 1) 2( 3 7) + 1 (3 28) = 0Þ 5x + 20 25 = 0Þ 5x = 5Þ x = 1

4. When the graph of linear equation is plotted, italways a straight line.

5. Now, BD = 2 2(2 1) ( 2 5)- + - - = 50

and AC = 2 2(5 2) (2 1)+ + - = 50

\ Area of square ABCD = 1 50 502

´ ´ = 25




Fundamental Principles of CountingFundamental Principle of Multiplication: If there are two jobs such that one of them can be completed

in n ways and second job can be completed in n ways, then the two jobs in succession can be completed in m nways.

Fundamental Principle of Addition: If there are two jobs such that they can be performed independentlyin m and n ways respectively, then either of the two jobs its can be performed in (m + n) ways.

Example 1: Find the number of ways in which n different prizes can be distributed among m (< n) persons,if each is entitled to receive at most n 1 prizes.

Solution. Total number of ways = m m ... to n times = mn

The number of ways in which one gets all the prizes = mThe required number of ways = mn mExample 2: There are 4 candidates for the post of a lecturer in Mathematics and one is to be selected by votes

of 5 men. Find the number of ways in which the votes can be given.Solution. Each man can vote for one of the 4 candidates and this can be done in 4 ways.Similar is the case with every other man. (\Repetition is

allowed)Hence, 5 men can vote in 45 ie, 1024 ways.

PermutationsEach of the arrangements which can be made by taking some or all number of things is called a permutation.Thus, the permutations which can be made by taking the letters a, b, c two at a time are 6. ie, ab, bc, ac, ba,

cb and ca. Each of these presenting a different arrangement of two letters. These six arrangements are calledpermutations of three things taken two at a time.

Permutation &Combination




EXERCISE1. Ten coins are tossed simultaneously. In how many

of the outcomes will the third coin turn up a head?(a) 3 28 (b) 3 29

(c) 210 (d) 29

2. If 10 persons meet at a meeting and shake handsexactly once with each other, what is the totalnumber of hand shakes?(a) 10 9 8 7 6 5 4 3 2 1(b) 10 10(c) 10 9(d) 45

3. N persons stand on the circumference of a circleat distinct points. Each possible pair of persons,not standing next to each other, sings a two-minute song one pair after the other. If the totaltime taken for singing is 28 minutes, what is N?(a) 5 (b) 7(c) 9 (d) None of these

4. In a chess competition involving some boys andgirls of a school, every student had to play exactlyone game with every other student. It was foundthat in 45 games both the players were girls andin 190 games both were boys. The number ofgames in which one player was a boy and theother was a girl is(a) 200 (b) 216(c) 235 (d) 256

ANSWERS

1. (d) 2. (d) 3. (b) 4. (a)

EXPLANATIONS

1. Total number of ways=2 2 1 2 2 2 2 2 2 2 = 29

2. Required number of ways = 10C2 = 10 9

2´

= 45

3. 2 (NC2 N) = 28 NC2 N =14

( )12

N NN

-- = 14

N2 N 2N = 28

Þ (N 7)(N + 4) = 0\ N = 7 as N ¹ 4

4. Let there were g girls and b boys. Number ofgames between two girls = gC2 Number of gamesbetween two boys = bC2

\( )1

2g g -

= 45

g2 g 90 = 0(g 10)(g + 9) = 0 \ g = 10 as g ¹

9

Also, ( )12

b b -= 190

b2 b 380 = 0(b 20)(b + 190) = 0 b = 20 as b ¹ 19

\ The total of games= (g + b)C2 = 30C2 = 30 29

2 1´

´

= 435\ Number of games in which one player is a boyand the other is a girl = 435 45 190 = 200




ProbabilityProbability is used to indicate a possibility of an event to occur. It is often used synonymously with chance.

(i) In any experiment if the result of an experiment is unique or certain, then the experiment is said to bedeterministic in nature.

(ii) If the result of the experiment is not unique and can be one of the several possible outcomes then theexperiment is said to be probabilistic in nature.

Various Terms Used in Defining Probability(i) Random Experiment: Whenever an experiment is conducted any number of times under identical

conditions and if the result is not certain and is any one of the several possible outcomes, the experiment iscalled a trial or a random experiment, the outcomes are known as events.eg, When a die is thrown is a trial, getting a number 1 or 2 or 3 or 4 or 5 or 6 is an event.

(ii) Equally Likely Events: Events are said to be equally likely when there is no reason to expect any one ofthem rather than any one of the others.eg, When a die is thrown any number 1 or 2 or 3 or 4 or 5 or 6 may occur. In this trial, the six events areequally likely.

(iii) Exhaustive Events: All the possible events in any trial are known as exhaustive events. eg, When a dieis thrown, there are six exhaustive events.

(iv) Mutually Exclusive Events: If the occurrence of any one of the events in a trial prevents the occurrenceof any one of the others, then the events are said to be mutually exclusive events. eg, When a die is thrownthe event of getting faces numbered 1 to 6 are mutually exclusive.

Classical Definition of ProbabilityIf in a random experiment, there are n mutually exclusive and equally likely elementary events in which n

elementary events are favourable to a particular event E, then the probability of the event E is defined as P (E)

P(E) = Favourabel Events

Total number of Events = ( )( )

n E mn S n

=

Probability




EXERCISE1. A box of electronic diode contains 120 standard

and 80 sub-standard ones. Two diodes are takenat random. What is the probability that one isstandard and the other is sub- standard ?

(a)96

199 (b)1633 (c)

24100 (d)

833

2. A box contains 20 white, 30 black, 40 blue and30 red balls. Compute the probability that one ofthe balls extracted at random from the box turnsout to be white, black or red.

(a)34 (b)

35 (c)

13 (d)

23

3. If seven coins are tossed, what is the probabilityof obtaining at least 2 heads ?

(a)1216 (b)

1516 (c)

1518 (d)

1520

4. If one rolls a fair-sided die twice, what is theprobability that the die will land on the samenumber on both the occasions ?

(a)112 (b)

16 (c)

124 (d)

18

ANSWERS

1. (a) 2. (d) 3. (b) 4. (b)

EXPLANATIONS

1. Total number of diodes are 200.\Probability of getting one standard diode andone sub-standard diode

= 120 80

1 1200

2

C CC

´=

120 80200 199

2

´

´ =

96199

2. Probability that the extracted ball is blue

=40

120 =13

\ Probability that the extracted ball is not blue

=113

- =23 .

3. Probability of getting no head = 7

072

C= 1

128

Probability of getting one head = 7

172C

= 7128

Probability of getting at least 2 heads

= 1 71128 128

- - = 120128 =15

164. Let E = Event of getting same number on both

occassions= (1, 1), (2, 2), (3, 3), (4, 4),

(5, 5), (6, 6)\ n(E) = 6

\Required probability = 26

6 =16




PercentagePer cent means per hundred . It is given by % symbol. Here x% means x per hundred or .

100x

Thus, any

percentage can be converted into an equivalent fraction by dividing it by 100.

eg 20% = 20 1 ;

100 5= 150% =

150 3100 2

=

Also, any fraction or decimal can be converted into its equivalent percentage by multiplying with 100.

eg 1 1 1005 5= ´ = 20%;

3 3 1002 2= ´ = 150%.

Important Formulae

1. Percentage increase = Increase 100

Original value´

2. Percentage decrease = Decrease 100

Original value´

3. If the price of the commodity increases by r% then the reduction in consumption so as not to increase the

expenditure is 100 %100

rr

é ù´ê ú+ë û

4. If the price of the commodity decreases by r% then the reduction in consumption so as not to increase the

expenditure is 100 %100

rr

é ù´ê ú-ë û

5. If A s income is r% more than B s income then B s income is less than A s income by 100 %100

rr

é ù´ê ú+ë û

.

6. If A s income is r% less than B s income then B s income is more than A s income by 100 %100

rr

é ù´ê ú

ë û.

Percentage




7. Let the population of a town be P and it increases at the rate of r% per annum, then

(a) Population after n years = 1100

nrP æ ö+ç ÷

è ø

(b) Population n years ago = 1100

nPræ ö

+ç ÷è ø

8. Let the present value of the machine be P and if it depreciates at the rate of r% per annum.

(a) Value of machine after n years = 1100

nrP æ ö-ç ÷

è ø

(b) Value of machine n years ago = 1 100

nn

rP æ ö-ç ÷

è ø

EXERCISE1. If the number of a fraction is increased by 150%

and the denominator is increased by 300%, the

resultant fraction is 5 .12

What was the original

fraction?

(a)23 (b)

13

(c)35 (d)

25

2. The boys and girls in a college are in the ratio of3 : 2. If 25% of the boys and 20% girls are adults,percentage of students who are minor is(a) 75% (b) 77%(c) 80% (d) None

3. The radius of a circle is increased by 2%. Thepercentage increase in the area is(a) 2.02% (b) 4.04%(c) 3% (d) 4%

4. If P is a % more than Q and Q is b% less than P,then(a) 1/a 1/b = 100 (b) 1/a 1/b = 1/100(c) 1/a + 1/b = 100 (d) 1/b 1/a = 1/100

ANSWERS

1. (a) 2. (b) 3. (b) 4. (d)

EXPLANATIONS

1. Let the original fraction =xy

New fraction = 250100400100

x

y =5

12 Þ250400

xy =

512 Þ

58

xy =

512

Þxy =

812 =

23

2. Suppose boys = 3x and girls = 2xNumber of minors= (75% of 3x) + (80% of 2x)

=75 803 2

100 100x xæ ö æ ö

´ + ´ç ÷ ç ÷è ø è ø

=9 84 5x x+ =

7720

x

Required percentage = 77 1 10020 5

xx

æ ö´ ´ç ÷

è ø= 77%

3. Initially let the radius be 100 m.Increase radius = 102 m

Original area = {p (100)2} m2

New area = [p (102)2] m2




Increase % = 2 2

2(102) (100) %

(100)ì üp´ - p´ï ïí ý

p´ï ïî þ

= (102 100)(102 100) %

100+ -

= 202 2 %

100´

= 4.04%

4. P is a% more than Q.P = Q + Q a/100

= Q (1 + a/100)= (Q/100) (100 + a) ...(i)

Q is b% less than P.Q = P P b/100

= (P/100) (100 b) ...(ii)Multiplying (i) and (ii), we get

PQ = (PQ/100)2 (100 + a)(100 b)(100 + a) (100 b) = 1002

1002 + 100(a b) ab = 1002

100(a b) = ab(a b)/ab = 1/100

ie, 1/b 1/a = 1/100




Cost PriceThe price at which an article is purchased is called the cost price or CP.

Selling PriceThe price at which an article is sold is called the selling price or SP.

FormulaeGain or Profit = SP CP

Gain per cent or Profit per cent = Gain Profit100 or 100CP CP

æ ö æ ö´ ´ç ÷ ç ÷

è ø è ø

SP = 100 Profit % CP

100+æ ö

´ç ÷è ø

Similarly, Loss = CP SP

Loss per cent = Loss 100CP

æ ö´ç ÷

è ø; SP =

(100 Loss%) CP100-

´

The Profit and Loss per cent is always calculated on the cost price.If a trader professes to sell his goods at CP but uses false weight, then Gain per cent or Profit per cent

= Error 100 %

True Value Erroræ ö

´ç ÷-è ø

Marked Price or List PricePrice that is indicated or marked on the article is called marked price or MP.

DiscountIt is reduction given on the Marked Price or List Price of an article.

d per cent = 100 discount ;

MP´

Selling Price = (100 %)

100d MP-

´

Profit and Loss




SP = 90% of ` 500 = ` 90 500

100æ ö

´ç ÷è ø

= ` 450

Sale price = ` 423

Additional discount = 27 100

450æ ö

´ç ÷è ø

= 6%

EXERCISE1. A shopkeeper marks his goods at such a price that

he can deduct 20% for cash and yet make 20%profit. The marked price of an item which costhim ` 180 is(a) ` 270 (b) ` 240(c) ` 245 (d) ` 260

2. A dealer buys an article marked at ` 40000 with20% and 10% off. He spends ̀ 1200 on its repairsand sells it for ` 30000. What is his gain or lossper cent?(a) 10% gain (b) 10% loss(c) no profit no loss (d) None of the above

3. Successive discount of 10% and 10% areequivalent to a single discount of.(a) 19% (b) 20%(c) 21% (d) 18%

ANSWERS

1. (a) 2. (c) 3. (a)

EXPLANATIONS

1. CP = ̀ 180,Gain = 20%

\ SP = ` 120 180100æ ö

´ç ÷è ø

= ` 216

Let the MP be ` x.Then, 80% of x = 216

80100

x´ = 216

Þ x =216 100

80´

= 270

Thus, MP is ` 270.2. CP = (80% of 90% of ` 40000) + ` (1200)

= ̀ 80 90 40000 1200

100 100é ùæ ö

´ ´ +ê úç ÷è øë û

= ` (28800 + 1200) = ` 30000\ CP = ` 30000 and SP = ` 30000So, no gain no loss in the transaction.

3. Let the CP be ` 100. Then,SP = 90% of 90% of ` 100

= ̀ 90 90 100

100 100æ ö

´ ´ç ÷è ø

= ̀ 81

\ Single discount = (100 81)% = 19%




RatioThe ratio of two quantities a and b is the fraction

ab and is expressed as a : b. Here a is the first term or

antecedent and b is the second term or consequent. Since the ratio expresses the number of times one quantitycontains the other, it is an abstract (without units) quantity.

A ratio remains unaltered if its numerator and denominator are multiplied or divided by the same number.eg, 4 : 3 is the same as (4 10) : (3 10) ie, 40 : 30.

20 : 15 is the same as 20 15:5 5

æ ö æ öç ÷ ç ÷è ø è ø

ie, 4 : 3.

A ratio is said to be a ratio of greater or less inequality or of equality according as antecedent is greater than,less than or equal to consequent .

If a > b, then a : b is called a ratio of greater inequality (eg, 4 : 3, 5 : 2, 11 : 3, ...)If a < b, then a : b is called a ratio of less inequality (eg, 3 : 4, 2 : 5, 3 : 11, ...)If a = b, then a : b is called a ratio of equality (eg, 1 : 1, 3 : 3, 5 : 5, ...)

From this we find that(i) If a > b and some positive number is added to each term of a : b, then the ratio is diminished.

If a > b, then (a + x) : (b + x) < a: b.(ii) If a < b and some positive number is added to each term of a : b, then the ratio is increased.

If a < b, then (a + x) : (b + x) < a : b.(iii) If a = b and some positive number is added to each term of a : b, then the ratio is unaltered. If a = b, then

(a + x) : (b + x) = a : b

Kinds of RatiosDuplicate Ratio: a2 : b2 is called duplicate ratio of a : b.Triplicate Ratio: a3 : b3 is called triplicate ratio of a : b.

Sub-Duplicate Ratio: :a b is called sub-duplicate ratio of a : b.

Sub-triplicate Ratio : 3 3:a b is called sub-triplicate ratio of a : b.

Ratio & Proportion




EXERCISE1. The ratio of expenditure and savings of a person

is 26: 3. If his monthly income is ` 7250, thenwhat is his monthly savings.(a) ` 290 (b) ` 350(c) ` 750 (d) ` 780

2. ` 750 is distributed in A, B and C such that A : B= 5 : 2, B : C = 7: 13 then what is A s part ?(a) ` 140 (b) ` 250(c) ` 260 (d) ` 350

3. 60m of a uniform wire weight 80 kg. What will141 m of the same wire weight ?(a) 144 kg (b) 188 kg(c) 288 kg (d) 282 kg

4. Ratio between two numbers is 5 : 6 and sum oftheir squares is 549. The numbers are(a) 10, 12 (b) 15, 18(c) 20, 24 (d) 30, 36

5. Ratio between three numbers is 1 : 2 : 3 and sumof their squares is 504. The numbers are(a) 6, 12, 18 (b) 3, 6, 12(c) 4, 8, 24 (d) 2, 4, 8

ANSWERS WITH SOLUTIONS

1. (c) 2. (d) 3. (b) 4. (b) 5. (a)

EXPLANATIONS

1. Let monthly expenditure = 26x and monthlysavings = 3xThen, monthly income = 26x + 3x = 29x

\ 29x = 7250Þ x = 250

\ Monthly savings = ` 3 250 = ` 750

2. A : B = 5 : 2 = 5 :12

B : C = 7 : 13 = 131 :7

A : B : C = 5 13:1 :2 7 = 35 : 14 : 26

\ A s part =3575075

´ = ` 350

3.6080 =

141x

Þ x = 188 kg4. Let the two numbers be 5x and 6x respectively.

(5x)2 + (6x)2 = 549Þ 25x2 + 36x2 = 549Þ 61x2 = 549Þ x2 = 9Þ x = 3

So, the two numbers are 5x and 6x ie, 15 and 18respectively.

5. Let the three number be x, 2x and 3x respectively(x)2 + (2x)2 + (3x)2 = 504Þ 14x2 = 504Þ x2 = 36Þ x = 6

So, the three numbers are x, 2x and 3x ie, 6, 12and 18 respectively.




PartnershipWhen two or more than two persons run a business jointly, they are called partners in the business and the

deal between them is known as partnership.Partnership is of two types

1. Simple Partnership2. Compound Partnership

1. Simple Partnership: When investments of all the partners are for the same period of time, the profit orloss is distributed among the partners in the ratio of their original investments.

Suppose A and B invest ` p and ` q respectively for a year in a business, then at the end of the year. Shareof A s profit (loss) : Share of B s profit (loss) = p : q.

2. Compound Partnership: When investments of all the partners are for different period of time, thenequivalent capitals are calculated for a unit of time and the profit or loss is divided in the ratio of the product oftime and investment.

Suppose A and B invest ` p and ` q for x months and y months respectively, then Share of A s profit (loss):Share of B s profit (loss) = px : qy.

Partners are of two types(i) Working Partner, and

(ii) Sleeping Partner(i) Working Partner: A partner who manages the business is called a working partner.

(ii) Sleeping Partner: A partner who only invests the money is called a sleeping partner.Example 1: A and B started a business with capitals of ` 25000 and ̀ 40000 respectively. Find the share of

A and B out of an annual profit of ` 6500.Solution. Ratio of shares of A and B = Ratio of their investments = 25000 : 40000 = 5 : 8

A s share = ` 5 6500

13æ ö

´ç ÷è ø

= ` 2500

and B s share = ` 8 6500

13´ = ` 4000

Partnership




EXERCISE

1. A, B and C start a business with ̀ 12000. A s shareis half the sum of the shares of B and C. The shareof B is 2/3 of the sum of the shares of A and C.Then, the share of C is(a) ` 3200 (b) ` 4800(c) ` 4000 (d) ` 3000

2. A started a business with an investment of` 84000. After x months B joins A with a capitalof ` 42000. If the ratio of profit at the end of theyear is 3 : 1, then x is(a) 6 months (b) 2 months(c) 4 months (d) 3 months

3. A, B and C started a business with ` 45000. Iftheir profits are ` 2400, ` 4000 and ` 5600. Findthe investment of A.(a) ` 9000 (b) ` 15000(c) ` 21000 (d) ` 8000

4. A, B and C rented a pasture by paying ̀ 2160 permonth. They put 60, 40 and 20 sheep respectively.A sells 1/3 of his sheep to B after 6 months andafter 3 months more C sells of his sheep to A. Findthe rent paid by C at the 2/5 end of the year.(a) ` 4355 (b) ` 3888(c) ` 2464 (d) ` 6224

ANSWER

1. (a) 2. (c) 3. (a) 4. (b)

EXPLANATIONS

1. A + B + C = 12000 ...(i)

A =1 ( )2

B C´ +

Þ B + C = 2ABy substituting the value of B + C = 2A in Eq. (i),we get

3A = 12000Þ A = ` 4000

Also, B =2 ( )3

A C´ +

Þ A + C =32B

By substituting the value of A + C = 32B

in Eq.

(i), we get32B B+ = 12000

Þ52B

= 12000

Þ B =12000 2

5´

= ` 4800

Share of C = ` [12000 (4000 +4800)]

= ` [12000 8800]= ` 3200

2. Ratio of profits of A and B= (84000 12) : 42000 (12 x)

Þ84000 12

42000 (12 )x´

´ - = 31

Þ 42000 (12 x) 3 = 84000 12

Þ (12 x) = 84000 1242000 3

´

´= 8

Þ x = 4Hence, B joined after 4 months

3. The ratio of the profit of three persons= 2400 : 4000 : 56000 = 3 : 5 : 7

A s investment = ̀ 3 45000

15æ ö

´ç ÷è ø

= ` 9000

4. A : B : C = [(60 6) + (40 3) + (48 3)] : [(40 6)+ (60 6)] : [(20 9) + (12 3)]= (360 + 120 + 144) : (240 + 360) : (180 + 36)= 624 : 600 : 216 = 26 : 25 : 9Total rent to be paid at the end of the year

= ` (2160 12) = ` 25920Rent paid by C at the end of the year




A Civil Servant should be well-versed in concepts of Square Root & Cube Root. In the Civil Services AptitudeTest Paper 2, in Basic Numeracy, certainly there will be asked some questions from square roots and cube roots ofnumber to test fast calculation skills of a candidate.

Square RootThe square root of a number is that number the product of which itself gives the given number, ie, the square

root of 400 is 20, the square root of 625 is 25.The process of finding the square root is called evaluation. The square root of a number is denoted by the

symbol called the radical sign. The expression 9 is read as root time , radical nine or the square root ofnine .

How to Find the Square Root of an Integer?(i) By the method of Prime Factors: When a given number is a perfect square, we resolve it into prime

factors and take the product of prime factors, choosing one out of every two.Example 1: Find the square root of 4356.Solution.

2 43562 21783 10893 363

11 12111

4356 = 2 2 3 3 11 11 = 22 32 112

4356 = 2 3 11 = 66

Thus from the above example it is clear that in order to find the complete square root of a given number every primefactor of that number should be repeated twice. Thus, we can make a number which is not a perfect square, a perfectsquare by multiplying or dividing the number by those factors of it which are not contained in pairs.

Square Root & Cube Root




EXERCISE1. Find 3 0.027

0.125(a) 0.6 (b) 0.3(c) 0.5 (d) 0.2

2. The largest three digit number which is a perfectcube is(a) 986 (b) 729(c) 981 (d) 864

3. Simplify 3 729.(a) 9 (b) 3(c) 8 (d) 6

4. What is the smallest number by which 1400 bedivided to make it a perfect cube?(a) 130 (b) 145(c) 160 (d) 175

5. Evaluate 3 0.000729(a) 0.09 (b) 0.9(c) 9.0 (d) 0.009

6. The cube root of 5.832 is(a) 0.18 (b) 0.28 (c) 2.8 (d) 1.8

7. Find the least number by which 175760 bemultiplied to make it a perfect cube.(a) 100 (b) 160(c) 80 (d) 27

8. Find the least number by which 234375 be dividedto make it a perfect cube.(a) 20 (b) 8(c) 15 (d) 10

ANSWERS

1. (a) 2. (b) 3. (b) 4. (d) 5. (a)6. (d) 7. (a) 8. (c)

EXPLANATIONS

1. 3 0.0270.125 = 3 27 1000

1000 125´

´=

3

327

125

=3 3

3 335

= 35 = 0.6

2. 94 = 729 and 103 = 1000So the required number = 729

3. 729 = 227 = 27

\ 3 27 = 3 33 = 34. 1400 = 23 52 7

To make it a perfect cube, it must be divided by52 7 = 175

5. 36

72910

=3

3 672910

=3 3

3 69

10=

9100 = 0.09

6. 3 5.832 = 3 58321000 =

3

358321000 =

1810 =1.8

7. 175760 = 24 5 133

To make it a perfect cube it must be multiplied by22 52 = 100.

8. 234375 = 57 3To make it a perfect cube it must be divided by5 3 = 15.




In simplification of an expression there are certain laws which should be strictly adhered to. These laws areas follows:

VBODMAS RuleThis rule gives the correct sequence in which the mathematical operation are to be executed so as to find out

the value of a given expression.Here, V stands for Vicnaculum (or Bar), B stands for Brcket , O stands for Of , D stands for Division , M

stands for Multiplication , A stands for Addition and S stand for Subtraction .(a) Here, VBODMAS gives the order of simplification. Thus, the order of performing the mathematical

operations in a given expression areFirst : Virnaculum or line bracket or barSecond: BracketThird: OfFourth: DivisionFifth: MultiplicationSixth: Addition &Seventh: SubtractionThe above order should strictly be followed.

(b) There are four types of brackets.(i) Square brackets [ ]

(ii) Curly brackets { }(iii) Circular brackets ( )(iv) Bar or Virnaculum

Thus, in simplifying an expression all the brackets must be removed in the order , ( ) , { } and [ ] .

Simplification




EXERCISE1. If x and y are positive integers and

( )3.5

x y-=

47 ,

then(a) y < x (b) y > x(c) y = x (d) y > = x

2. In a fraction, if 2 is subtracted from thedenominator, the faction becomes 1. If 1 issubtracted from both the numerator and thedenominator, the fraction becomes 3/4. What isthe denominator of the fraction?(a) 6 (b) 7(c) 8 (d) 9

3. If x + y z = m and if, x y + z = n, then x is equalto(a) (m + n)/2 (b) m n(c) 2m + n (d) m + n

4. It is required to change a rupee coin into 2 paiseand 5 paise coins with the total number of coinsequal to 26. Find the number of each type of coins.(a) 10 and 16 (b) 12 and 14(c) 10 and 20 (d) 14 and 14

5. Given that 9/2x + 3y = 21 and 1/2x 8y = 4. Findthe value of 12x 12y.(a) 12 (b) 30(c) 25 (d) 60

6. Let A = (x + 1)/(x 1) and B = (x 1)/(x + 1).Determine the value of A B.(a) 0 (b) x/(x2 1)(c) 4x/(x2 1) (d) None of these

7. If the numerator of a fraction is double and thedenominator is increased by 3, the new fractionis 3/5. What is the original fraction, if itsdenominator is more than twice the numeratorby 1?(a) 3/7 (b) 6/13(c) 1/3 (d) 5/11

8. For what value of x, 8 + (x 3)2 have the leastvalue?(a) 3 (b) 0(c) 3 (d) 5

9. 3.7 (10)7 is equal to(a) 370000 (b) 3700000(c) 37000000 (d) 370000000

10. 2( 5 5)+ is equal to(a) 5 (b) 10(c) 15 (d) 20

ANSWERS

1. (a) 2. (d) 3. (a) 4. (a) 5. (d)6. (c) 7. (a) 8. (c) 9. (c) 10. (d)

EXPLANATIONS

1. 3.5x y-

=47 \ x y = 2

As x and y are positive integersSo, x > y.

2. Suppose the fraction is xy .

So, 2x

y - = 1

x = y 2 ...(i)

11

xy-

- = 34

4x 4 = 3y 34x = 3y + 1 ...(ii)

4(y 2) = 3y + 1y = 9

3. x + y z = m and x y + z = nAdding the above two we have,2x = m + n or, x = (m + n)/2.

4. Let x be the number of 5 paise coins, then (26 x)will be the number of 2 paise coins.So, x5 + (26 x)2= 100

5x + 52 2x = 1003x = 48

x = 16Number of 5 paise coins = 16Number of 2 paise coins = 26 16 = 10

5. 9/2x + 3y = 21 ...(i)1/2x 8y = 4 ...(ii)




Adding Eqs. (i) and (ii),10/2x 5y = 25

5x 5y = 25x y = 5

12x 12y = 12 5 = 60.

6. A B = 1 11 1

x xx x+ -

-- +

= 2 2

2( 1) ( 1)

1x x

x+ - -

-

2 2

21 2 1 2

1x x x x

x+ + - - +

-= 2

41

xx -

7. Let the fraction be 2 1x

x +

Then, 2

2 1 3x

x + +=

35 Þ 10x = 6x + 12

Þ 10x 6x = 12 Þ x = 3

So, the fraction is 37 .

8. Clearly for x = 3, given expression has least value.9. 3.7(107) = 37000000

10. 2( 5 5)+

2(2 5)4 5 = 20




Highest Common FactorThe highest common factor of two or more given numbers is the largest of their common factors. It is known

as GCD also.eg, Factors of 20 are 1, 2, 4, 5, 10, 20

Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36Here greatest and common factor of 20 and 36 is 4.\ HCF of 20 and 36 is 4.

Least Common MultipleThe least common multiple of two or more given numbers is the least of their common multiples.eg, Multiple of 25 are 25, 50, 75, 100, 125, 150, 175, ....

Multiple of 30 are 30, 60, 90, 120, 150, 180, 210, ....Here 150 is least common multiple of 25 and 30\ LCM of 25 and 30 is 150.

Using Division MethodExample 1: Determine the HCF and LCM of 36, 48, 64 and 72.Solution. To find HCF

36 ) 48 ( 1 36 12 ) 36 ( 3

36

12 ) 64 ( 560

4 ) 12 ( 3 12 4 ) 72 (18

432 32

\ HCF of 36, 48, 64 and 72 is 4.

HCF & LCM




To find LCM2 36, 48, 64, 722 18, 24, 32, 362 9, 12, 16, 182 9, 3, 4, 93 3, 1, 4, 34 1, 1, 4, 1

1, 1, 1, 1LCM = 2 2 2 2 3 4 = 576

EXERCISE1. The HCF of 168, 189 and 231 reduced by 8, gives

(a) 13 (b) 14(c) 17 (d) 21

2. Among the surds 3 32, 4, 2 and 4 6 the largestone is(a) 2 (b) 3 4(c) 3 2 (d) 4 6

3. The GCD and LCM of two numbers are 66 and384 respectively. If the first number is divided by2, the resulting answer is 66. The second numberis(a) 192 (b) 196(c) 384 (d) 576

4. The LCM and GCD of two numbers are 240 and16 respectively. If the two numbers are in the ratio3 : 5, the numbers are(a) 24,40 (b) 21,35(c) 36,60 (d) 48,80

5. The LCM of two numbers is 280 and the ratio ofthe numbers of 7 : 8. Find the numbers.(a) 70 and 48 (b) 42 and 48(c) 35 and 40 (d) 28 and 32

ANSWERS

1. (a) 2. (b) 3. (a) 4. (d) 5. (c)

EXPLANATIONS

1. HCF of 168, 189, 231 is 21Required number = 21 8 = 13

2. 2 = (64)1/12

3 4 = (256)1/12

3 2 = (16)1/12

3 6 = (216)1/12

\ 3 4 is largest.83. First number= 66 2 = 132

\ 132 second number = GCD LCM132 x = 66 384

x = 19284. Suppose two numbers are 3x and 5x.

Then, 3x 5x = GCD LCM15x2 = 16 240

x2 = 256\ x = 16

85. Let the two numbers are 7x and 8x and LCM is56x.It is given that LCM = 280ie, 56x = 280 and x = 5ie, numbers are 35 and 40.




According to the syllabus of Civil Services Preliminary Exam CSAT Paper II, some questions may be askedfrom orders of magnitude . So, the deep study of this chapter is necessary. In this chapter, we study the increasingor decreasing order related to distance, time, area etc.

Example 1: Ajay, Akshay and Saroj cover a distance of 133 km2 , 33500 m and 290 hactometre respectively

in an hour. Who has the maximum speed?

Solution. Distance covered by Ajay = 133 km2 = 67 1000 m = 33500 m

Distance covered by Akshay = 33500 mDistance covered by Saroj = 290 hactometre

= 290 100 m = 29000 mSince, distance covered by Ajay and Akshay are maximum and equal. Hence, Ajay and Akshay have maximum

speed.

EXERCISE1. In the women cricket team of 11 players, each of

four players Mithali Raj, Anjum, Jhulan andSharda are replaced by a new player of 28 yr,then the following respective changes occur.(i) Average age of team decreases by 0.5 yr(ii) Average age of team decreases by 1 yr(iii) Average age of team increases by 0.5 yr(iv) Average age of team decreases by 0.75 yrWhich of the following players has maximumage?(a) Mithali Raj (b) Anjum(c) Jhulan (d) Sharda

2. HCF of 105, 150 and 210 is x, HCF of 126, 396,

1080 is y and HCF of 440, 180 and 280 is z. Whichof the following is greatest?(a) x (b) y(c) z (d) All are equal

3. A and B can do a piece of work in 72 days, B andC can do it in 120 days, A. and C can do it in 90days. Who is more efficient?(a) A (b) B(c) C (d) Can t be determined

4. Which is smallest among 3 1 2, ,4 3 7 and

3 ?5

Orders of Magnitude




(a)34 (b)

13 (c)

27 (d)

35

5. There are two rooms of size 1m x 1m x 1m and 95cm x 90 cm x 115 cm. Which one is morevacuumed?(a) First room (b) Second room(c) Both are equal vacuumed(d) Can t be determined

ANSWERS

1. (b) 2. (c) 3. (a) 4. (c) 5. (a)

EXPLANATIONS

1. Age of Mithali Raj = 28 + 11 0.5 = 33.5 yearAge of Anjum = 28 + 11 1 = 39 yearAge of Jhulan = 28 11 0.5 = 22.5 yearAge of Sharda = 28 + 11 0.75 = 36.25

yearHence, Anjum is oldest.

2. HCF of 105, 150, 210105 = 3 5 7150 = 2 3 52

210 = 2 3 5 7\ x = 3 5 = 15HCF of 126, 396, 1080

126 = 2 3 3 7396 = 2 2 3 11

1080 = 2 2 2 3 3 3 5y = 2 3 3 = 18

HCF of 440, 180, 280440 = 2 2 2 5 11180 = 2 2 5 3 3280 = 2 2 2 5 7

\ z = 2 2 5 = 20Hence, z is maximum.

3. Combined efficiency of A and B = 1

72 ...(i)

Combined efficiency of B and C = 1

120 ...(ii)

Combined efficiency of A and C =190 ...(iii)

Adding Eqs (i), (ii) and (iii),

2 (A + B + C) =1 1 1

72 120 90+ +

=5 3 4

360+ +

=12360 =

130

Þ A + B + C =160

\ Combined efficiency of A, B and C

=160 . ..(iv)

\ Subtracting Eq. (i) from Eq. (iv), we get

C s efficiency = 1 160 72

- =1

360Subtracting Eq. (ii) from Eq. (iv), we get

A s efficiency = 1 160 120

- =1

120Subtracting Eq. (iii) from (iv), we get

B s efficiency = 1 160 90

- =1

180Cearly, A is most efficient.

4.3 0.754= ,

1 0.333= ,

2 0.287= ,

3 0.605=

Clearly, 0.28 ie, 27 is smallest.

5. The room which has more volume is morevacuumed.Volume of first room = 1m 1m 1m= 1m3 = (100)3 cm3 = 1000000 cm3

Volume of second room = 95 cm 90 cm 115 cm= 983250 cm3

Clearly, first room is more vacuumed.




Unitary method is the basic area of arithmetic. In the CSAT paper this portion of Basic numeracy will helpyou to solve myriad problems.

Direct ProportionTwo quantities are said to be directly proportional, if on the increase in one the other increases proportionally

or on the decrease in one the other decreases proportionally.eg, More the numbers of articles, More is the cost.More the number of workers, More is the work done.Less the number of articles, Less is the cost.Less the number of workers, Less is the work done.

Indirect ProportionTwo quantities are said to be indirectly proportional, if on the increase in one the other decreases proportionally

or on the decrease in one the other increases proportionally.eg, More the number of workers, less is the number of days required to finish a work. More the speed, less is

the time taken to cover a certain distance.Less the number of workers, more is the number of days required to finish a work. Less the speed, more is the

time taken to cover a certain distance.

Chain RuleWhen a series of variables are connected with one another, that we know how much of the first kind is

equivalent to a given quantity of second, how much of the second is equivalent to a given quantity of the thirdand so on. The rule by which we can find how much of the last kind is equivalent to a given quantity of the firstkind is called the Chain Rule.

Example 1: If 12 apples cost ` 216, what is the cost of 3 dozen apples ?Solution. Let the required cost be ` x. Also, 3 dozen apples = 35 apples more apples, more cost (Direct

Proportion);Apples Cost in `

12 21636 x

12 x = 36 216 Þ x = ´36 21612 = ` 648

Unitary Method




EXERCISE1. If 24 men working 9 h a day can do a piece of

work in 36 days, in how many days will 18 menworking 6 h a day do double the work?(a) 144 days (b) 120 days(c) 136 days (d) 152 days

2. A camel can walk a certain distance in a desert in48 days when it rests at an Oasis 6 h each day.How long will the camel take to walk half thedistance, if it walks at half the speed and reststwice as long each day?(a) 66 days (b) 72 days(c) 76 days (d) 68 days

3. 5 men can complete a work in 12 days and 9women take 20 days to complete the same work.How many days will 6 men and 12 women taketo complete the work?(a) 8 days (b) 6 days(c) 4 days (d) 7 days

4. 6 men and 10 children can do a piece of work in24 days. A child takes double the time to do awork than the man. In how many days 8 mencan complete the work?(a) 33 days (b) 36 days(c) 32 days (d) 39 days

ANSWERS

35. (a) 36. (b) 37. (b) 38. (a)

EXPLANAIONS

1. Let the required number of days be x.Less men, More days (Indirect Proportion)Less working hours, More days (IndirectProportion)

More work, More days (Direct Proportion)Men Hours Work Days24 9 1 3618 6 2 x

Þ x = 24 9 2 3618 6 1

´ ´ ´ = 144 days

2. In the first case the camel wlks (24 6) h= 18 h with a speed s covering a distance d .In the second case the camel works (24 12) h

= 12 h with a speed 2s

covering a distance 2d

.

Less distance, Less days (Direct Proportion)Less speed, More days (Indirect Proportion)Less hours, More days (Indirect Proportion)

Distance Speed Hours Daysd s 18 48

2d

2s

12 x

Þ x = 2 18 48

2 12x s

d s´

´ ´ ´´

= 72 days

3. 1 man can complete the work in (5 12) days =60 days1 women can complete the work in (9 20) days= 180 days

1 man 1 days work = 1 ,160 woman s 1 days work

= 1

180 (6 men + 12 women) 1 days work

= 1 16 1260 180

æ ö´ + ´ç ÷

è ø=

1 110 15æ ö

+ç ÷è ø

=5

30 =16

\ 6 men and 12 women will finish the work in 6days.

4. 2 children = 1 man Þ (6 men + 10 children) = 11menLet the required number of days be x.Less men, More days (Indirect Proportion)

Men Days11 248 x

Þ x =11 24

8´

= 33 days




AverageThe average of a given number of quantities of the same kind is expressed as

Average = Sum of the quantities

Number of the quantitiesAverage is also called the Arithmetic Mean.Also, Sum of the quantities = Average Number of the quantities

Number of quantities = Sum of the quantities

Average

If all the given quantities have the same value, then the number itself is the average.If all the given quantities are not all the same, then the average of the given quantities is alwaysgreater, then the smallest number and always less than the largest number. Equivalently, atleast oneof the numbers is less than the average and atleast one is greater then the average.If each of the given quantities is increased by a constant p, then their average is also increased by p.If each of the given quantities is decreased by a constant p, then their average is also decreased by p.If each of the given quantities is multiplied by a constant p, then their average is also multiplied by p.Whenever the given quantities form an arithmetic sequence and if the given quantities has odd terms,then the average is the middle term in the sequence and if the given quantities has even terms, thenthe average of the sequence is the average of the middle two terms.In order to calculate the weighted average of a set of numbers, multiply each number in the set by thenumber of times it appears, add all the products and divide by the total number of numbers in the set.If the speed of an object from A to B is x km/h and from B to A is y km/h,then the average speed during

the whole journey is 2 km/hxyx y+ .

If the average of N1 quantities is x and N2 quantities is y then the average of total (N1 + N2) quantities

is given by 1 2

1 2

( )N x N yN N

+

+

Average




EXERCISE1. Five years ago the average age of four men is 48

yr. Now, a new man joins and the average ageincreases by 2 yr. What is the age of the new man?(a) 36 yr (b) 42 yr(c) 41 yr (d) 38 yr

2. The mean yearly salary of an employee of acompany was ` 20000. The mean yearly salariesof male and female employees were ` 20800 and` 16800 respectively. Find the ratio of males tofemales employed by the company(a) 3 : 2 (b) 4 : 1(c) 2 : 1 (d) 5 : 3

3. Average of two numbers is 14.5 and square rootof their product is 10. What are the numbers ?(a) 16 and 9 (b) 25 and 4(c) 4 and 16 (d) 25 and 9

4. The average age of a group of four men whoseages are in the ratio 2 : 3 : 4 : 5 is 42 yr, what isthe age of the eldest person in this group ?(a) 60 yr (b) 48 yr(c) 36 yr (d) 24 yr

ANSWERS

1. (d) 2. (b) 2. (b) 3. (a)

EXPLANATIONS

1. Sum of the ages of the four men five year ago= (48 4) year = 192 year

Present sum of the ages of the four men= (192 + 5 4) year = 212 year

Now, 50 =212 Age of the new man

5+

\ Age of the new man = (50 5 212) year= 38 year

2. Let the number of males be x and the number offemales be y.Sum of the salaries of the men = 20800xSum of the salaries of the females = 16800y

Now, 20000 =20800 16800x

x y+

+

Þ 20000 (x + y) = 20800x + 16800yÞ 800x = 3200y

Þxy =

41 Þ x : y = 4 :

13. Let the number be a and b. Then,

2a b+

= 14.5

Þ a + b = 29Þ ab = 10Þ ab = 100

(a b)2 = (a + b)2 4ab=(29)2 (4 100)= 441Þ (a b) = 21

On solving a + b = 29 and a b = 21, we get a =25 and b = 4.

4. Let the ages of the four men be 2x, 3x, 4x and 5xyear respectively.

Then, 42 =2 3 4 5

4x x x x+ + +

Þ 14x = 42 4

Þ x =42 4

14´

= 12

Hence, the age of the eldest person = 5x = (5 12)year = 60 year




SolidAnything that occupies space is called a Solid. In addition to area, a solid figure has volume also. It has three

dimensions namely, length, breadth and height. For solid two different types of areas namely, lateral surfacearea or curved surface area and total surface area are defined.

1. PrismA solid having two congruent and parallel faces, called bases and whose other faces, the lateral faces are

parallelograms, formed by joining corresponding vertices of the bases is called a Prism.

2. Right PrismA prism in which bases are perpendicular to the lateral edges is called a Right Prism. The base of the prism

can be a polygon.In a right prism

(i) Number of lateral surfaces = Number of sides of the base of the prism(ii) Total number of surfaces of a prism = Number of lateral surfaces + 2

(iii) Lateral surface area = Perimeter of base Height(iv) Total surface area = Lateral surface area + 2 (Area of base)(v) Volume = Area of base Height

3. CuboidA right prism in which the base is a rectangle is called a Cuboid. If l is the length and b the breadth of the

base and h the height, then

h

I

b

Lateral surface area = 2 (l + b)h sq unitTotal surface area = 2(l + b)h + 2lb = 2 (lb + bh + lh) sq unitVolume = lbh cu unit

The longest diagonal of the cuboid = 2 2 2l b h+ + unit

Volume and SurfaceArea of Solid Figures




EXERCISE1. The area of the base of a rectangular tank is 6500

cm2 and volume of water contained in it is 2.6m3. The depth of water (in metres) in the tank is(a) 2.5 (b) 3(c) 4 (d) 5.5

2. A pyramid on a square base has four equilateraltriangles on its four other faces, each edge being10 m. Find its volume.(a) 200 m3 (b) 230.7 m3

(c) 235.7 m3 (d) 253.7 m3

3. Find the slant surface of a pyramid 21 cm high,standing on a square base of 40 cm side(a) 2320 cm2 (b) 2230 cm2

(c) 2330 cm2 (d) 2220 cm2

4. A bucket of the shape of the frustum of a cone isof height 45 cm. If the radii of its edges are 28 cmand 7 cm then determine the capacity of the bucket(a) 48510 cm3 (b) 48550 cm3

(c) 45800 cm3 (d) 45830 cm3

ANSWERS

1. (c) 2. (c) 3. (a) 4. (a)

EXPLANATIONS

1. Let the depth of water be x m.

Then 6500

10000x´ = 2.6

x = 2.6 10000

6500´

= 4 m

2. Let OABCD be the given pyramid which has asquare base. The four faces of the pyramid areequilateral triangles.

A

D

B

C

X Z

O

\ each edge of the pyramid is 10 m

Volume = 1 area of base height3

´ ´

where area of base = (10)2 = 100

and height = 2 2OZ XZ-

= 2 2(5 3) 5- =5 2

\ Volume = 1 100 5 23

´ ´ = 235.7 m3

3. Let OABCD be the pyramid standing on a squarebase ABCD.Here OX = 21 cm, AB = BC = 40 cm

Þ XY = 12

AB = 20 cm

In DOXY,

A

D

B

C

X Z

O

OY = 2 2OX XY+

2 221 28+ = 29




\ Area of DOBC = 12

BC OY´ ´

= 1 40 292

´ ´

= 580 cm2

\ Slant surface of pyramid= 4 (D OBC)

(Q base is a square)= 4 580 = 2320 cm2

4. R = 28 cm, r = 7 cm, h = 45 cm

\ l = 2 2( )h R r+ -

= 2 2(45) (21)+




ClockA clock has 2 hands, the smaller one is called the hour hand or short hand while the larger one is called the

minute hand or long hand.The face of a clock is a circle which subtends an angle of 360 at the centre.

Some Important PointsIn every hour

1. (a) Both the I ands coincide once. At this point the angle between them is 0 ..(b) The hands are straight (point in opposite directions) once. At this point the angles between them are

180 .(c) The hands are twice perpendicular to each other. At this point the angle between them is 90 .

2. (a) In 60 min the minute hand covers 360 .

Thus, in 1 min the minute hand covers 360 660

°æ ö

= °ç ÷è ø

(b) In 12 h the hour hand covers 360 .

Thus, in 1 min the hour hand covers 360 1

12 60 2

°°æ ö

=ç ÷´è ø

Thus, in of to minute, the minute hand gains 1 16 5 ,2 2

°°æ ö

- =ç ÷è ø

than the hour hand.

3. (a) When the two hands are at right angles, they are 15min spaces apart.(b) When the two hands are in opposite directions, they are 30 min spaces apart.(c) In 60 min the minute hand gains 55 min on the hour hand.(d) The minute hand moves 12 times as fast as the hour hand.

4. (a) Too Fast: If a clock indicates 7 : 1.5, when the correct time is 7, it is said to be 15 min too fast.(b) Too Slow: If a clock indicates 7 : 30, when the correct time is 7 45 , it is said to be 15 min too slow.

Example 6: What was the day of the week on 26th June 1816 ?

Clocks and Calendar




EXERCISE1. The last day of February, 2006 was a

(a) Monday (b) Tuesday(c) Wednesday (d) Thursday

2. The time on the watch is 9 : 15 and the hour handpoints towards West. The direction of the minuteshand is(a) North (b) South(c) East (d) West

3. How much does a watch lose per day, if its handscoincide every 64 min ?(a) 96 min (b) 90 min

(c)103411 min (d)

83211 min

ANSWERS

1. (b) 2. (c) 3. (c)

EXPLANATIONS

1. The last day of February 2006 was Tuesday.2. So, when hour hand is pointing towards West,

then minute hand will be pointing towards Eastat 9 : 15.

3. Normally, hands of a watch coincide after 565

11 min.

So, lose per hour = 51 min

11

\ Lose per day = 524 1 min

11´ =

12024 min11

= 1034 min11




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SAMPLE MATERIAL

OF OUR STUDY KIT

REASONING

Under this we deal with different types of questions based on English Alphabets, which could be asked inCSAT.

Important Facts About Letters1. Position number of letters in English alphabets.

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¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 262. Position number of letters in English alphabets in reverse 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 Z¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯

26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 13. We know A, E , I, 0 and U are vowels of English alphabet and remaining letters are consonants of English

alphabets.4. A ® 4 M (A to M) letters are called first half of English alphabets.5. N ® 4 Z (N to Z) letters are called second half of English alphabets.6. To the left means Z ® A (Z to A)7. To the right means A ® Z (A to Z)8. From A ® Z (A to Z) letters are called left to right of English alphabets.9. From Z ® A (Z to A) letters are called right to left of English alphabets.

Types of Question Based on Alphabet TestThere are four types of questions based on Alphabet test:

Type I Arrangement According to DictionaryArranging words in alphabetical order implies to arrange them in the order as they appear in a dictionary .

For this arrangement, first we shall consider the first letter of each word. Arrange the words in the order in whichthese letters comes in the English alphabets.

Alphabet Test




Directions (Q. No. 1-10): In each of the followingQuestions, five words are given which of them willcome in the middle it all of them are arrangedalphabetically as in a distionary?

1. (a) Bishop (b) Bifocal(c) Bicycle (d) Bitter

2. (a) Parasite (b) Party(c) Petal (d) Paste

3. (a) Research (b) Rational(c) Round (d) Rustic

4. (a) Nature (b) Native(c) Narrate (d) Diastole

5. (a) Didactic (b) Dictum(c) Dictionary (d) Diastole

6. (a) Outrage (b) Outcase(c) Overture (d) Ovary

7. (a) Gradine (b) Gradient(c) Graduate (d) Grading

8. (a) Nozzle (b) Nausea(c) Nostril (d) Normal

9. (a) Prominent (b) Prohibit(c) Promise (d) Prolong

10. (a) Descant (b) Descent(c) Derive (d) Derrick(a) 41I (b) 6 # W

EXERCISEANSWERS WITH SOLUTION

1. (a) 2. (d) 3. (c) 4. (b) 5. (c)6. (d) 7. (d) 8. (d) 9. (d) 10. (d)

EXPLANATIONS

1. Bicycle, Bifocal, Bishop, Bitter, Brink2. Parasite, Party, Paste, Petal, Prick3. Rational, Research, Round, Rural, Rustic4. Narrate, Nascent, Native, Nature, Naughty5. Diastole, Dictate, Dictionary, Dictum, Didactic6. Outcast, Outrage, Ovary, Overtake, Overture7. Gradient, Gradine, Grading, Gradual, Graduate8. Nausea, Nomenclature, Normal, Nostril, Nozzle9. Programme, Prohibit, Prolong, Prominent, Promise

10. Derive, Derogate, Derrick, Descant, Descent




Here, we deal with the questions having information regarding arrangement. We are giving some objectsand then we have to arrange them according to information provided. Objects are arranged either in row or in acircle on the basis of such conditions. In some questions, we will also deal with other arrangements like square/pentagon/ hexagonal.

Different Types of Sitting ArrangementThere are two types of questions which are asked in various competitions

Type 1 Arrangement around a Closed PathIn such questions, we are giving some clues regarding arrangement. We have apply these clues on a circle

and using these information, we have to find the solutions of questions associated with them. In this arrangement,we also deal square/pentagon/ hexagon, questions.

Before solving type 1 questions, following facts are necessary to know.

For Circular ArrangementIn this arrangement some persons are sitting around a circle and they facing the centre.

LeftRight

1. Left movement also called clockwise rotation.2. Right movement also called anticlockwise rotation.

For Rectangular Arrangement

Right Left A B

C

DA « B (Fornt with each other) C « D (Front with wach other)

Sitting Arrangements




EXERCISEDirections (Q. Nos. 1 to 3) Read the followinginformation to answer the questions based on it.Seven letters are arranged in a line as follows

(i) E and F have one latter between them.(ii) G is to the right of A.

(iii) B is to the immediate left of F.(iv) There is one letter between D and A.(v) D is not G s neighbour

(vi) G and F have two letters between them.1. Which letter is second to the left of letter A?

(a) C (b) B(c) D (d) E

2. Which letter will be exactly in the middle of theletter series so obtained?(a) D (b) A(c) E (d) None of these

3. Which pair of the letters is adjacent to the letterB?(a) A and C (b) G and E(c) E and F (d) C and D

ANSWERS

1. (c) 2. (d) 3. (c)

EXPLANATIONS

Explanation (Q. Nos. 60 to 62) The given figureshows the arrangement of given seven letters :

D C A G E B F

60. Letter D is second to the left of letter A.61. It is clear from the diagram that letter G is in the

middle of the letter arrangement.62. Clearly, letters E and F are adjacent to B.

R Q

S

P V

T

U




The basic approach for the problems of this type is more or less similar to that of coding and decoding. Onehas to study the symbols or the geometrical figures and their meanings carefully. Then, the meanings are to beused in place of those symbols in answering the questions.

The questions can be categorised into two types

Symbols and NotationsSymbols for these types of questions stand for mathematical operations like +, , , , > , <, ³, £, = and #. So,

the students must replace the symbols by mathematical operations and apply the BODMAS rule to find the valueof the given expression. Other symbols which can be used are DÑ, *, @, $, etc, with proper definitions. Someexamples are given below

Example 1: If + means , means , means and means , and mean + then 15 3 15 + 5 2= ?

(a) 0 (b) 10(c) 20 (d) 6

Solution. (b) 15 3 = 15 + 5 2after changing the signs = 15 = 3 + 15 5 2 = 5 + 15 10 =10Example 2: If 2 * 3 = 12, 3 * 4 = 20 and 4 * 5 = 30, then 2 * 6 is

(a) 18 (b) 12(c) 21 (d) None of these

Solution. (c) The numbers on both sides of * are increased by one and then multiplied to get the answer.2*6 = 3 7 = 21Example 3: If x $ y = (x + y + xy 1) (x + y + xy + 1), then the value of (4 $ 10) is.

(a) 2915 (b) 2195(c) 2951 (d) 2955

Solution. (a) As per the definition of $, (4$10) would be (4 + 10 + 4 10 - 1) (4 + 10 + 4 10 + 1) = 2915. So,answer is (a)

Mathematical Operations




EXERCISEDirections (Q. Nos. 1 to 5) In the followingquestions, symbols Å, f, , @, have the followingmeaningsA Å B means A is not less than B .A f B means A is not less than or equal to B .A B means A is not less than or greater than to BA @ B means A is not greater than or equal to B .A B means A is not greater than B .Based on the statements given in each of the questionsbelow, find out which of the conclusions follows.Mark

(a) if only one I follows but not both(b) if either conclusion I or conclusion II follows(c) if neither conclusion I nor conclusion II follows(d) if both conclusion I as well as conclusion II follow91. Statements R Å C, C f T, T P

Conclusions I. R f PII. R P

92. Statements R Å C, C T, T Å PConclusions I. R f P

II. R P93. Statements R @ C, C Å T, T @ P

Conclusions I. C f PII. R @ T

94. Statements R C, C T, T f PConclusions I. R @ T

II. P C95. Statements R C , C @ T, T P

Conclusions I. R @ PII. P Æ C

ANSWERS

1. (a) 2. (b) 3. (c) 4. (c) 5. (d)




First we should know some mathematical operations. They are add (+), subtraction ( ), multiply ( ) anddivision ( ), greater than (>), less than (<). This test is set up to test candidates skill in mathematical operations.The questions involving these operations are set using artificial symbols. You are required to substitute the realsigns and solve the questions accordingly, to get the answer.

Different Type of QuestionsThere are three types of questions based on mathematical operations which are asked in various competitive

examinations. They are,

Problem-Solving by SubstitutionIn such type of questions you have some substitutes for various mathematical symbols or numerals followed

by a question involving calculation of an expression or choosing the correct/incorrect equation.

Rule BODMASBracketsOfDivisionMultiplicationAdditionSubtractionWhile solving a mathematical operations proceed according to the BODMAS formula.Example 1: If + means minus means divided by means plus and means multiplied by then

which of the following will be the value of expression 7 3.5 2 4 + 5 ?(a) 4 (b) 5(c) 11 (d) None of these

Solution. (b) Using the proper notations in the given expression, we have= 7 3.5 2 4 + 5 = 7 + 3.5 + 2 4 5= 2 + 2 4 5 = 2 + 8 5 = 10 5 = 5

Arithmetical Reasoning




EXERCISE41. Which of the following operations will result in

22?(a) 16 12 + 8 13 15(b) 16 12 8 13 + 15(c) 16 12 8 + 13 15(d) 16 + 12 8 13 15

42. If 6«5 = 31, 7«8 = 57, 3«4 = 13, then 9«10 = ?(a) 90 (b) 91(c) 81 (d) 19

43. If 879 = 8, 625 = 1 and 586 = 9 then, 785 = ?(a) 6 (b) 7(c) 8 (d) 9

44. If given, 12 (169) 5, 4 (20) 2 and 1 (26) 5 then 7(?) 3(a) 78 (b) 68 (c) 58 (d) 36

45. If 6 8 3 = 638, 9 0 2 = 920, then 5 7 4 =?(a) 574 (b) 745(c) 475 (d) 547

ANSWERS

1. (c) 2. (b) 3. (a) 4. (c) 5. (d)

EXPLANATIONS

1. According to the question,16 12 8 + 13 15

= 16 12 138´

+ 15

= 24 + 13 15= 37 15 = 22

Hence, option (c) is the correct answer.2. As, 6 « 5 = 6 5 + 1 = 31

7 « 8 = 7 8 + 1 = 57and 3 « 4 = 3 4 + 1 = 13Similarly, 9 « 10 = 9 10 + 1 = 91

3. 879 Þ (7 + 9) 8 = 8625 Þ (2 + 5) 6 = 1

and 586 = (8 + 6) 5 = 9Similarly, 785 Þ (8 + 5) 7 = 6

4. As, 122 + 52 Þ 144 + 25 = 16942 + 22 Þ 16 + 4 = 20

and 12 + 52 Þ 1 + 25 = 26Similarly, 72 + 32 = 49 + 9 = 58

5. As, 6 8 3 = 638and 9 0 2 = 920Similarly, 5 7 4 = 5 4 7




Meaning of AnalogyAnalogy means Similar items . There is three types of Analogy

(a) Number Analogy(b) Letter Analogy(c) Word Analogy

In questions based on analogy, a pair of numbers/letters/words is given that have certain relationship betweenthem. This pair is followed by a third numbers/letters/words. The candidate is required to identify the relationshipbetween the pair of numbers/letters/words given and find out the FOURTH numbers/letters/wore such that therelationship between the third and the fourth numbers/letters/words is similar to the relationship that existsbetween the first and the second numbers/letters/words.

Number AnalogyTypical relationships between the numbers in a given pair can be any of the following :One number is a multiple of the other.One number is the square or square root of the other.One number is the cube or cube root of the other.The two numbers can be consecutive, even, odd or prime numbers.

Example 1: 3 : 81 : : 6 : ?(a) 1296 (b) 1269(c) 1692 (d) 1926

Solution. (a) n : n4 relation here (3) and (3)4 = (81)Similarly, (6) and (6)4 = 1296Example 2: Find the missing term 10 : 100 : : ? : 121

(a) 10 (b) 11(c) 12 (d) 13

Solution. (b) Square of first term is the second term.102 = 100, so 112 = 121

Analogy




EXERCISE130. Machine is to mechanic as baby is to

(a) mother (b) pediatrician(c) ward (d) class Teacher

131. A mirror always (a) distorts(b) reflects(c) reveals the truth(d) retracts

132. The pair of words is given below. Words of thispair have certain relationship of each other. Thispair is followed by four pairs of words. Select apair of words out of these four pairs of words whosewords have the same relationship to each otheras the words of the original pair.Rectangle : Octagon(a) Pentagon : Heptagon(b) Cone : Sphere(c) Triangle : Hexagon(d) Angle : Quadrilateral

133. Three words which have something in commonamong themselves are given below. Choose thealternative which is most appropriate description

about the three words.Species : Genera : Family(a) These are biological terms(b) These give information about living things for

classification(c) These are trains of animal kingdom(d) These are groups of animals

ANSWERS

1. (a) 2. (b) 3. (c) 4. (a)

EXPLANATIONS

130. As machine is related to mechanic, similarly babyis related to mother.

131. A mirror always reflects.132. A rectangle has four sides while an octagon has

eight sides i.e., second has double side than first.Similarly, triangle has three sides while a hexagonhas six sides.

133. Species, genera and family are biological terms.




Alphabet ClassificationIn this type of classification, a group of jumbled letters, typically consisting a single or two or three or four

letters are put together. The pattern or order in which they are grouped is to be identified and students need tofind out which groups have the same pattern or relationship between the letters. There will be only one choice,which will have a different pattern from the rest and hence becomes the answer option.

Example 1: Find the odd one among the following.(a) LY (b) GU(c) DQ (d) JW

Solution. (b) Corresponding places in the first half and the second half of letters, except option (b).Find the odd man out.

(a) AK (b) CM(c) EP (d) DN

Solution. (c) Except EP {option (c)}, the rest has a gap of 10 letters between them.Example 2: Find the odd man out.

(a) A (b) D(c) Y (d) U

Solution. (d) Except option (d), the remaining letters represents the square number positions in Englishalphabet.

Number ClassificationIn such questions, students need to choose the odd number from the given options. The numbers may belong

to a particular pattern, i.e., they may be odd, even, prime, rational, squares, cubes and they may also be codedinto binary digits (0 s and 1 s), etc. and only one of the choices will not follow the same pattern.

Example 3 : Find the odd man out.(a) 35 (b) 55(c) 45 (d) 65

Solution. (c) Except option (c), the remaining are prime products of 5.Example 6 : Find the odd man out.

(a) 10 (b) 17(c) 26 (d) 38

Classification




Directions (Q. No. 1-10): Choose the word whichis look like the other words in the group

1. (a) House (b) Cottage(c) School (d) Palace

2. (a) Tamato (b) Cucumber(c) Brinjal (d) Carrot

3. (a) Brick (b) Heart(c) Bridge (d) Spade

4. (a) Hostel (b) Hotel(c) Inn (d) Club

5. (a) Kennel (b) House(c) Stable (d) Aviary

6. (a) Cow (b) Deer(c) Donkey (d) Rhinoceros

7. (a) Guava (b) Litchi(c) Papaya (d) Watermelon

8. (a) Turtle (b) Lamb(c) Colt (d) Bitch

9. (a) Rigveda (b) Yajurveda(c) Atharvaveda (d) Ayurveda

10. (a) Producer (b) Director(c) Investor (d) Financier

ANSWERS

1. (c) 2. (d) 3. (a) 4. (d) 5. (b)6. (c) 7. (d) 8. (d) 9. (d) 10. (b)

EXPLANATIONS

1. All except School are dwelling places.2. Carrot is the only vegetable which grows

underground.3. All except Brick are suits of cards.4. All except Club are places where people can stay.5. All except House are places to rear one or the other

animal.6. All except Donkey have horns.7. All except Watermelon grow on trees, while

watermelon grows on creepers.8. All except Bitch are young ones of animals, while

watermelon grows on creepers.9. AllExcept Ayurveda are names of holy scriptures,

the four Vedas. Ayurveda is a branch of medicine.

Example 12 : Find the odd man out.(a) Diamond (b) Bridge(c) Heart (d) Spade

Solution. (b) Except option (b), rest are the suits of cards.Example 13: Find the odd man out.

(a) Tailor (b) Barber(c) Carpenter (d) Blacksmith

Solution: (b) Except option (b) rest all require raw material to work.

EXERCISE




NUMBER SERIESPrime Number Series

Example 1. 4, 9, 25, 49, 121, 169,(a) 324 (b) 289(c) 225 (d) 196

Solution. (b) The given series is a consecutive square of prime number series. The next prime number is 289.Example 2. 5, 7, 13, 23,

(a) 25 (b) 27(c) 29 (d) 41

Solution. (d) The difference between prime numbers is increasing. 7 is next prime to 5; 13 is second to nextprime to 7; 23 is third to next to 13. Hence, next should be fourth to next prime to 23. Hence, required number is 41.

Multiplication SeriesExample 3. 4, 8, 16, 32, 64 256

(a) 96 (b) 98(c) 86 (d) 106

Solution. (a) The numbers are multiplied by 2 to get the next number.64 2 = 128

Example 4. 5, 20, 80, 320, 1280(a) 5120 (b) 5220(c) 4860 (d) 3642

Solution. (a) The numbers are multiplied by 4 to get the next number.1280 4 = 5120

Difference SeriesExample 5. 3,6,9,12,15, . 21

(a) 16 (b) 17(c) 20 (d) 18

Solution. (d) The difference between the numbers is 3.15 + 3 = 18

Series




Directions (Q. Nos. 1 to 82) Find the missing ternin each of the following series.

1. 2, 4, 8, 16, 32, 128(a) 64 (b) 65(c) 66 (d) 67

2. 35, 29, 24, 20(a) 14 (b) 15(c) 16 (d) 17

3. 4, 7, 5, 9, 11,7,13(a) 6 (b) 8(c) 9 (d) 3

4. 6,11,8,13, 15,12,17(a) 9 (b) 14(c) 11 (d) 10

5. 265, 295, 355, 385, . : ....(a) 544 (b) 454(c) 445 (d) 545

6. 5, 9, 17,33, 129(a) 55 (b) 45(c) 65 (d) 75

7. 11, 13, 17, 19, 29, 31(a) 25 (b) 26(c) 27 (d) 23

8. 2, 5, 3, 8, 5, 11, 6, 9(a) 12 (b) 13(c) 14 (d) 15

EXERCISE

9. 6, 5, 9, 10, 12, 15, 20, 18(a) 14 (b) 15(c) 16 (d) 17

10. 81, 86, 79, 84, 77, (a) 82 (b) 28(c) 83 (d) 38

SOLUTIONS1. (a) 2. (d) 3. (a) 4. (d) 5. (c)6. (e) 7. (d) 8. (d) 9. (b) 10. (a)

EXPLANATIONS

1. The series is + 2, + 4, + 8, + 16, and so on.2. The series is 6, 5, 4, 3, 2, and so on.3. The sequence consists of two series 4, 5, 6, and

7, 9, 114. The sequence consists of two series 6, 8, 10, and

11, 13, 15, .5. The sequence is + 30, + 60, + 30, + 60, and so

on.6. The sequence is + 4, + 8, + 16, + 32, and so on.7. The series is of prime number series.8. 2 + 3 = 5, 3 + 5 = 8, 5 + 6 = 11, missing number =

6 + 9 = 159. Sequence consists of two series 6, 9, 12, and 5,

10, 1510. The sequence is + 5, 7, + 5, 7, and so on.




What is Coding-Decoding ?For transmitting secret messages from one place to another, especially in defense services, Coding is used.

Decoding is the ability to break the secret code. The codes are based on various principles or patterns. In CSAT,questions based on coding-decoding could be given to judge the intelligence and mental ability of the candidates.

The coded word itself does not make any sense unless we know the coding principle. For coding-decoding,following basic knowledge is required.

1. Forward Order of LettersA B C D E F G H I1 2 3 4 5 6 7 8 9J K L M N 0 P Q R

10 11 12 13 14 15 16 17 18S T U V W X Y Z

19 20 21 22 23 24 25 26

2. Reverse Order of LettersA B C D E F G H I26 25 24 23 22 21 20 19 18J K L M N 0 P Q R

17 16 15 14 13 12 11 10 9S T U V W X Y Z8 7 6 5 4 3 2 1

3. Opposite LettersA-Z, H-S, B-Y, I-R, C-X, J-Q, D-W, K-P, E-V, L-0, F-U, M-N, G-T.The questions based on coding-decoding are broadly categorised into following categories

Coding-Decoding




EXERCISEDirections: The questions follows are based oncodes. Read the instructions carefully and answer.117. In, certain code, 95789 is written as TGKPT and

2436 is written as ALUR. How is 24539 written inthat code ?(a) ALEUT (b) ALGUT(c) ALUGT (d) ALGRT

118. If white is called blue, blue is called red, red iscalled yellow, yellow is called green, green is calledblack, black is called violet and violet is calledorange, then what would the colour of humanblood be ?(a) Red (b) Green(c) Yellow (d) Violet

119. In a certain language, MADRAS is coded asNBESBT. How is BOMBAY coded in the samelanguage ?(a) CPNCBX (b) CPNCBZ(c) CPOCBZ (d) CQOCBZ

120. In a certain code dog is coded as 496 , monkeyis coded as 893210 and pig is coded as 576 .Using this code how will you code the wordinkpen ?(a) 468016 (b) 732513(c) 735213 (d) 486108

ANSWER WITH SOLUTION

1. (b) 2. (c) 3. (b) 4. (b)

EXPLANATIONS

117. 95789 = TGKPT2436 = ALUR

24539 = ALGUT118. The colour of human blood is red and red is called

yellow. So, the colour of human blood is yellow.119. B O M B A Y C P N C B Z

+1+1

+1+1

+1+1

120. dog ® 496monkey ® 893210

pig ® 576inkpen ® 732513




What is Blood Relations ?Blood relation logical problems mainly deal with the hierarchical structure of a family i.e., grand-parents,

parents and children etc. Different relationships between the family members of different generations will begiven. To solve the questions related to blood relations, the entire family tree has to be drawn by putting thevarious relationships.

In such problems, the aptitude of candidate is shown by the knowledge of the various blood relations. Thetypical relationships that are commonly used in blood relation problems are summarized as followsv Father s or Mother s son = Brotherv Father s or Mother s daughter = Sisterv Father s or Mother s brother = Unclev Father s or Mother s sister = Auntv Father s or Mother s father = Grandfatherv Father s or Mother s mother = Grandmotherv Brother s or Sister s Son = Nephewv Brother s or Sister s Daughter = Niecev Uncle s or Aunt s son or daughter = Cousinv Sister s Husband = Brother-in-lawv Brother s wife = Sister-in-lawv Son s wife = Daughter-in-lawv Daughter s Husband = Son-in-lawv Husband s or wife s sister = Sister-in-lawv Husband s or wife s Brother = Brother-in-law

To develop a blood relation tree, some standard symbols are used in this chapter to indicate the relationshipsamong the family members. It is not compulsory to follow them, You can design your own symbols to draw thefamily tree quickly and accurately.v P is male = Pv P is female = Pv Gender of P is not known = Pv P and Q are married to each other P Û Qv P and Q are sibling = P « Q

Blood Relations




EXERCISEDirections (Q. Nos. 1 to 4) Read the followinginformation carefully and answer the questionsgiven below. There are six children playing footballnamely G, H, I, J, K and L. G and K are brothers. Lis the only sister of K. I is the only son of G s uncle.H and J are the daughters of the brother of I sfather.

1. How is J related to G ?(a) Sister (b) Niece(c) Cousin (d) Uncle

2. How is I related to L ?(a) Cousin (b) Son(c) Uncle (d) Brother

3. How many male players are there ?(a) One (b) Three(c) Four (d) Five

4. Showing the man receiving the prize Suraj saidHe is the brother of my uncle s daughter . Who

is the man to Suraj?(a) Brother (b) Nephew(c) Sister (d) Cousin

ANSWERS

1. (c) 2. (a) 3. (b) 4. (d)

EXPLANATIONS

Solutions (1to 4)

H IJ LSister

Brother Uncle

Only sister

GBrother

K

1. J is the cousin of G.2. I is the cousin of L.3. There are three male players, I, G and K.4. Uncle s daughter means cousin sister.

Brother of cousin sister is cousin brother.




For Any Guidance Call ou

The problems in this chapter deal with the linear distance or displacement or direction between starting pointand the final point in X Y dimensions.

Example 1: One morning after sunrise, Sita and Gita were standing in a chowk in Mumbai with their backtowards each other. Sita s shadow fell exactly towards right hand side. Which direction was Gita facing ?

(a) East (b) West(c) North (d) South

Solution: (c)North

Gita

Sita

South

West East

Sun

So, the answer is North.Example 2: A girl was going towards west, then she turned left, then turned 90 in clockwise direction. In

which direction was she going now ?(a) East (b) West(c) North (d) None of these

Solution: (b)

90o

Clockwisedirection

Starting Point

N

W E

S

So, the answer is West.Example 3: Amit walks 2 km Northward and takes a left turn, walks 5 km and then turns right, walks 3 km

and again turning right, walks 5 km. In which direction is he now from the starting point ?

Direction Sense Test




(a) East (b) North(c) West (d) South

Solution: (b)North

2 km

Starting Point

5 km

5 kmN

W E

S

So, answer is North.

EXERCISEDirections (Q. Nos. 1to 3) Study the informationgiven below carefully to answer these questions.On a playground, Dinesh, Kunal, Nitin, Atul andPrashant are standing as described below, facingthe North.

I. Kunal is 40 m to the right of Atul.II. Dinesh is 60 m to the South of Kunal.

III. Nitin is 25 m to the West of Atul.IV. Prashant is 90 m to the North of Dinesh.1. Who is the North-East of the person who is to the

left to Kunal ?(a) Dinesh (b) Nitin(c) Atul (d) None of these

2. If a boy walks from Nitin, meets Atual followedby Kunal, Dinesh and Prashant, then how manymetres has he walked if he has travelled thestraight distance all through ?(a) 155 m (b) 185 m(c) 215 m (d) 245 m

3. The clinic of doctor faces the West. From thebackside of his clinic, he walks straight 100 m thenturns to the left and walks 100 m again. Finally,he runs towards right and stops after walking 50m. Now in which direction is the Doctor from thestarting point ?(a) South-West (b) North-East(c) South-East (d) North-West

4. Bhavika and Sunaina start simultaneously

towards each other from two places 100 m apart.After walking 30 m Bhavika turns left and goes10 m, then she turns right and goes 20 m andthen turns right again and comes back to the roadon which she had started walking. If both Bhavikaand Sunaina walk with the same speed, what isthe distance between them at this point of time ?(a) 70 m (b) 10 m(c) 40 m (d) 20 m

5. A is East of B and West of C , H is South-Westof C and B is South-East of X . Who is thefarthest West ?(a) C (b) A(c) X (d) B

ANSWERS

1. (d) 2. (c) 3. (b) 3. (d) 5. (c)

EXPLANATIONS




1. PrashantP

30 m

Nitin Atul Kunal25 m A 40 m

60 m

K

Dinesh

N

N

S

W E

Left of Kunal is Atul, Prashant is in North-Eastof Atul.

2. Required distance = NA + AK + KD + AP(From above figure)= 25 + 40 + 60 + 90 = 215 m

3.50 m

100 m

Start100 m

End N

S

W E

So, doctor is North-East direction from startingpoint.

4. 20

10

30

Bhavika Sunaina100 m

10




The process of Example of thing/number through the diagramatic medium from the given group of elementsis called Venn diagram.

Generally two types of questions could be asked from this.

Type I1. Find out the number/thing: The questions asked from this .type contain a compound diagram, in which

different places are denoted by different number/letters. Each diagram stands for different class. Candidates arerequired to find out the number of thing in a special class through these diagrams or the numbers used in thediagram.

Directions (Q. Nos. 1 to 5) Answer these questions based on the diagram given below.

1

2

3 4

5 7 8 9

10 11

12

ChristiansProfessionalsFemales

Asians

Example 1: Asian Non-Christian Females who are Professional are represented by(a) 3 (b) 10 (c) 8 (d) 11

Solution. (b) Asian, Non-Christian females who are professionals are represented by 10 .Example 2: Asian Females who are neither Professional nor Christians are denoted by

(a) 6 (b) 9 (c) 10 (d) 3Solution. (a) Asian females who are neither professional nor Christians are denoted by 6 .Example 3: Non-Asian Professional Christian males are represented by

(a) 10 (b) 11 (c) 12 (d) 9Solution. (c) Non-Asian professional Christian males are represented by 12 .Example 4: Christian Females who are Non-Professional and Asian are represented by

(a) 5 (b) 10 (c) 9 (d) NoneSolution. (d) All Christians females of Asia are Professionals.

Logical Venn Diagrams




EXERCISE1. What is the sum of the numbers which appear in

one figure only?(a) 44 (b) 56(c) 37 (d) 51

2. The difference between the sum of the numberswhich appear only in two figures and the sum ofthe numbers which appear only in one figure is(a) 27 (b) 28(c) 9 (d) 17

3. If the sum of the numbers which fall within thecircle subtracted from the number which occursin all the three shapes the result is(a) 11 (b) 16(c) 25 (d) 27

4. Adding the sum of the numbers which appear inthe circle and only in one of the two rectangleswith the number which appears in both therectangles only the results is(a) 26 (b) 24(c) 45 (d) 34

ANSWERS

1. (d) 2. (a) 3. (d) 4. (b)

EXPLANATIONS

1. Sum of the numbers which appear in one figureonly = 7 + 8 + 11 + 13 + 12 = 51

2. Sum of the numbers which appear in only twofigures.

= 9 + 5 + 10 = 24Sum of the numbers which appear in only onefigure = 51.So, difference = 51 24 = 27

3. Sum of the numbers in the circle = 5 + 6 + 10 + 12= 33 Number which is present in all the threeshape = 6 So, difference = 6 33 = 27

4. Sum of the numbers which appear in circle andonly one of the rectangle = 5 + 10 = 15 Sum of thenumbers which appear in both rectangles = 9 So,the sum = 9 + 15 = 24




In this chapter questions contain a figure, a set of figures, an arrangement or a matrix, each of which bearscertain characters, be it numbers, letters or a group/combination of letters/numbers which follow a particularpattern. You are required to identify and decipher this pattern and accordingly find the missing character in thefigure.

Example 1: 5

109

6

16 2

21 51

53 ?

15 13

22 17 19 48

(a) 7 (b) 25(c) 49 (d) 129

Solution.(b) The pattern is(16 6)2 + (5 2)2 = 102 + 32 = 109

(22 15)2 + (21 19)2 = 72 + 22 = 53So, the missing number = (17 13)2 + (51 48)2 = 42 + 32 = 25

Example 2: 0 7

? 26

(a) 45 (b) 50(c) 60 (d) 63

Solution. (d) Moving clockwise direction, the numbers are13 1 = 0, 23 1 = 7, 33 1 = 26 and 43 1 = 63

Example 3: 3 7

6561 81

(a) 9 (b) 18(c) 24 (d) 27

Solution. (a) Starting from 3 and moving clockwise, the number in each quadrant is the square of that inthe previous quadrant.

So, the missing number = 32 = 9

Inserting theMissing Character




EXERCISEDirection (Q. Nos. 1 to 5) Find teh missingcharacter

66.

12 6

8

3

47

24

5 13 ?

5

(a) 14 (b) 10(c) 48 (d) 24

67.

3 2

3

6

54

9

4 70 50

110

(a) 80 (b) 40(c) 90 (d) 130

68.11

9 8

12

8 16

15 189 ?

13 14

(a) 48 (b) 12(c) 44 (d) 56

69.7

10 8

8

7 4

10 129 ?

8 9

(a) 17 (b) 25(c) 21 (d) 31

70.1

66

6

9 9

9 2718 ?

34

(a) 5 (b) 9(c) 18 (d) 20

ANSWERS WITH SOLUTIONS

1. (b) 2. (d) 3. (b) 4. (a) 5. (d)

EXPLANATIONS

1. 2 2 2 2 2 23 4 5, 7 24 25 5 12 13+ = + = + =

So, missing number = 2 26 8 10+ =

2. (3 + 4) 10 = 70, (2 + 3) 10 = 50, (6 + 5) 10 =110So, missing number (9 + 4) 10 = 130

3.9 12 11 15 13 88, 9

4 4+ + + +

= =

So, missing = 18 14 16 12

4+ +

=

4. (9 + 6) 5 = 10, (10 + 8) 7 = 11So, missing number = (12 + 9) 4 = 17

5. 6 6 1 6, 9 4 9 18´ ´ = ´ ´ =

So, missing number = 27 3 9 27´ ´ =




In this chapter, we deal with questions which are followed with a sequence consisting numbers, ranking andtime. We have to find answers on the basis of given condition. The importance of such types of questions cannotbe over-emphasised as their presence in a test of reasoning is almost certain. Though no explanations are requiredas how to attempt these questions in exams.

In this chapter, generally we will deal three types of questions. They are based on

Type 1 Number TestIn these types of questions, a number, a set of numbers, series of digit is given and the candidate is asked to

trace out digit following certain given conditions.Example 1 How many 5s are there in the following number sequence which are immediately preceded by 7

and immediately followed by 6?7 5 5 9 4 5 7 6 4 5 9 8 7 5 6 7 6 4 3 2 5 6 7 8

(a) 1 (b) 2(c) 3 (d) 4

Solution. (a) Here,7 5 5 9 4 5 7 6 4 5 9 8 7 5 6 7 6 4 3 2 5 6 7 8Preceded by 7 and followed by 6So, there is only one such 5.Example 2: How many even numbers are there in the following series of numbers, each of which is immediately

preceded by an odd number, but not immediately followed by an even number?5 3 4 8 9 7 1 6 5 3 2 9 8 7 3 5

(a) Nil (b) 1(c) 2 (d) 3

Solution. (d) There are three such even numbers 6, 2, 8 each of which is preceded by an odd number and notfollowed by an even number.

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

Number, Rankingand Time Sequence Test




EXERCISEDirections (Q. Nos. 70 to 74) Study the sets of numbers

given below and answer the question, whichfollow

972 682 189 298 7511. If one is added to the lowest number and two is

added to the highest number, what will be thedifference between the second digit of the smallestnumber and third digit of the highest number?(a) 5 (b) 7 (c) 9 (d) 8

2. If in each number, first and the last digits areinterchanged, which of the following will be thethird highest number?(a) 972 (b) 682 (c) 189 (d) 298

3. If in each number, all the three digits are arrangedin descending order, which of the following willthe third highest number?(a) 972 (b) 682 (c) 189 (d) 298

4. If in each number, second and the third digits areinterchanged, what will be the sum of first digitof the smallest number and last digit of highestnumber?(a) 7 (b) 6 (c) 9 (d) 8

5. If one is added to the smallest odd number andone is subtracted from the highest odd number,which of the following will be obtained if thesecond digit of the highest number is subtractedfrom the second digit of the lowest number soformed?(a) 6 (b) 5 (c) 4 (d) 3

ANSWERS

1. (a) 2. (b) 3. (a) 4. (d) 5. (c)

EXPLANATIONS

1. 189 + 1 = 190; 972 + 2 = 974Hence, required difference = 9 4 = 5

2. After interchanging first and last digit, numbersare ® 279, 286, 981, 892, 157Hence, third highest number = 286 Þ 682

3. 972, 862, 981, 982, 751Hence, third highest number = 972

4. After interchanging second and third digit,numbers are ®927, 628, 198, 289, 715Smallest number = 198Highest number = 927Hence, required sum = 1 + 7 = 8

5. (c) Smallest odd number = 189Highest odd number = 751

Required number = (189 + 1) and (751 1)= 190 and 750

Hence, required difference = 9 5 = 4




These questions contain the necessary qualifications required to be fulfilled by a candidate who is applyingfor certain job/promotion/facility, along with the bio-data. You are supposed to assess the candidate s eligibility orpotential for the same and decide upon the further course of action to be taken from among the given alternatives.

Example 1: Read the following information carefully to answer the questions given belowThe criteria for granting the admission to a MBA course is as follows.A candidate must

(i) be at least a graduate with first class.(ii) not be more than 25 yr as on August 15, 2010.(iii) secure minimum 50% marks in the Entrance Test.(iv) be fluent in Hindi and English.

However, If a candidate(A) fulfils all other criteria except (ii) above but is less than 30 yr and also belongs to back ward class, should be

given admission.(B) fulfills all other criteria except (i) above, but is a postgraduate with minimum 55% marks, should be referred

to chairman-Admissions.Based on the above criteria and the information given in each of the following questions, you have to take

the decision in regard to each case. You are not to assume anything. These cases are given to you as on 15-8-2010.

Eligibility Test





EXERCISEDirections (Q. Nos. 1 to Q. 10) Study the followinginformation carefully and answer the questionsgiven below

Following are the conditions for selecting PersonnelManager an organization

The candidate must(i) be a graduate with at least 50% marks.

(ii) have a postgraduate degree/diploma in PersonnelManagement/HR with at least 60 per cent marks.

(iii) not be more than 35 yr as on 1.6.2009.(iv) have post-qualification work experience of at least

five years in the Personnel/HR Division of anorganisation.

(v) have secured at least 45 per cent marks in theselection process.

In the case of a candidate who satisfies allthe conditions except

(A) at (iii) above, but has post-qualification workexperience of at least ten years, the case is to bereferred to the Director-Personnel.

(B) at (iv) above, but has post-qualification workexperience as Deputy Personnel Manager of atleast three years, the case is to be referred toPresident-Personnel.

In each questions below are given details of onecandidate. You have to take one of the following coursesof action bases on the information provided and theconditions and sub-conditions given above and markthe number of that course of action as your answer.You are not to assume anything other than theinformation provided in each question. All these casesare given to you as on 1.6.2009.

Mark answer (a) if the candidate is to be selected.Mark answer (b) if the candidate is not to be

selected.Mark answer (c) if the information provides is

inadequate to take a decision.Mark answer (d) if the case is to be referred to

the Director- Personnel.1. Meena Srivastava was born on 6th March 1978.

She has been working as Deputy PersonnelManager in an organization for the past five yearsafter completing her postgraduate diploma in HR

with 68% marks. She has secured 50% marks inboth graduation and selection process.

2. Ketan Desai was born on 5th January 1979. Hehas been working for the past five years in thepersonnel deptt of an organisation after completinghis postgraduate diploma in PersonnelManagement with 64% marks. He has secured40% marks in the selection process and 52% marksin graduation.

3. Anant Joshi has been working in the personneldepartment of an organisation for the past sixyears. He was born on 7th November 1977. Hehas secured 60% marks in postgraduate degreein Personnel Management. He has also secured55% marks in both graduation and selectionprocess.

4. Mohan Bajpai was born on 10th April 1975. Hehas secured 55% marks in graduation and 65%marks in postgraduate diploma in PersonnelManagement. He has been working in the HRDeptt, of an organisation for the past six yearsafter completing his postgraduate diploma.

5. Gopal Sharma has been working for the past fiveyears in the HR Deptt. of an organisation aftercompleting his postgraduate diploma in HR with62% marks. He has secured 50% marks in bothgraduation and selection process. He was born on29th May 1974.

6. Arun Vohra has secured 55% marks ingraduation. He has been working in the personneldeptt. of an organisation for the past eleven yearsafter completing his postgraduate degree inPersonnel Management with 65% marks. He hassecured 50% marks in the selection process. Hewas born on 12th August 1972.

7. Asha Dhar has secured 52% marks in graduationand 62% marks in postgraduate degree inPersonnel Management. She has also secured 48%marks in the selection process. She has beenworking for the past seven years in the personneldeptt. of an organisation after completing herpostgraduate degree. She was born on 8th June1974.

8. Sudha Ghosal was born on 20th October 1976.She has been working as Deputy PersonnelManager for the past six years in an organisationafter completing her post graduate degree in HRwith 67% marks. She has secured 60% marks in




graduation and 45% marks in the selectionprocess.

9. Amit Saxena was born on 25th July 1973. He hasbeen working in the personnel deptt. of anorganisation for the past eleven years aftercompleting his postgraduate diploma in HR with70% marks. He has secured 60% marks in bothgraduation and selection process.

10. Navin Das was born on 14th April 1978. He hasbeen working in the personnel deptt. of anorganisation for the past six years after completinghis postgraduate diploma in HR with 65% marks.He has secured 45% marks in both graduationand selection process.

ANSWERS

1. (a) 2. (b) 3. (a) 4. (c) 5. (d)6. (d) 7. (d) 8. (a) 9. (d) 10. (b)

EXPLANATIONS

1. Meena Srivastava should be selected.2. Ketan Desai should not be selected as he scored

40% marks in selection process.3. Anant Joshi should be selected.4. We do not know the marks in selection process for

Mohan Bajpai. So, data is in adequate.5. Gopal Sharma exceeds the limit of 35 yr age, so,

the case should be referred to the DirectorPersonnel.

6. Arun Vohra also exceeds the limit of 35 yr age, so,the case should be referred to the DirectorPersonnel.

7. Asha Dhar is more than 35 yr of age, so her caseshould be referred to the Director Personnel.

8. Sudha Ghosal should be sellected.9. Amit Saxena is more than 35 yr of age, so his case

should be referred to Director Personnel.10. Navin Das scored less marks in graduation. So,

he should not be selected.




The word Syllogism is also referred to Logic . Syllogism is an important section of logical reasoning andhence, a working knowledge of its rules is required on the part of the candidate. Hence, it can be expressed as theScience of thought as expressed in language . The questions based on syllogism can be solved by using Venndiagrams and some rules devised with the help of analytical ability.

With this unique characteristic, this test becomes an instrument of teaching the candidates to follow the rulesand work as per the instructions without an error. Here, only the basic concept and rules, which have a bearingon reasoning faculty could alone help. There are some terminology which are used in syllogism.

PropositionIt is also referred to as Premises . It is a sentence which asserts that either a part of, or the whole of, one sets

of objects-the set identified by the subject term in the sentence expressing that sentence either is included in, or isexcluded from, another set-the set identified by the predicate term in that sentence.

Types of PropositionCategorical Proposition There is relationship between the subject and the predicate without any condition.Example : I. All beams are logs.

II. No rod is stick.Hypothetical Proposition: There is relationship between subject and predicate which is asserted

conditionally.Example : I. If it rains he will not come.

II. If he comes, I will accompany him.Disjunctive Proposition In a disjunctive proposition the assertion is of alteration.Example : I. Either he is brave or he is strong.

II. Either he is happy or he cannot take revenge.

Parts of PropositionIt consists of four parts.

1. Quantifier: In quantifier the words, all , no and some are used as they express quantity. All and no areuniversal quantifiers because they refer to every object in a certain set. And quantifier some is a particularquantifier because it refers to at least one existing object in a certain set.

2. Subject: It is the word about which something is said.

Syllogism




1. Statement: I. All pens are pencils.II. Some pens are erasers.

III. Some erasers are clips.Conclusions I. Some clips are pens.

II. No clip is a pen.III. Some erasers are pencils.IV. No eraser is a pencil.

(a) Only I and II follow(b) III and either I or II follow(c) Only III follows(d) Either I or II, and either III or IV

2. Statement: I. Some books are papers.II. Some papers are plastic

III. No plastic is black.Conclusions I. Some papers are not black.

II. All papers are not black.III. Some papers are black.IV. Some books are black.

(a) Only I follows(b) Either II or III follows(c) Only I and IV follow(d) Only I, III and IV follow

3. Statement: I. Some doors are windows.II. All windows are black.

III. Some black are brown.Conclusions I. Some windows are brown.

II. All doors are black.III. Some doors are black.IV. No window is brown.

(a) Only III follows(b) Either I or IV and III follow(c) Only II follows(d) Only IV follows

4. Statement: I. All teachers are doctors.II. All doctors are engineers.

III. All engineers are typists.Conclusions I. Some typists are teachers.

II. All doctors are typists.III. Some engineers are teachers.IV. All doctors are teachers.

(a) Only I and II follow(b) Only I and III follow(c) Either II or IV follows(d) None of these

ANSWERS

1. (d) 2. (b) 3. (b) 4. (d)

EXPLANATIONS

1.Pencils

Pens

ClipsErasers

Hence, either I or II and either III or IV follows.2.

Books Papers Plastic Black

Hence, either II or III follows.3.

Doors Windows

Black

Brown

Hence, either I or IV and III follows.4.

Typists

Engineers

Doctors

Teachers

Hence, only I, II and III follow.

EXERCISE





Such type of questions consist of a Statement followed by certain arguments in favour of or against theStatement. Candidates would be required to distinguish between the strong and weak arguments.

Strong arguments are those which are both important and directly related to the question. Weak argumentsare those which are of minor importance and also may not be directly related to the question or may be related toa trivial aspect of the question. A weak argument is very simple, superfluous, ambiguous and long drawn one.

Following points should be taken into consideration while choosing a strong argument1. A strong argument should give the realistic diagnosis of the situation described in the Statement.2. A strong argument should give the deep analysis of the topic deal within the Statement.3. A strong argument should relate with the Statement and be supported up by facts or established notions.4. A strong argument should not be mere reiteration of the situation given in the Statement.

Following examples will help the students to have an understanding of the logic used to solve these questions.Types of Questions that could be Asked in CSATThere are two types of questions which may be asked.

Type 1 Two Arguments BasedIn these questions a Statement is followed by two arguments. Candidates are required to distinguish between

the strong and weak arguments. Generally both the arguments are contrary to each other and refer to positiveand negative results.Directions (Q. Nos. 1 to 2) Study the instructions carefully and answer the questions that follows.

In making decisions about important question it is desirable to be able to distinguish between strong andweak argument so far as they relate to the questions. Weak arguments may not be directly related to the

question and may be of minor importance or may be related to the trivial aspect of the question. Each questionbelow is followed by two arguments numbered I and II. You have to decide which of the arguments is a `strongargument and which is a `weak argument. Give answer (a) if only argument I is strong, (b) if only argument IIis strong, (c) if neither I nor II is strong and (d) if both I and II are strong.

ExampleI Statement: Will the newly elected members fulfil their promises?Arguments

I. Yes, otherwise their very existence will be in danger.II. No, elected members never seem to remember their promises and commitments.

Solution. (d) Both the arguments are strong. Elected members have to face the electorates after each

Statement and Arguments




completion of their terms as their existence as members is decided by people. Secondly, at the time of elections, somany commitments are made which are hardly fulfilled.

Example 2 Statement: Should parent play with their children?Arguments

I. Yes, it helps in building up a healthy and much needed companionship between children and parents.II. No, children treat their parent like equals and there is no distance left.

Solution. (a) Argument I is strong because a close companionship bridges the gap between parents andchildren. Argument II is not supported by a positive logical aspect of the Statement: and hence, is a weakargument.

EXERCISEDirections: In making decisions about important

questions, it is desirable to be able to distinguishbetween strong arguments and weakarguments. Strong arguments must be bothimportant and directly related to the question.Weak arguments may not be directly related tothe question and may be of minor importance ormay be related to the trivial aspects of thequestion.

Each question below is followed by threearguments numbered I, II and III. You have todecide which of the arguments is a strongargument and which is a weak argument.

64. Should smoking cigarettes and drinking alcoholby the actors be completely banned in the moviesin India ?Arguments

I. Yes, this will significantly reduce the trendof smoking cigarettes and drinking alcoholamong the youth in India.

II. No, there should be no such ban on thecreative pursuits of the film maker.

III. No, the films portray the society and hencesuch scenes should be an integral part of themovie if the storyline demands so.

(a) None is strong(b) Only I and II are strong(c) Only II and III are strong(d) Only I and III are strong

65. Should sale of vital human organs be made legalin India ?Arguments

I. No, it goes against our culture.

II. No, this will lead to unhealthy practices.III. Yes, this will bring an end to the illegal

trading of human organs.(a) None is strong(b) Only I and II are strong(c) Only III is strong(d) Only II and III are strong

66. Should the conscription of citizens for defianceservices be made compulsory in India ?Arguments

I. Yes, this is the only way to tackle the serousshortage of manpower in defence services.

II. No, instead the compensation package bemade comparable to other job sectors toattract people to join defiance services.

III. Yes, many other countries have made thiscompulsory.

(a) Only I is strong(b) Only II is strong(c) Only I and II are strong(d) Only either I or II is strong

ANSWERS

1. (d) 2. (a) 3. (d)

EXPLANATIONS

1. Only I and III are strong. A reduction in trendswill be a desirable consequence. Also a ban willtake away from the power of the portrayal. II isweak.

2. None is strong.I. Weak because talking of culture is irrelevant




in a case which would have made no sensein the absence of modern medicaltechnology.

II. Weak as it is simplistic.

III. Superflous (unhealthy practices)3. All are weak.

I. Weak (Not true argument)II. Weak because instead of getting into the

reason it provides an alternative.




When we see clouds in the sky. We take preassumption that it may be rain. Each action has an assumptionone in positive and another in negative. Let us suppose a baby born it may be a boy or a girl. So, here we take twoassumptions.

The candidate will be required to assess the given statement and decide which of the given assumptions isimplicit in the Statement. To understand the pattern of these questions, it is very essential to know what theterms Statement and Assumptions do stand for.

Hence, An assumption is something that can be supposed or assumed on the basis of a given statement.

Types of Questions Based on AssumptionType 1 Two-Assumptions Based

In this type of questions a statement: is given, followed by two assumptions. The candidate is required toassess the given statement: and then decide which of the given assumptions to implicit in the Statement: .Directions: In each of the illustrations below is given a Statement: followed by Assumptions numberedI and II. Consider the Statement: and decide which of the given Assumptions is implicit? Give answeras

(a) if only assumption I is implicit(b) if only assumption II is implicit(c) if neither I nor II is implicit(d) if both I and II are implicit1. Statement: The Union Government has decided to withdraw existing tax relief on various small savings

schemes in a phased manner to augment its tax collection.Assumptions:

I. People may still continue to keep money in small savings schemes and also pay taxes.II. The total tax collection may increase substantially.

Solution. (d) Any measure is taken assuming that it would be accepted by the people. Therefore, both theassumptions are implicit in the statement .

Statement and Assumptions




Directions: In each question below is given aStatement followed by three Assumptionsnumbered I, II and III. An assumption is somethingsupposed or taken for granted. You have toconsider the Statement and the followingAssumptions and decide which of the Assumptionsis implicit in the Statement, then decide which ofthe answer (a), (b), (c) and (d) is correct answerand indicated it on the answer sheet.

1. Statement: We must be prepared to face anyeventuality and all the assignments must becompleted as per their schedule-Director tells thefaculty members.Assumptions:

I. There is possibility of any seriouseventuality.

II. Dates are fixed for all the assignments.III. Faculty members are supposed to complete

the assignments.(a) All are implicit(b) Only II and III are implicit(c) None is implicit(d) Only III is implicit

2. Statement: Training must be given to all theemployees for increasing productivity andprofitability.Assumptions:

I. Training is an essential component ofproductivity.

II. Employee can t function effectively withoutproper training.

III. Profitability and Productivity aresupplementary to each other.

(a) None is implicit(b) All are implicit(c) Only III is implicit(d) Either I or II is implicit

3. Statement: In the recently held All IndiaCommerce Conference, the session onManagement of Service Sector in Indiasurprisingly attracted large number of participantsand also received a very good media coverage inthe leading newspapers.

Assumptions:I. People were not expecting such an

encouraging response for service sector.II. Service sector is not managed properly in

India.III. Media is always very positive towards service

sector.(a) Only I is implicit(b) All are implicit(c) None is implicit(d) Either I or III is implicit

4. Statement: The situation of this area stillcontinues to be tense and out of control. Peopleare requested to be in their homes only.Assumptions:

I. There had been some serious incidents.II. People will not go to the office.

III. Normally will be restored shortly.(a) All are implicit(b) Only I is implicit(c) Only I and III are implicit(d) Only I and II are implicit

ANSWERS

1. (a) 2. (d) 3. (c) 4. (d)

EXEPLANATIONS

1. According to the given Statement we can clarifyall the given Assumptions are implicit.

2. Either I or II is implicit as training has beennecessitated in the Statement , ie it is related tothe efficiency and effectiveness of an employee.

3. None is implicit as people always expect suchopportunities and media is positive to both serviceand other sectors as well as service sector is alsomanaged in India.

4. Only Assumptions I and II follow as the situationis tense, it means that some serious incident hasoccurred. Secondly, it is given that situation stillcontinues to be tense, if means that people maynot go to their officer. However, we cannot saywhen the normally will be restored.

EXERCISE




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In such types of questions a situation would be presented and some courses of action are suggested in thecontext of those situations. These types of questions are designed to test candidate s decision making ability. Inother words a course of action is a step or administrative decision to be taken for improvement, follow up orfurther action with regard to the problem on the basis of data provided .

To solve these questions, the candidates are advised to keep in mind the following important points:1. Correct course of action should either lessen the problem or improve the situation created by the problem.2. Simple problem must have simple course of action and not a complex one which may create more problems

than to solve or reduce it.3. Course of action should be feasible and should relate with the practical aspect of life.

Type of Questions that could be Asked in CSATType 1 Two Courses of Action Based

In these type of questions a Statement is given followed by two courses of action numbered I and II.The candidate is required to grasp the Statement, analyse the problem or policy it mentions and then decide asto which of the courses of action logically follow(s).Directions (Examples 1 to 2) In each of the questions given below is a Statement followed by two coursesof action numbered I and II. A course of action is a step or administrative decision to be taken forimprovement, follow up or further action in regard to the problem, policy etc. On the basis of informationsgiven in the Statement you have to assume everything in the Statement to be true, then decide which ofthe two given courses of action logically follow.

Give your answer as(a) If only I follows (b) If only II follows(c) If neither I nor II follows (d) If both I and II follow

Example 1: Statement: A large number of engineering graduates in our country are not in a position tohave gainful employment at present and the number of such engineers are likely to grow in future.Courses of Action:

I. The government should launch attractive employment generating schemes and encourage these graduatesto opt for such schemes to effectively use their expertise and knowledge.

II. This happened due to poliferation of engineering colleges in the country and there by lowering the qualityof the engineering graduates. Those colleges, which are not equipped to impart quality education should beclosed down immediately.

Statement andCourses of Action




Solution. (a) Only course of action I seems to be suitable for pursuing. The first line of course of action II isnot a course of action and second line does not properly address the problem.

Example 2: Statement: There have been many instances of dacoity and looting in many passenger trainsthis years.Courses of Action:

I. The railway authority should immediately deploy one policemen in each compartment in all thepassenger trains.

II. The passengers travelling by train should be given training on how to tackle the dacoits and looters.Solution. (c) Considering the insufficient number of security personnel the course of action I seems to be

untenable. Similarly, course of action II is not practically feasible. Thus, neither course of action I nor II follows.

EXERCISE

1. Statement: Besides looks and appearances, it isalso important to develop on self from within.Courses of Action:

I. One should not pay attention to fashion.II. One should pay attention to fashion.

III. Looks on self development should beencouraged.

(a) Only I follows (b) Only II follows(c) Only I and III follow(d) Only III follows

2. Statement: Despite increasing BPO jobs in ourcountry, a large number of educated youth areunemployed.Courses of Action

I. Government should give unemploymentallowance to all unemployed youth.

II. Government should introduce variousschemes in different areas that will generateemployment opportunities.

III. Efforts should be made by the society andthe Government to encourage the youth forvocational education.

(a) Only I and 11 follow(b) Only II and III follow(c) Only I and III follow(d) Only II follows

3. Statement: Cases of asthma sufferers have beenrising particularly in the big cities.Courses of Action:

I. Civic authorities should ensure adequate

supply of medicines at normal rates.II. Civic authorities need to control the air

pollution caused due to emission fromvehicles.

III. Act of tree-cutting without permission shouldbe severely punished.

(a) Only I and II follow(b) Only II and III follow(c) Only III follows(d) Only II follows

4. Statement: Many students at School and Degreelevel are not able to master the subjects even ifthey have passed out with high scores.Courses of Action:

I. Education Boards should examine and revisethe examination system to tap the real talent.

II. Examination system at all levels should beso designed as to discourage rote learning.

III. Difficulty level of the examination papersshould be significantly increased.

(a) Only I follows(b) Only 11 follows(c) Both I and II follow(d) Either I or II follows

ANSWERS

1. (d) 2. (b) 3. (a) 4. (c)




EXPLANATIONS

1. The Statement stresses the need for all-roundpersonality development of an individual. So, onlyIII follows.

2. Only II and III follow as during various schemesin different areas, it will reduce theunemployment. If the government and societyintroduce vocational education, it will also reduceunemployment.

36. Only I and II follow as civic authorities shouldensure adequate supply of medicine at normal rateas well as controlling pollution is necessary.

37. Only I and II follow as an examining theexamination system, the defects of the educationsystem may be removed, also the system ofeducation should be redesigned as to discouragethe rote learning.




Conclusion is a fact that can be truly inferred from the contents of a given sentence. There may be questionsin the CSAT that may consist of a statement or a set of statements, followed by certain inference(s) based on thefacts of statements. Here candidates are required to approach the questions for solution from a different angle.This approach basically emphasises the need for being more systematic and logical in drawing inferences. Therefore,consequent effect of a statement has to be analysed before reaching the correct conclusion(s).

Types of Questions: There may be two types of questions which may be asked in CSAT.

Type 1 Logical ConclusionsHere statement and conclusions are based on logical conclusions.

Example 1Statement: These apples are too expensive to be bad.Conclusions I. When apples are in short supply, the prices go up.

II. The higher the selling price, the superior is the quality of the commodity.Solution. According to the statement quality is directly proportional to the price. Hence, higher the sellingprice, the superior is the quality of the commodity.

Example 2Statements: In a one day cricket match the total runs made by a team were 200, out of which 160 runswere mode by spinners.Conclusions I. 80 % of the team consists of spinners.

II. The opening batsman were spinners.Solution. Team may consists or the number of spinners more or less than given in conclusion 1. Hence,

conclusion I does not follow. Secondly, it is not known from the statement that opening batsman were spinners.Hence, conclusions II does not follow.

Type 2 Mathematical ConclusionsSuch type of questions are quite similar to mathematical operations.Example (Q. Nos. 3 to 5) In the following questions, the symbols , .@ @ = are used asfollows.A B means A > B A B means A = BA = B means A = B A @ B means A < BA @ B means A < B

Statement and Conclusions




Directions (Q. Nos. 1 to 3) In the followingquestions few symbols have been used and thesesymbols convey the meaning as under.

P @ Q ® P > Q P @ Q ® P ³ QP = Q ® P = QP Q ® P < Q P Q ® P < QNow in each of the following questions assumingthe three statements to be true, state which. ofthe following conclusions I and II given below isdefinitely true.Give answer(a) if only conclusion I is true; Give answer(b) if only conclusion II is true; Give answer(c) if conclusion I and II both are correct; Give

answer(d) if either I and II are true; Give answer (e) if

neither I nor II is correct.18. Statements M = C, L F, C @ I.

Conclusions I. = II. M @ L19. S tatements II. = U @ V, V S

Conclusions I. V TII. T = V

20. Statements B @ CConclusions I. C @ A

II. A D

ANSWERS

1. (b) 2. (a) 3. (d)

EXPLANATIONS

Solutions (Q. Nos. 1 to 3)Finally, @ Þ >

@ Þ ³

= Þ =

Þ <

Þ £

1. Here, M = C > L < FNow, I. C = F Þ C = F (False)

II. M @ L Þ M > L (True)2. Here, = > <

Now, I. V T Þ V< T (True)II. T = V Þ T = V (False)

3. Here, A = B > C > DNow, I. C @ A Þ C > A

(False)II. A D Þ A < D

(False)

EXERCISE




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Under this, the questions may consist of a brief passage followed by certain inferences based on it. Thesepassages are based on social or economic conditions.

Candidates must note that it is very important for them to possess logical skills, comprehension capacity andability for interpretation. They must be skillful enough to comprehend the full implications of the passage andarrive at the correct answer. It is expected of the students to acquire as much knowledge as possible of phrasalverbs, vocabulary and nuances of the English language.

In this type of questions a passage is given on any topic followed by conclusions in the form of statements. Acandidate is required to mark out the answer in the following ways

(i) Mark (a) if the statement is definitely true.(ii) Mark (b) if the statement is probably true, though not definitely true.

(iii) Mark (c) if the conclusions is neither true nor false because the data given in the passage are inadequate.(v) Mark (d) if the conclusion is definitely false.

A candidate must note that all these conclusions are to be arrived at in the light of what has been discussedin the passage.

In the following passage the methodology will be discussed as to how to opt for right option-{a, b, c, d) whicha candidate is expected to select for a given conclusion.

For the sake of the convenience of the candidate, each option mentioned above will be discussed and analysedin detail in the light of the passages given below.

ExamplesDirections (Q. Nos. 1 to 4) Read the following passage and examine each inference given below it in thecontext of this passage. Mark your answer as

(a) if the inference is definitely true (b) if the inference is probably true(c) if the data provided is inadequate (d) if the inference is `definitely falseIn the commodities business size does matter. This is common wisdom. The Indian sugar industry, the second

largest in the world after Brazil, has traditionally been fragmented, which led to widespread sickness and largenumber of mills going bankrupt, a situation exacerbated by a slew of government controls - which are, meaningfully,getting diluted since August 1998. Its now been more than seven-and-a-half years since the industry was delicensed.No official permission is required either to build a new factory or for brownfield expansion plan, except that theremust not be any violation of command area norms. Even then, there aren t many who have the capacity to playthe volumes game at the cyclic sugar business.

Deriving Conclusion




1. India has not yet been able to consolidate its firm stand in the international sugar market.2. At present the Indian sugar industry has been made considerably free from Government controls.3. Prior to 1998, Indian sugar industry was considerably lower in the world ranking of large nations.4. Most of the bankrupt sugar mills in India are funded by the Govt to revive their units.

Solutions.1. (a) If we go through the passage then we find it is the real concern of the passage. Hence, India has not yet

been able to consolidate its firm stand in the international sugar market.2. (b) According to the passage since August 1998, government control on sugar mills is getting diluted. But we

do not know how much the government control has been diluted.3. (c) There is no such information regarding the position of the Indian sugar industry (prior to August 1998)

in the world ranking of large nations.4. (c) There is no such information that we can say most of the bankrupt sugar mills in India are funded by the

Govt to revive their units.

EXERCISEPassage

The jeweller-next-door may have reasons to worry,thanks to the organised retail and branded goods hittingthe right chord from Indian consumers. The recentchanges in lifestyle goods industry and the diamondsindustry threaten to impact the family jeweller segment,which currently controls 97% of India s fragmentedjeweller retail market. A study , suggests that as India sjewellery market matures, it is expected to get moreorganised and the share of family jeweller is expectedto come down. The family jeweller segment is the largestsegment of the market and hence most likely to beimpacted by these changes. Family jewellers will haveto bring in new practices and range of designs andcustomisation of jewellery would differentiate theplayers. Currently, organised retailers are enlarging thepie but the traditional players are not feeling the impactyet.

31. Share of business of the small-time jewellers willreduce substantially in the near future.

32. Family jewellers have never customised theirdesigns in the past.

33. Big retail companies have the capability to bringin more competition in the jewellery market.

34. Family jewellers at present control about two-thirds share of the entire jewellery market.

35. There is a perceptible change in the choices of thecustomers in recent times with regard to lifestyleproducts.

ANSWERS

1. (b) 2. (c) 3. (a) 4. (d) 5. (a)

EXPLANATIONS

1. According to the passage, big retail companies maydominate the jewellery market in the coming days.Hence, it is likely that the share of business of thesmall-time jewellery will reduce substantially inthe near future.

2. It is clear from the passage that it seems thatfamily jewellers did not focus seriously oncustomisation of their jewellery. But because ofthe word never we cannot opt for probably true .

3. That is why the passage raises concerns aboutfamily jewellers.

4. It is clear from passage that family jewellers atpresent control about 97% share of the entirejewellery market.

5. Given inference is definitely true.




According to the dictionary, Assertion refers to stating or claiming something forcefully and that of Reasonis fact. This test is meant to judge the candidate s knowledge and with it the aim is to determine his ability toreason out correctly.

Under, we shall deal with the combination of Assertion and Reason and relate with each other in order to findtheir correct coordination. Here, four alternative comments on these are given and the correct one is to be chosen.This is again an important feature of logical reasoning. Following illustrations will fully illustrate the type of suchquestionsDirections (Q. Nos. 1 to 3) In each of the illustrations questions, there are two statements labelled asAssertion (A) and Reason (R). Mark your answer as

(a) if both A and R are true and R is the correct explanation of A(b) if both A and R are true but R is not the correct explanation of A(c) if A is true but R is false(d) if A is false but R is true

Example 1Assertion (A): Most of ancient civilisations grew near the rivers.Reason (R): The main occupation of man was agriculture.Solution. The Assertion is correct because most of the ancient civilisations grew near the rivers as land overthere was fertile and water was easily available. But the Reason is not the correct explanation of the AssertionHence, option (b) is true.

Example 2Assertion (A): Seeds should be treated with fungicide solution.Reason (R): Seeds do not germinate, unless treated with fungicide solution.Solution: Seeds are treated with fungicide before sowing to avoid seed borne disease. But, it is not a truefact that unless seeds are treated with fungicide solution, they cannot germinate. Hence, option (c) is true.

Example 3Assertion (A): Appendix is a vestigial organ in the human body.Reason (R): It does not participate in digestion.

Assertion and Reason




Solution: We know that, appendix is a vestigial organ in the human body and does not participate indigestion. Hence, both Assertion and Reason are correct and Reason fully explains Assertion. Hence, optionas (a) is our answer.

EXERCISEDirections (Q. Nos. 1 to 5) Choose the correctalternative from the following options as givenbelow for the Assertion (A) and Reason (R) givenin each of the questions.

(a) Both A and R are true and R is the correctexplanation of A

(b) Both A and R are true but R is not the correctexplanation of A

(c) A is true but R is false(d) A is false but R is true24. Assertion (A): Food materials should not be

soaked in water for a long time.Reason (R): Washing leads to loss of vitamin-Aand vitamin-D from the food stuff.

25. Assertion (A): Water kept in earthen pots getscooled in summer.Reason (R): Evaporation causes cooling.

26. Assertion (A): Bangladesh exports jute fromIndia.Reason (R): Bangladesh has most of the jutemills.

27. Assertion (A): We should avoid black clothes insummer.Reason (R): Black is good absorber of heat.

28. Assertion (A): Pressure cookers are fitted withebonite handles.Reason (R): Ebonite is strong.

ANSWERS

1. (c) 2. (a) 3. (c) 4. (a) 5. (c).

EXPLANATIONS

1. Food materials should not be soaked in water fora long time because it leads to loss of vitamins.However, the Reason is false.

2. Earthen pots let the water evaporate throughtheir pores and hence keep the water cool.

3. India imports raw jute from Bangladesh. As afterBangladesh was created, the areas of juteproduction went to Bangladesh while the jute millsleft in India.

4. Both Assertion and Reasons are true and Reasonexplain the Assertion as we avoid black cloth insummer as they are good absorber of heat.

5. The handles of pressure cookers are made ofebonite as it being a bad conductor of heat.




We make several statements in our day-to-day life and invariably come across statement, which are funnyand leads to a sudden twist to the conversion. Basically, punchlines are usually the last lines of a conversation/story, etc, which provide it with humour and climax or we can say that it is the trial part of a joke or a comedysketch. A given statement would fit as a punchline if, it passes the following three tests.

I. It must be a climax.II. It must be funny.

III. It must bring in sudden twist.In these types of questions, an incident is described but the punchline is missing. Considering the incident,

you have to decide which of the two statements fits as a punchline.As such, for all practical purposes, it can be said the reader should not bother about this test and may skip it.

Climax test may become relevant at a later date when the format of the questions changes.A funny statement is defined as a statement which makes an average human being laugh or at least smile.The third and final criterion for a suggested statement to fit as a punchline is that it must have a sudden

twist so that, it brings about something not expected. The keyword here, is twist into something not expected. So,there must be an element of surprise in it.

Types of Questions Asked in Various CompetitionsWe will see punchlines after having a look at the format in which the questions are put.

Directions: We come across many funny incidents in different walks of life. One of the funny incidentsis the punchline or a climax which gives the incident a sudden transformation or twist, (into somethingnot expected).

It is this punchline which makes the incident funny.In each of the following questions, an incident is described but the punchline is missing-indicated by a blank.

After the incident, two statements numbered I and II are given considering the incident, you have to decidewhich of the two statements as a punching.

Give your answers as(a) if you think only statement I fits(b) if you think only statement II fits(c) if you think both the statement I and II fit and the wavelengths of approach in both the statement are also

more less the same(d) if you think both I and II fit but the ideas or wavelengths of approach in both the statements are different

and contrasting

Punchlines




EXERCISEDirections (Q. No. 1 to 5) We come across manyfunny incidents related to different walks of life.One of the funny incidents is the punchline or aclimax-which gives the incidents a suddentransformation or twist (into something notexpected). It is this punchline which makes theincident funny. In each of the funny questions anincident is described but the punchline is missing-indicated by a blank. After the incident, twostatements numbered I and II are given.Considering the incident, you have to decide whichof the two statements fits as a punchline.

36. The doctor asked, Do you permit your wife to haveher own way?The man replied:_____

I. No Sir, she has it without my permission.II. Yes, but only if, there is enough petrol in

the tank.(a) Neither(b) Only I (c) Only II(d) Both with contrasting ideas

37. Our life became a picnicI. Ever since, we started using paper plates.

II. Ever since, we started using thepsychiatrist s advice.

(a) Only I(b) Neither(c) Both with same idea(d) Both with contrasting ideas

38. A worker says to his colleague: I am caught in apower struggle with my boss. I

I. Have to supply candles to his housewhenever there is a power failure.

II. Have the struggle and he has the power.(a) Only I(b) Only II(c) Neither(d) Both with contrasting ideas

39. I wish I were Adam. For then_______I. If I cracked a joke, nobody would say, I ve

heard that before.II. I would ve seen the best of both the worlds.

(a) Only I(b) Only II(c) Both with same idea(d) Both with contrasting ideas

40. Judge: You have committed the most heinouscrime of murdering both your parents.Convict: Yes Sir, But I hope

I. That the jury would look with pity into thecase of an orphan.

II. That the jury would not order the lastsurviving member of my family to be killed.

(a) Only I (b) Only II(c) Both with same idea(d) Both with contrasting ideas

ANSWERS

1. (d) 2. (a) 3. (d) 4. (d) 5. (c)

EXPLANATIONS

1. Both sentences are funny so, they are punchlinewith contrasting ideas.

2. Only sentence I is funny follow the sentence eversince we started using paper plates .

3. I is funny as the struggle of the worker insupplying candles to his boss in times of powerfailures has been called power struggle . II isfunny as the word power struggle has beendichotomised with the boss having the power andthe clerk having the struggle! The ideas arecontrasting.

4. Both are funny because in both of them, thereare funny reasons for wishing to be Adam.

5. Both are funny with same idea. The convict haskilled his parents and now seeks pity because heis an orphan/he is the last survivor of his family.




This test is mainly to judge a candidate s ability to use his presence of mind to tackle a given situation, he maycome across anytime in life. For example, just think if you are going to appear in a test, and on the way you findan injured person. In this situation, what will you do?

So, at anytime we can face such problems. The candidate is, thus, expected to choose the best response whichshall present him/her as a good person or a sincere professional.

Types of QuestionsExample (Q. Nos. 1 to 5) Such questions consists four probable answers as an alternatives. You have toselect most appropriate alternative as the answer.

Example 1In a bus you realize that someone has left his/her wallet. You would

(a) give the money to the beggar(b) hand it over to the bus conductor(c) try to find his/her contact number and inform the owner(d) leave the wallet as it is

Solution. If you are an honest man then, you will try to find his/her contact number and inform the ownerof the wallet. In this way, that wallet will be reached in right hands. So option (c) is our answer.

Example 2Do you think that one should change his job often and face new situation?

(a) No, unless compelled one should not leave his old job(b) Yes, every new job is challenging and one should accept the challenge(c) No, as it takes time to get adjusted(d) No, as the new situation may not suit you

Solution. Most appropriate answer will be option (b). Because every new job is challenging and one shouldaccept the challenge. Unless you accept the challenges you can not get different views of life.

Situation Reaction Tests




EXERCISEDirections (Q. Nos. 1 to 5): In the followingquestions consist four portable answers as analternatives. You have to select most appropriatealternative as the answer.

29. You are in the parking area of a shoppingcomplex. And, suddenly the electricity fails andthere is total darkness. You will(a) try and take help from someone around(b) crawl towards your vehicle(c) shout for help(d) wait till the lights come

30. You have received a gift early, which your auntwants you to open on our birthday, which is twoweeks away. You(a) really want to open it and keep thinking it,

but do not open it(b) leave it for a while but eventually open it,

because you could not wait(c) quickly open it, because she would not come

to know(d) honour her wish, because you know that the

gift would not run away31. The front office in the organization you work for,

has a very uncomfortable physical set-up to workin. You will(a) launch a campaign to set the things right(b) complain to seniors about it(c) ignore everything and concentrate on your job(d) manage some how with reluctance

32. There has been a recent death in your family, andyou are still grieving. However, your quarterlyappraisal is round the corner, and for this youhave to catch up with a lot of work. What wouldyou do?(a) Take the help of your organization counsellor

to get overcome your emotions

(b) Ignore the appraisal and continue grievingsince the appraisal happens every threemonths, you feel you can make up the nexttime

(c) You will just try your best to wriggle out ofthe situation by asking your superior to justpostpone the appraisal for you this time

(d) You will get back to the work immediately33. You are a sincere and dedicated manager in a

reputed five star hotel. You have been appointedas the chief manager of the Guwahati branchwhich needs to be developed. Your salary has beenhiked,(a) you give it a shot for two months and see how

it goes(b) you accept the challenge and go ahead with

this project(c) you accept another offer and leave the job(d) you crib for limited resources and try to

convince the superior to send somebody elseinstead of you

ANSWERS

1. (b) 2. (d) 3. (a) 4. (d) 5. (b)

EXPLANATIONS

1. As electricity fails and there is total darkness. Youwill crawl towards your vehicle.

2. You honour her wish because you know that thegift would not run away.

3. You will campaign to set the things right.4. Death is one of the truth. But to lead your life you

will have to get back to the work immediately.5. You should accept the challenge and go ahead with

this project.




When we examine things then we seek to explain why the things happened the way they did. We categorizethese questions as cause and effect reasoning. The strong points behind any reason are known as cause and theimpact of the cause is known as effect .

Usually in such questions the candidates are asked to determine whether a given event is the cause or theeffect of some other event. Clearly, the cause must occur before the effect and the effect happens at same point oftime after the cause. This test is step to test candidates ability to analyse a pair of given statements and tocorrelate them of cause and effect. There may be several necessary conditions for the occurrence of an event andthat they must all be included in the sufficient condition. Further going on practise first we should learn somerules. These are

Rule 1: The cause will always occur before the effect. Hence, if two events are given then the effect thatis chronologically antecedent to the other can only be regarded as a possible cause.Rule 2: A necessary condition for the occurrence of a specified event is a circumstance in whose absencethe event cannot occur.Rule 3: A sufficient condition for the occurrence of an event is a circumstance in whose presence theevent must occur.Rule 4: Both the events express generalized results that may not be backed by any specific cause butmay influence certain other factors.Rule 5: The effects in both the given statements may be caused or triggered by a third unmentionedevent which may thus be called the common cause of the given events.

Basic Question Format: In such questions, two statements numbered I and II are given. There may be thecause and effect relationship between the two statements. These two statements may be the effect of the samecause or independent causes. These statements may be independent causes without having any relationship.Read both the statements in each question and mark your answer accordingly. Give answer

(a) If statement I is the cause and statement II is its effect(b) If statement II is the cause and statement I is its effect(c) If both the statements I and II are independent causes(d) If both the statements I and II are effects of independent causes

Cause and Effect




EXERCISEDirections (Q. Nos. 1 to 10): In each of the followingquestions two statements numbered I and II aregiven. There may be cause and effect relationshipbetween the two statements. These two statementsmay be the effect of the same cause or independentcauses. These statements may be independentcauses without having any relationship. Readboth the statements in each question and markyour answer as.

(a) If statement I is the cause and statement II is itseffect

(b) If statement II is the cause and statement I is itseffect

(c) If both the statements I and II are independentcauses

(d) If both the statements I and II are effects ofindependent causes

1. I. There is sharp decline in the production of oilseeds this year

II. The government has decided to increase theimport quantum of edible oil.

2. I. The life today is too fast, demanding and fullof variety in all aspects which at times leadsto stressful situations

II. Number of suicide cases among teenagers ison increase

3. I. There is unprecedented increase in the numberof young unemployed in comparison to theprevious year.

II. A large number of candidates submittedapplications against an advertisement for thepost of manager issued by a bank.

4. I. All the schools in the area had to bee keptclosed for the most part of the week.

II. Many parents have withdrawn their childrenfrom local schools.

5. I. There has been a high increase in the incidentsof atrocities against women in the city duringthe past few months.

II. The police authority has been unable to nabthe culprits who committing crime againstwomen.

6. I. Majority of citizens in the locality belong tohigher income group.

II. The sales in the local super market arecomparatively much higher than in other

localities.7. I. This year the cut-off percentages for admission

to junior colleges have increased over the lastyear.

II. This year performance of students in Xth finalexam was considerably higher than theprevious year.

8. I. The conditions of most of the nationalhighways are very bad.

II. Government has now sanctioned a hugeamount of money to maintain the nationalhighways.

9. I. Rain and thunder showers bashed the cityduring the past three days.

II. Many people stayed indoor during the pastthree days.

10. I. There has been a considerable increase in thesale of fat-free food articles.

II. Now people have become more conscious abouttheir health condition and food habits.

ANSWERS

1. (a) 2. (a) 3. (a) 4. (d) 5. (c)6. (b) 7. (b) 8. (a) 9. (a) 10. (b)

EXPLANATIONS

1. A sharp decline in oil seed production is bound toreduce oil supply and import of oil is the onlymeans to restore the essential supply.

2. The main cause of frustration among the youth isstressed occurred in day life. Frustration is boundto lead them to take harsh steps as suicide.

3. An increase in the number of unemployed youthis bound to draw in huge crowds for a singlevacancy.

4. Closing the schools for a week and the parentswith drawing their wards from the local schoolsare independent issues, which must have beentriggered by different individual causes.

5. Clearly both the given statements are not corelated to each other as well as they are causes.An increase in the cases of atrocities on womenand the police being unable to nab the culpritsinvolved in the same independent happening inthemselves.

6. The comparatively high, sales in a particularlocality are indicative of the high paying capality




of the residents of that locality.7. Since class X results were higher, the cut off

percentages for junior colleges (Class X) are boundto increase.

8. Clearly statement I is the cause and statement IIis the effect as the bad condition of the highwayhas prompted the government to take the step.

9. Rain and thunder showers forced the people tostay indoors. So, statement I is the principal causeand statement II is its effects.

10. Health consciousness has led to the sale of fat freefood articles. So, statement II is the cause andstatement I is its effect.




What is Analytical Reasoning ?Analytical reasoning involves puzzles in which the relationship among the groups of objects, people, cities

and activities etc. is given. In such questions, a bunch of information is given that creates a puzzle in candidate smind. The candidates are required to keep in mind these conditions, analyse the relationship and arrange themin suitable form to answer the questions. Such questions may deal with sitting arrangement or scheduling theactivities etc.

(1) To solve these questions, candidates need to arrange the complicated set of information. So, read themcarefully.

(2) Rather using lengthy expressions, use initials and symbols to save time.(3) While reading the set of information, highlight the key words.(4) Now, arrange the set of information in list, table or diagram.(5) Try to eliminate the answer choices, then work through the remaining choices to get the correct answer.

Directions (Q. Nos. 1 to 5) Read the following information carefully and answer the questions givenbelow.

Six lectures A, B, C, D, E and F are to be organised in a span of seven days from Sunday to Saturday, onlyone lecture on each day in accordance with the following

(i) A should not be organised on Thursday.(ii) C should be organised immediately after F.(iii) There should be a gap of two days between E and D.(iv) One day there will be no lecture (Friday is not that day), just before that day D will be organised.(v) B should be organised on Tuesday and should not be followed by D.

Example 1: Which of the following is the last lecture in the series ?(a) A (b) B(c) C (d) Can t he determined

Example 2: Which of the following information is not required in finding the complete sequence of organisationof lectures ?

(a) (i) only (b) (ii) only(c) (i) and (ii) only (d) All are required

Solutions.

Lectures D X B E F C A

Days Sunday Monday Tuesday Wednesday Thursday Friday Saturday

1. (a) 2. (d) 3. (a) 4. (d) 5. (a)

Analytical Reasoning




EXERCISEDirections (Q. Nos. 1 to 5) These questions are based on the arrow diagram of a travel network fromDelhi to Mumbai and middle stations are A to G. The figures along side the arrows indicate the timeconsumed in hours to cover the distance between two stations.

A

D G

F C B

E

Delhi

1h

5h3h

2h

3h

Mumbai

2h

2h3h

4h

1. Which is the shortest route one can take to travelfrom Delhi to Mumbai ?(a) Delhi BDG Mumbai(b) Delhi BEFG Mumbai(c) Delhi BCFG Mumbai.(d) Delhi ADG Mumbai

2. If a critical route is defined as the route whichtakes the longest time. then the critical routebetween Delhi and Mumbai is(a) Delhi ADG Mumbai(b) Delhi BEFG Mumbai(c) Delhi BCFG Mumbai(d) None of these

3. If Mahesh starts from Delhi at 9.00 am in themorning for Mumbai and if, his activities enrouteare as follows

(i) He spends 30 min at B for lunch.(ii) At C, he takes 45 min for shopping.(iii) At E, he takes a tea break for 15 min.(iv) His car breaks down at G and it takes about

an hour to repair.Find that at what time he will reach Mumbai ?(a) Mid-night (b) 11 pm(c) 1:30 am (d) None of these

4. How many routes are there to travel from Delhito Mumbai ?(a) 2 (b) 4(c) 1 (d) None of these

5. A person travels to Mumbai via Delhi, B, C, E, Fand G and returns via G, D, A and back to Delhi.How many hours has he travelled ?

(a) 29 h (b) 31 h(c) 28 h (d) 32 h

A N S W E R S1. (d) 2. (b) 3. (d) 4. (d) 5. (a)

EXPLANATIONS

1. By addition of travel times given along side thearrows, the total time taken to travel along a routecan be calculated. The shortest path is Delhi ADGMumbai and it takes 14 H.

2. The root which takes the longest time betweenDelhi and Mumbai is Delhi BEFG Mumbai.

3. Delhi

D = 9 cm A = 12 NoonD = 12:30 pm

A = 2:30 pmD = 2:15 pm

B C

EFG

MumbaiA = 2:30 pm

A = 8: 30 pmD = 9:30 pm

A = D = 6:60 pm A = 4:14 pmD = 2:15 pm

Mumbai ¬ G ¬ F ¬D = 9 am A = 0:30 Noon A = 2:30 pm A = 4:15 pmD = 12:30 pm D = 3:15 pm D = 4:30 pmMumbai G FA = 2:30 am A = 8:30 pm A = D = 6:60 pm D =9:30pm

4. There are following routes to travel from Delhi




and Mumbai(i) Delhi A D G Mumbai.

(ii) Delhi B E F G Mumbai.(iii) Delhi B C F G Mumbai.(iv) Delhi B C E F G Mumbai.(v) Delhi G D G Mumbai

So, total of 5 routes.5. Total hours = (3 + 2 + 1 + 2 + 2 + 5) + (5 + 3 + 5 +

1) = 29 h




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