Handa Ka Funda - Old CAT Papers - Maths

OLD CAT Papers - MATH CAT 2008, CAT 2007, CAT 2006, CAT 2005 & CAT 2004 –

Sorted TOPIC wise

Version 1.0

Ravi Handa Avinash Maurya

http://handakafunda.com/

Complied by: www.handakafunda.com Old CAT Papers - MATH

Home More e-books Answers

VIDEOS

DOUBT CLEARING

CONTENT DEVELOPMENT

Articles / Books / Questions on Math,

General Knowledge, Group Discussion (GD)

& Personal Interviews (PI)

LIVE EVENTS

Quizzes for corporates, schools, colleges

and clubs.

WHAT handakafunda.com DOES?

The pool of 50 videos on our website covers the entire Math syllabus for MBA Entrance Exams (CAT/ XAT / MAT and others) [Absolutely FREE !! ]

Get your doubts clarified on our

forum by expert Math / DI / LR

faculties.

[Absolutely FREE !!]

>>Click on the topics to visit their respective webpage<<

http://www.handakafunda.com/

http://handakafunda.com/downloads.php

http://handakafunda.com/services.php

http://handakafunda.com/forum/

http://www.handakafunda.com/forum/














Preface

The central idea behind this eBook comes from what we believe is the best way to use old / previous years CAT papers. There are plenty of websites where you can get the papers from. As a matter of fact, most coaching institutes also inculcate these questions in their preparation some way or the other. But most of them provide it as question papers / mock tests. However, we believe it would be most helpful to a student – in the final days of his / her preparation if he / she could get the questions sorted topic wise. Keeping that in mind, we started with sorting the questions and compiling them. The questions are divided in 5 categories, namely – Number System, Arithmetic, Algebra, Geometry, and Modern Math. We do understand that some of the questions cannot be classified as purely questions of one category – so we have taken some poetic license in cases like that. All the questions from CAT papers 2008, 2007, 2006, 2005 and 2004 are covered in this eBook. If you have any doubts, with any of the questions – you can post it on the forum and we would solve it for you. You can also post any other doubts on the forum. We skipped the years prior to 2004 because the questions in those days were much simpler than what gets asked these days. 2009 was an online exam and hence the questions were not available.

We would love to hear what you think of the eBook. For that you can use the feedback page or contact us directly. Our contact details are given at the end of the eBook.

Ravi Handa Avinash Maurya

How to use this eBook effectively?

Home page:-

Click on “Home” (at the bottom of every page) to go to the main page titled HOME. All topics under HOME are hyperlinked to the first page of that topic.

Suppose, one wants to go from Algebra to Geometry. Click “Home” and then click Geometry. This will take one from any page in Algebra to the first page of Geometry.

Answer:- Click on “Answers” (at the bottom of every page) to go to the page titled “Grand Answer Sheet”. All the answers are given on this page year-wise (sorted topic wise).



http://handakafunda.com/forum

http://www.handakafunda.com/feedback.php



Algebra

Number System

Geometry

Modern Math

HOME

Arithmetic





Number System

CAT – 2008

1. The integers 1, 2, …., 40 are written on a blackboard. The following operation is then repeated 39 times: In each

repetition, any two numbers say a and b, currently on the blackboard is erased and a new number a + b - 1 is written.

What will be the number left on the board at the end?

(1) 820 (2) 821 (3) 781 (4) 819 (5) 780 2. What are the last two digits of 7

2008?

(1) 21 (2) 61 (3)01 (4)41 (5)81

3. Three consecutive positive integers are raised to the first, second and third powers respectively and then added. The sum so obtained is a perfect square whose square root equals the total of the three original integers. Which of the following best describes the minimum, say m, of these three integers?

(1) 1 ≤ m ≤ 3 (2) 4 ≤ m ≤ 6 (3) 7 ≤ m ≤ 9 (4) 10 ≤ m ≤ 12 (5) 13 ≤ m ≤ 15

Directions for Questions 5 and 6:

Marks (1) if Q can be answered from A alone but not from B alone. Marks (2) if Q can be answered from B alone but not from A alone. Marks (3) if Q can be answered from A alone as well as from B alone. Marks (4) if Q can be answered from A and B together but not from any of them alone. Marks (5) if Q cannot be answered even from A and B together. In a single elimination tournament, any player is eliminated with a single loss. The tournament is played in multiple rounds subject to the following rules:

(a) If the number of players, say n, in any round is even, then the players are grouped in to n/2 pairs. The players in

each pair play a match against each other and the winner moves on to the next round.

4





(b) If the number of players, say n, in any round is odd, then one of them is given a bye, that is, he automatically

moves on to the next round. The remaining ( n - 1) players are grouped into ( n - 1)/2 pairs. The players in each

pair play a match against each other and the winners moves on to the next round. No player gets more than one

bye in the entire tournament.

Thus, if n is even, then n / 2 players move on to the next round while if n is odd, then (n + 1)/2 players move on to the

next round. The process is continued till the final round, which obviously is played between two players. The winner in

the final round is the champion of the tournament.

5. Q: What is the number of matches played by the champion?

A: The entry list for the tournament consists of 83 players. B: The champion received one bye.

6. Q: If the number of players, say n, in the first round was between 65 and 128, then what is the exact value of n?

A: Exactly one player received a bye in the entire tournament.

B: One player received a bye while moving on to the fourth round from third round

CAT – 2007

1. Consider four digit numbers for which the first two digits are equal and the last two digits are also equal. How many such

numbers are perfect squares?

(1) 2 (2) 4 (3) 0 (4) 1 (5) 3

Directions for Questions 2 : Each question is followed by two statements A and B. Indicate your responses based on the following directives:

Mark (1) if the question can be answered using A alone but not using B alone.

Mark (2) if the question can be answered using B alone but not using A alone. Mark (3) if the question can be answered using A and B together, but not using either A or B alone. Mark (4) if the question cannot be answered even using A and B together.

2. Consider integers x, y and z. What is the minimum possible value of x2 + y

2 + z

2 ?

A: x + y + z = 89

B: Among x, y, z two are equal.

3. Suppose you have a currency, named Miso, in three denominations: 1 Miso, 10 Misos and 50 Misos. In how many ways can you

pay a bill of 107 Misos?

(1) 16 (2) 18 (3) 15 (4) 19 (5) 17





4. How many pairs of positive integers m, n satisfy?

_

where n is an odd integer less than 60?

(1) 4 (2) 7 (3) 5 (4) 3 (5) 6

CAT - 2006

1. Which among 21/2

, 31/3

, 41/4

, 61/6

and 121/12

is the largest?

(1)21/2

(2)31/3

(3)41/4

(4)61/6

(5) 121/12

2. If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/4, then what is the value of abc/def ? (1) 3/8 (2) 27/8 (3) 3/4 (4) 27/4 (5) 1/4

3. The sum of four consecutive two-digit odd numbers, when divided by 10, becomes a perfect square. Which of the

following can possibly be one of these four numbers?

(1)21 (2)25 (3)41 (4)67 (5)73

4. When you reverse the digits of the number 13, the number increases by 18. How many other two-digit numbers

increase by 18 when their digits are reversed?

(1) 5 (2) 6 (3) 7 (4) 8 (5)10

5. The number of employees in Obelix Menhir Co. is a prime number and is less than 300. The ratio of the number of

employees who are graduates and above, to that of employees who are not, can possibly be:

(1) 101:88 (2) 87:100 (3) 110:111 (4) 85:98 (5) 97:84

CAT – 2005

1. If R =(3065

- 2965

)/ (3064

+ 2964

), then

(1) 0 < R ≤ 0.1 (2) 0.1 < R ≤ 0.5 (3) 0.5 < R ≤ 1.0 (4) R > 1.0

2. If x = (163 + 17

3 + 18

3 + 19

3), then x divided by 70 leaves a remainder of:

(1) 0 (2) 1 (3) 69 (4) 35





3. The digits of a three-digit number A are written in the reverse order to form another three-digit number B. If B > A and B - A is perfectly divisible by 7, then which of the following is necessarily true?

(1) 100 < A < 299 (2) 106 < A < 305 (3) 112 < A < 311 (4) 118 < A < 317

4. The rightmost non-zero digit of the number 302720 is:

(1) 1 (2) 3 (3) 7 (4) 9

CAT - 2004

1.

2.

3. The remainder, when (1523 + 2323) is divided by 19, is

(1) 4 (2) 15 (3) 0 (4) 18





Arithmetic

CAT - 2008

1. Rahim plans to drive from city A to station C, at the speed of 70 km per hour, to catch a train arriving there from B.

He must reach C at least 15 minutes before the arrival of the train. The train leaves B, located 500 km south of A, at

8:00 am and travels at a speed of 50 km per hour. It is known that C is located between west and northwest of B, with

BC at 60° to AB. Also, C is located between south and southwest of A with AC at 30° to AB. The latest time by which

Rahim must leave A and still catch the train is closest to

(1) 6:15 am (2) 6:30 am (3) 6:45 am (4) 7:00 am (5) 7:15 am


Five horses, Red, White, Grey, Black and Spotted participated in a race. As per the rules of the race, the persons

betting on the winning horse get four times the bet amount and those betting on the horse that came in second get

thrice the bet amount. Moreover, the bet amount is returned to those betting on the horse that came in third, and

the rest lose the bet amount. Raju bets Rs. 3000, Rs. 2000 Rs. 1000 on Red, White and Black horses respectively and

ends up with no profit and no loss.

2. Which of the following cannot be true?

(1) At least two horses finished before Spotted

(2) Red finished last

(3) There were three horses between Black and Spotted

(4) There were three horses between White and Red

(5) Grey came in second

3. Suppose, in addition, it is known that Grey came in fourth. Then which of the following cannot be

true?

(1) Spotted came in first

(2) Red finished last

(3) White came in second

(4) Black came in second

(5) There was one horse between Black and White





CAT -2007

Directions for Questions 1 & 2: Cities A and B are in different time zones. A is located 3000 km east of B. The table below describes the schedule of an airline operating non-stop flights between A and B. All the times indicated are local and on the same day.

Departure Arrival

City Time City Time

B 8:00 am A 3:00 pm

A 4:00 pm B 8:00 pm

Assume that planes cruise at the same speed in both directions. However, the effective speed is influenced by a steady wind blowing from east to west at 50 km per hour.

1. What is the time difference between A and B?

(1) 2 hours (2) 2hours and 30 minutes (3) 1 hour

(4) 1 hour and 30 minutes (5) Cannot be determined

2. What is the plane's cruising speed in km per hour? (1) 550 (2) 600 (3) 500 (4) 700 (5) Cannot be determined 3. Ten years ago, the ages of the members of a joint family of eight people added up to 231 years. Three years later, one member died at the age of 60 years and a child was born during the same year. After another three years, one more member died, again at 60, and a child was born during the same year. The current average age of this eight-member joint is nearest to

(1) 22 years (2) 21 years (3) 25 years (4) 24 years (5) 23 years

Directions for Questions 4 & 5 :

Each question is followed by two statements A and B. Indicate your responses based on the following directives:

Mark (1) if the question can be answered using A alone but not using B alone.

Mark (2) if the question can be answered using B alone but not using A alone.

Mark (3) if the question can be answered using A and B together, but not using either A or B alone.

Mark (4) if the question cannot be answered even using A and B together.

4. The average weight of a class of 100 students is 45 kg. The class consists of two sections, I and II, each with 50 students. The average weight, WI, of Sections I is smaller than the average weight, WII, of section II. If the heaviest student, say Deepak, of section II is moved to section I, and the lightest student, say Poonam, of Section I is moved, to Section II, then the average weights of the two sections are switched, i.e., the average weight of Sections I becomes W II

and that of Section II becomes WI. What is the weight of Poonam?

A : Wn - WI = 1.0 B : Moving Deepak from Section II to I (without any move from I to II) makes

the average weights of the two sections equal.





5. ABC Corporation is required to maintain at least 400 kiloliters of water at all times in its factory, in order to meet safety and regulatory requirements. ABC is considering the suitability of a spherical tank with uniform wall thickness for the purpose. The outer diameter of the tank is 10 meters. Is the tank capacity adequate to meet ABC's requirements?

A : The inner diameter of the tank is at least 8 meters. B : The tank weighs 30,000 kg when empty, and is made of a material with density of 3 gm/cc.

Directions for Questions 6 & 7:

Shabnam is considering three alternatives to invest her surplus cash for a week. She wishes to guarantee maximum return on her investment. She has three option, each of which can be utilized fully or partially in conjunction with others.

Option A : Invest in a public sector bank. It promises a return of +0.10%. Option B : Invest in mutual funds of ABC Ltd. A rise in the stock market will result in a return of + 5%, while a fall will entail a

return of - 3%.

Option C: Invest in mutual funds of CBA Ltd. A rise in the stock market will result in a return of - 2.5%, while a fall will entail a

return of + 2%.

6. The maximum guaranteed return to Shabnam is

(1) 0.10% (2) 0.20% (3) 0.15% (4) 0.30% (5) 0.25%

7. What strategy will maximize the guaranteed return to Shabnam?

(1) 36% in option B and 64% in option C (2) 64% in option B and 36% in option C (3) 1/3 in each of the three options (4) 30% in option A, 32% in option B and 38% in option C (5) 100% in option A


Mr. David manufactures and sells a single product at a fixed price in a niche market. The selling price of each unit is Rs. 30. On

the other hand, the cost, in rupees, of producing x units is 240 + bx + cx2, where b and c are some constants. Mr. David noticed

that doubling the daily production from 20 to 40 units increases the daily production cost by 662/3 %. However, an increase in

daily production from 40 to 60 units results in an increase of only 50% in the daily production cost. Assume that demand is

unlimited and that Mr. David can sell as much as he can produce. His objective is to maximize the profit.

8. How many units should Mr. David produce daily?

(1) 100 (2) 70 (3) 150 (4) 130 (5) Cannot be determined

9. What is the maximum daily profit, in rupees, that Mr. David can realize from his business?

(1) 920 (2) 840 (3) 760 (4) 620 (5) Cannot be determined

10. A confused bank teller transposed the rupees and paise when he cashed a cheque for Shailaja, giving her rupees insteadof paise and paise instead of rupees. After buying a toffee for 50 paise, Shailaja noticed that she was left with exactly three times as much as the amount on the cheque. Which of the following is a valid statement about the cheque amount?

(1) Over Rupees 7 but less than Rupees 8 (2) Over Rupees 22 but less than Rupees 23 (3) Over Rupees 18 but less than Rupees 19 (4) Over Rupees 4 but less than Rupees 5 (5) Over Rupees 13 but less than Rupees 14





CAT – 2006

1. A group of 630 children is arranged in rows for a group photograph session. Each row contains three fewer children than the row in front of it. What number of rows is not possible?

( 1 ) 3 ( 2 ) 4 ( 3 ) 5 ( 4 ) 6 ( 5 ) 7

Answer Questions 2 on the basis of the information given below:

An airline has a certain free luggage allowance and charges for excess luggage at a fixed rate per kg. Two passengers, Raja and Praja have 60 kg of luggage between them, and are charged Rs 1200 and Rs 2400 respectively for excess luggage. Had the entire luggage belonged to one of them, the excess luggage charge would have been Rs 5400.

2. What is the weight of Praja's luggage?

(1) 20 kg (2) 25 kg (3) 30 kg (4) 35 kg (5) 40 kg

3. Arun, Barun and Kiranmala start from the same place and travel in the same direction at speeds of 30, 40 and 60 km per hour

respectively. Barun starts two hours after Arun. If Barun and Kiranmala overtake Arun at the same instant, how many hours

after Arun did Kiranmala start?

(1) 3 (2) 3.5 (3) 4 (4) 4.5 (5) 5

CAT – 2005

1. A chemical plant has four tanks (A, B, C and D), each containing 1000 litres of a chemical. The chemical is being pumped from

one tank to another as follows: From A to B @ 20 litres/minute From C to A @ 90 litres/minute From A to D @ 10 litres/minute From C to D @ 50 litres/minute From B to C @ 100 litres/minute From D to B @ 110 litres/minute

Which tank gets emptied first, and how long does it take (in minutes) to get empty after pumping starts?

(1) A, 16.66 (2) C, 20 (3) D, 20 (4) D, 25

2. A jogging park has two identical circular tracks touching each other, and a rectangular track enclosing the two circles. The edges

of the rectangles are tangential to the circles. Two friends, A and B, start jogging simultaneously from the point where one of

the circular tracks touches the smaller side of the rectangular track. A jogs along the rectangular track, while B jogs along the

two circular tracks in a figure of eight. Approximately, how much faster than A does B have to run, so that they take the same

time to return to their starting point?

(1) 3.88% (2) 4.22% (3) 4.44% (4) 4.72%





Directions for questions 3 and 4 : Answer the questions on the basis of the information given below. Ram and Shyam run a race between points A and B, 5 km apart. Ram starts at 9 a.m. from A at a speed of 5 km/hr, reaches B, and returns to A at the same speed. Shyam starts at 9 : 45 a.m. from A at a speed of 10 km/hr, reaches B and comes back to A at the same speed.

3. At what time do Ram and Shyam first meet each other? (1) 10 a.m. (2) 10 : 10 a.m. (3) 10 : 20 a.m. (4) 10 : 30 a.m.

4. At what time does Shyam overtake Ram?

(1) 10 : 20 a.m. (2) 10 : 30 a.m. (3) 10 : 40 a.m. (4) 10 : 50 a.m.

5. A telecom service provider engages male and female operators for answering 1000 calls per day. A male operator can handle

40 calls per day whereas a female operator can handle 50 calls per day. The male and the female operators get a fixed wage of Rs 250 and Rs 300 per day respectively. In addition, a male operator gets Rs 15 per call he answers and a female operator gets Rs 10 per call she answers. To minimize the total cost, how many male operators should the service provider employ assuming he has to employ more than 7 of the 12 female operators available for the job?

(1) 15 (2) 14 (3) 12 (4) 10

CAT – 2004

1. Two boats, traveling at 5 and 10 kms per hour, head directly towards each other. They begin at a distance of 20 kms from

each other. How far apart are they (in kms) one minute before they collide?

(1) 1/12 (2) 1/6 (3) 1/4 (4) 1/3

2. In Nuts and Bolts factory, one machine produces only nuts at the rate of 100 nuts per minute and needs to be cleaned for 5

minutes after production of every 1000 nuts. Another machine produces only bolts at the rate of 75 bolts per minute and

needs to be cleaned for 10 minutes after production of every 1500 bolts. If both the machines start production at the same

time, what is the minimum duration required for producing 9000 pairs of nuts and bolts?

1. 130 minutes 2. 135 minutes

3. 170 minutes 4. 180 minutes

3. Karan and Arjun run a 100-metre race, where Karan beats Arjun by 10 metres. To do a favour to Arjun, Karan starts 10 metres

behind the starting line in a second 100-metre race. They both run at their earlier speeds. Which of the following is true in

connection with the second race?

1. Karan and Arjun reach the finishing line simultaneously.

2. Arjun beats Karan by 1 metre.

3. Arjun beats Karan by 11 metres.

4. Karan beats Arjun by 1 metre.





4. A milkman mixes 20 litres of water with 80 litres of milk. After selling one-fourth of this mixture, he adds water to replenish the quantity that he has sold. What is the current proportion of water to milk?

(1).2 : 3 (2).1 : 2 (3)1 : 3 (4)3 : 4

5.

6.

7. A sprinter starts running on a circular path of radius r metres. Her average speed (in metres/minute) is nr during the first 30

seconds, nr/2 during next one minute, nr/4 during next 2 minutes, nr/8 during next 4 minutes, and so on. What is the ratio of

the time taken for the nth round to that for the previous round?

(1) 4 (2) 8 (3) 16 (4) 32

Directions for Questions 8 and 9: Answer the questions on the basis of the information given below.

In an examination, there are 100 questions divided into three groups A, B and C such that each group contains at least one question. Each question in group A carries 1 mark, each question in group B carries 2 marks and each question in group C carries 3 marks. It is known that the questions in group A together carry at least 60% of the total marks.

8. If group B contains 23 questions, then how many questions are there in group C?

(1) 1 (2) 2 (3) 3 (4) Cannot be determined

9. If group C contains 8 questions and group B carries at least 20% of the total marks, which of the following best describes the

number of questions in group B?

(1) 11 or 12 (2) 12 or 13 (3) 13 or 14 (4) 14 or 15





Algebra

CAT - 2008

1. A shop stores x kg of rice. The first customer buys half this amount plus half a kg of rice. The second customer buys half

the remaining amount plus half a kg of rice. Then the third customer also buys half the remaining amount plus half a kg

of rice. Thereafter, no rice is left in the shop. Which of the following best describes the value of x?

(1) 2 < x < 6 (2) 5 < x < 8 (3) 9 < x < 12 (4) 11< x < 14 (5) 13 < x < 18

2. If the roots of the equation x3- ax

2 +bx - c =0 are three consecutive integers, then what is the smallest possible value

of b?

(1)-1/ √3 (2)-1 (3)0 (4)1 (5) 1/ √3

CAT -2007 No questions were asked from this topic in this year.

CAT - 2006

1. If x = -0.5, then which of the following has the smallest value?

(1) 21/x

(2) 1/x (3) 1/x2 (4) 2

x (5) 1/√-x

2. What are the values of x and y that satisfy both the equations?

2 0.7x

. 3 -1.25y

= 8√6√27

4 °. 3 x

. 90.2y

= 8 . (81)1/5

(1) x = 2, y = 5 (2) x = 2.5, y = 6 (3) x = 3, y = 5 ( 4 ) x = 3 , y = 4 ( 5 ) x = 5 , y = 2

3. The number of solutions of the equation 2x + y = 40 where both x and y are positive integers a n d x ≤ y is:

(1) 7 (2) 13 (3) 14 (4) 18 (5) 20





CAT - 2005

1. For which value of k does the following pair of equations yield a unique solution for x such that the solution is positive?

x2 - y

2 = 0

(x - k)2 + y

2 = 1.

(1) 2 (2) 0 (3) √2 (4) - √2

2. Let x = √ √ √ √ then x equals;

(1) 3 (2) (√13 – 1)/2 (3) (√13 + 1)/2 (4) √13

CAT – 2004

1. The total number of integer pairs (x, y) satisfying the equation x + y = xy is

(1) 0 (2) 1 (3) 2 (4) None of the above

2. Each family in a locality has at most two adults, and no family has fewer than 3 children. Considering all the families

together, there are more adults than boys, more boys than girls, and more girls than families. Then the minimum

possible number of families in the locality is

(1) 4 (2) 5 (3) 2 (4) 3

3. Let u = (log2x)2 - 6 log2x + 12 where. x is a real number. Then the equation xu = 256, has

1. no solution for x 2. exactly one solution for x 3. exactly two distinct solutions for x 4. exactly three distinct solutions for x





Geometry

CAT – 2008

1. In a triangle ABC, the lengths of the sides AB and AC equal 17.5 cm and 9 cm respectively. Let D be a point on the line

segment BC such that AD is perpendicular to BC. If AD = 3 cm, then what is the radius (in cm) of the circle

circumscribing the triangle ABC?

(1) 17.05 (2) 27.85 (3) 22.45 (4) 32.25 (5) 26.25

2. Consider obtuse-angled triangles with sides 8 cm, 15 cm and x cm. If x is an integer, then how many such triangles

exist?

(1) 5 (2) 21 (3) 10 (4) 15 (5) 14

3. Consider a square ABCD with midpoints E, F, G, H of AB, BC, CD and DA respectively. Let L denote the line passing

through F and H. Consider points P and Q, on L and inside ABCD, such that the angles APD and BQC both equal 120°.

What is the ratio of the area of ABQCDP to the remaining area inside ABCD?

4. Two circles, both of radii 1 cm, intersect such that the circumference of each one passes through the centre of the

circle of the other. What is the area (in sq. cm) of the intersecting region?

(1) π/3 - √3/4 (2) 2π/3 + √3/2 (3) 4π/3 - √3/2 (4) 4π/3 + √3/2 (5) 2π/3 - √3/2

5. Consider a right circular cone of base radius 4 cm and height 10 cm. A cylinder is to be placed inside the cone with one

of the flat surface resting on the base of the cone. Find the largest possible total surface area (in sq. cm) of the cylinder.





CAT -2007

1. Rahim plans to draw a square JKLM with a point O on the side JK but is not successful. Why is Rahim unable to draw the square? A: The length of OM is twice that of OL. B: The length of OM is 4 cm.

2. Two circles with centres P and Q cut each other at two distinct point A and B. The circles have the same radii and neither P nor Q

falls within the intersection of the circles. What is the smallest range that includes all possible values of the angle AQP in degrees?

(1) Between 0 and 30 (2) Between 0 and 60 (3) Between 0 and 75

(4) Between 0 and 45 (5) Between 0 and 90

CAT - 2006

1. The length, breadth and height of a room are in the ratio 3:2:1. If the breadth and height are halved while the length is

doubled, then the total area of the four walls of the room will

(1) remain the same (2) decrease by 13.64% (3) decrease by 15%

(4) decrease by 18.75% (5) decrease by 30%

Answer Questions 2 and 3 on the basis of the information given below:

A punching machine is used to punch a circular hole of diameter two units from a square sheet of aluminium of width 2

units, as shown below. The hole is punched such that the circular hole touches one corner P of the square sheet and

the diameter of the hole originating at P is in line with a diagonal of the square.

2. The proportion of the sheet area that remains after punching is:

(1) (Π+2)/8 (2) (6- Π)/8 (3) (4 - Π)/4 (4) (Π -2)/4 (5) (14-3 Π)/6

3. Find the area of the part of the circle (round punch) falling outside the square sheet.

(1) Π /4 (2) (Π -1)/2 (3) (Π -1)/4 (4) (Π -2)/2 (5) (Π -2)/4

P





4. A semi-circle is drawn with AB as its diameter. From C, a point on AB, a line perpendicular to AB is drawn meeting the

circumference of the semi-circle at D. Given that AC = 2 cm and CD = 6 cm, the area of the semi-circle (in sq. cm) will

be:

(1) 32Π (2) 50 Π (3) 40.5 Π (4) 81 Π (5) undeterminable

5. An equilateral triangle BPC is drawn inside a square ABCD. What is the value of the angle APD in degrees?

(1) 75 (2) 90 (3) 120 (4) 135 (5) 150

CAT - 2005

1. What is the distance in cm between two parallel chords of lengths 32 cm and 24 cm in a circle of radius 20 cm? (1) 1 or 7 (2) 2 or 14 (3) 3 or 21 (4) 4 or 28

2. Two identical circles intersect so that their centres, and the points at which they intersect, form a square of side 1 cm. The area in sq cm of the portion that is common to the two circles is:

(1) π/4 (2) π/2 - 1 (3) π/5 (4) √2 – 1

3. A rectangular floor is fully covered with square tiles of identical size. The tiles on the edges are white and the tiles in the interior are red. The number of white tiles is the same as the number of red tiles. A possible value of the number of tiles along one edge of the floor is:

(1) 10 (2) 12 (3) 14 (4) 16

4. In the following figure, the diameter of the circle is 3 cm. AB and MN are two diameters such that MN is perpendicular

to AB. In addition, CG is perpendicular to AB such that AE : EB = 1 : 2, and DF is perpendicular to MN such that NL : LM =

1 : 2. The length of DH in cm is:

(1) 2√2 – 1 (2) (2√2 – 1)/2 (3) (3√2 – 1)/2 (4) (2√2 – 1)/3

5. Four points A, B, C, and D lie on a straight line in the X-Y plane, such that AB = BC = CD, and the length of AB is 1 metre. An ant at A wants to reach a sugar particle at D. But there are insect repellents kept at points B and C. The ant would not go within one metre of any insect repellent. The minimum distance in metres the ant must traverse to reach the sugar particle is:

(1) 3√2 (2) 1+π (3) (4π)/3 (4) 5





6. Rectangular tiles each of size 70 cm by 30 cm must be laid horizontally on a rectangular floor of size110 cm by 130 cm, such that the tiles do not overlap. A tile can be placed in any orientation so long as its edges are parallel to the edges of the floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is:

(1) 4 (2) 5 (3) 6 (4) 7

7. In the X-Y plane, the area of the region bounded by the graph of |x+y| + |x - y| = 4 is:

(1) 8 (2) 12 (3) 16 (4) 20

8. Consider a triangle drawn on the X-Y plane with its three vertices at (41, 0), (0, 41) and (0, 0), each vertex being

represented by its (X, Y) coordinates. The number of points with integer coordinates inside the triangle (excluding all the points on the boundary) is:

(1) 780 (2) 800 (3) 820 (4) 741

9. Consider the triangle ABC shown in the following figure where BC = 12 cm, DB = 9 cm, CD = 6 cm and ∠BCD = ∠BAC.

What is the ratio of the perimeter of the triangle ADC to that of the triangle BDC? (1) 7/9 (2) 8/9 (3) 6/9 (4) 5/9

10. P, Q, S, R are points on the circumference of a cirlce of radius r, such that PQR is an equilateral triangle and PS is a diameter of the circle. What is the perimeter of the quadrilateral PQSR?

(1) 2r(1+√3) (2) 2r(2+√3) (3) r(1+√5) (4) 2r +√3

CAT -2004

1. A father and his son are waiting at a bus stop in the evening. There is a lamp post behind them. The lamp post, the

father and his son stand on the same straight line. The father observes that the shadows of his head and his son's head

are incident at the same point on the ground. If the heights of the lamp post, the father and his son are 6 metres, 1.8

metres and 0.9 metres respectively, and the father is standing 2.1 metres away from the post, then how far (in metres)

is the son standing from his father?

(1) 0.9 (2) 0.75 (3) 0.6 (4) 0.45

Directions for Questions 2 to 4 GEOMETRY: Answer the questions on the basis of the information given below.

In the adjoining figure, I and II are circles with centres P and Q respectively. The two circles touch each other and have

a common tangent that touches them at points R and S respectively. This common tangent meets the line joining P and

Q at O. The diameters of I and II are in the ratio 4 : 3. It is also known that the length of PO is 28 cm.

A





2. What is the ratio of the length of PQ to that of QO?

(1) 1 : 4 (2) 1 : 3 (3) 3 : 8 (4) 3 : 4

3. What is the radius of the circle II?

(1) 2 cm (2) 3 cm (3) 4 cm (4) 5cm

4. The length of SO is

(1) 8 √3 cm (2) 10 √3 cm (3) 12 √3 cm (4) 14 √3 cm

5. A rectangular sheet of paper, when halved by folding it at the mid point of its longer side, results in a rectangle,

whose longer and shorter sides are in the same proportion as the longer and shorter sides of the original rectangle. If

the shorter side of the original rectangle is 2, what is the area of the smaller rectangle?

6.





7. If the lengths of diagonals DF, AG and CE of the cube shown in the adjoining figure are equal to the three sides of a triangle, then the radius of the circle circumscribing that triangle will be

1. equal to the side of the cube

2. √3 times the side of the cube

3. 1√3 times the side of the cube

4. impossible to find from the given information 0

8. Let C be a circle with centre P0 and AB be a diameter of C. Suppose P1 is the mid point of the line segment P0B, P2 is

the mid point of the line segment P1B and so on. Let C1, C2, C3, ... be circles with diameters P0P1, P1P2, P2P3 ...

respectively. Suppose the circles C1, C2, C3, are all shaded. The ratio of the area of the unshaded portion of C to that of

the original circle C is

(1) 8 : 9 (2) 9 : 10 (3) 10 : 11 (4) 11 : 12

9. On a semicircle with diameter AD, chord BC is parallel to the diameter. Further, each of the chords AB and CD has

length 2, while AD has length 8. What is the length of BC?

(1) 7.5 (2) 7 (3) 7.75 (4) None of the above

10. A circle with radius 2 is placed against a right angle. Another smaller circle is also placed as shown in the adjoining

figure. What is the radius of the smaller circle?





Modern Math

CAT -2008


Let f (x) = ax + bx + c, where a, b and c are certain constants and a ≠ 0. It is known that f (5) = -3 f (2) and that 3 is a root

of f (x) = 0.

1. What is the other root of f (x) = 0?

(1) -7 (2) - 4 (3) 2 (4) 6 (5) cannot be determined

2. What is the value of a + b + c?

(1) 9 (2) 14 (3) 13 (4) 37 (5) cannot be determined

3. The number of common terms in the two sequences 17, 21, 25, ... , 417 and 16, 21, 26, ... , 466 is

(1) 78 (2) 19 (3) 20 (4) 77 (5) 22


The figure below shows the plan of a town. The streets are at right angles to each other. A rectangular park (P) is

situated inside the town with a diagonal road running through it. There is also a prohibited region (D) in the town.

4. Neelam rides her bicycle from her house at A to her office at B, taking the shortest path. Then the number of possible

shortest paths that she can choose is

(1) 60 (2) 75 (3) 45 (4) 90 (5) 72

D

P

A C

B





5. Neelam rides her bicycle from her house at A to her club at C, via B taking the shortest path. Then the number of

possible shortest paths that she can choose is

(1) 1170 (2) 630 (3) 792 (4) 1200 (5) 936

6. Let f (x) be a function satisfying f (x) f (y) = f (xy) for all real x, y. If f (2) = 4, then what is the value of f (1/2)? (1) 0 (2) ¼ (3) ½ (4) 1 (5) Cannot be determined

7. Suppose, the speed of any positive integer n is defined as follows:

seed(n) = n, if n < 10

= seed (s(n)), otherwise,

Where s(n) indicates the sum of digits of n. For example,

Seed (7) = 7, seed(248) = seed(2 + 4 + 8) = seed(14) = seed(1 + 4) = seed(5) = 5 etc. How many

positive integers n, such that n < 500, will have seed (n) = 9?

(1) 39 (2) 72 (3) 81 (4) 108 (5) 55

8. How many integers, greater than 999 but not greater than 4000, can be formed with the digits 0, 1, 2, 3 and 4, if

repetition of digits is allowed?

(1) 499 (2) 500 (3) 375 (4) 376 (5) 501

9. What is the number of distinct terms in the expansion of (a +b + c)20

?

(1) 231 (2) 253 (3) 242 (4) 210 (5) 228

CAT -2007

1. In a tournament, there are n team T1, T2,…., Tn, with n > 5. Each team consists of k players, k > 3. The following pairs

of teams have one player in common:

T1 & T2, T2 & T3, ….., Tn-1 & Tn, and Tn & T1

No other pair of teams has any player in common. How many players are participating in the tournament, considering

all the n teams together?

(1) k(n - 1) (2) n(k - 2) (3) k(n - 2) (4) (n - 1)(k - 1) (5) n(k - 1)





Directions for Questions 2 & 3: Let S be the set of all pairs (i, j) where 1≤ i < j ≤ n, and n ≥ 4. Any two distinct members of S are called "friends" if they have one constituent of the pairs in common and "enemies" otherwise. For example, if n = 4, then S = { (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)}. Here, (1, 2) and (1, 3) are friends, (1, 2) and (2, 3) are also friends, but (1, 4) and (2, 3) are enemies.

2. For general n, how many enemies will each member of S have?

(1)1/2(n2 -3n -2) (2) 2n -7 (3) 1/2(n

2 - 5n + 6)

(4) 1/2(n

2 -7n +14) (5) n -3

3. For general n, consider any two members of S that are friends. How many other members of S will be common friends of both these members?

(1)2n-6 (2) 1/2n(n-3) (3) n-2 (4) 1/2(n

2 -7n +16) (5) 1/2(n

2 -5n +8)

4. Consider the set S = {2, 3, 4, ….., 2n + 1), where n is a positive integer larger than 2007. Define X as the average of the

odd integers in S and Y as the average of the even integers in S. What is the value of X - Y?

(1) 1 (2)1/ 2n (3) (n+1)/2n (4) 2008 (5) 0

5. A function f (x) satisfies f (1) = 3600, and f (1) + f (2) + ... + f (n) = n2 f (n), for all positive integers n > 1. What is the value

of f(9)?

(1) 240 (2) 200 (3) 100 (4) 120 (5) 80


6.

7.





y + x

8. The price of Darjeeling tea (in rupees per kilogram) is 100 + 0.10n, on the nth

day of 2007 (n = 1, 2, ................. , 100), and then remains constant. On the other hand, the price of Ooty tea (in rupees per kilogram) is 89 + 0.15n, on the n

th

day of 2007(n = 1, 2,…. , 365). On which date in 2007 will the prices of these two varieties of tea be equal?

(1) April 11 (2) May 20 (3) April 10 (4) June 30 (5) May 21

9. A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value of f(x) at x = 10?

(1) - 159 (2) - 110 (3) - 180 (4) - 105 (5) - 119

CAT - 2006

1. Consider a sequence where the nth

term, tn = n/(n+2), n = 1 , 2 , . . . . The value of t3 x t4 x t5 x....x t53 equals:

(1) 2/495 (2) 2/477 (3) 12/55 (4) 1/1485 (5) 1/2970

2. A survey was conducted of 100 people to find out whether they had read recent issues of Golmal, a monthly magazine. The summarized information regarding readership in 3 months is given below:

Only September: 18; September but not August: 23; July: 48; July and August: 10; September and July: 8; September: 28; none of the three months: 24.

What is the number of surveyed people who have read exactly two consecutive issues (out of the three)? (1) 7 (2) 9 (3) 12 (4) 14 (5) 17

3. The graph of y - x against y + x is as shown below. (All graphs in this question are drawn to scale and the same scale has

been used on each axis.)

Which of the following shows the graph of y against x?

y - x



4. Consider the set S = {1, 2, 3, 1000}. How many arithmetic progressions can be formed from the elements of S that start

with 1 and end with 1000 and have at least 3 elements? ( 1 ) 3 ( 2 ) 4 ( 3 ) 6 ( 4 ) 7 ( 5 ) 8

5. What values o f x satisfy x2/3

+ x1/3

- 2 ≤ 0?

( 1 ) - 8 ≤x ≤1 ( 2 ) - 1 ≤x ≤8 ( 3 ) 1 < x < 8 ( 4 ) 1 ≤x ≤8 ( 5 ) - 8 ≤x ≤8

6. Let f(x) = max (2x + 1 , 3 - 4x), where x is any real number. Then the minimum possible value of f(x) is:

(1) 1/3 (2) 1/2 (3) 2/3 (4) 4/3 (5) 5/3

7. There are 6 tasks and 6 persons. Task 1 cannot be assigned either to person 1 or to person 2; task 2 must be assigned to

either person 3 or person 4. Every person is to be assigned one task. In how many ways can the assignment be done?

(1) 144 (2) 180 (3) 192 (4)360 (5)716

8. If log y x = (a . log z y) = (b . log x z) = ab, then which of the following pairs of values for (a, b) is not possible?

(1) (-2, 1/2) (2) (1,1) (3) (0.4,2.5) (4) (Π, 1/Π) (5) (2,2)



CAT – 2005

1. In a chess competition involving some boys and girls of a school, every student had to play exactly one game with every

other student. It was found that in 45 games both the players were girls, and in 190 games both were boys. The number

of games in which one player was a boy and the other was a girl is:

(1) 200 (2) 216 (3) 235 (4) 256

2. Let g(x) be a function such that g(x+1) + g(x-1) = g(x) for every real x. Then for what value of p is the relation g(x+p) = g(x) necessarily true for every real x?

(1) 5 (2) 3 (3) 2 (4) 6

3. Three Englishmen and three Frenchmen work for the same company. Each of them knows a secret not known to others. They need to exchange these secrets over person-to-person phone calls so that eventually each person knows all six secrets. None of the Frenchmen knows English, and only one Englishman knows French. What is the minimum number of phone calls needed for the above purpose?

(1) 5 (2) 10 (3) 9 (4) 15

4. Let n! = 1 x 2 x 3 x ... x n for integer n ≥ 1. If p = 1! + (2 x 2!) + (3 x 3!) + ... + (10 x 10!), then p + 2 when divided by 11! leaves a remainder of:

(1) 10 (2) 0 (3) 7 (4) 1

5. If a1 = 1 and an + 1 - 3an + 2 = 4n for every positive integer n, then a100 equals:

(1) 399

- 200 (2) 399

+ 200 (3) 3100

- 200 (4) 3100

+ 200

6. Let S be the set of five-digit numbers formed by the digits 1, 2, 3, 4 and 5, using each digit exactly once such that exactly two odd positions are occupied by odd digits. What is the sum of the digits in the rightmost position of the numbers in S?

(1) 228 (2) 216 (3) 294 (4) 192

7. If x ≥ y and y > 1, then the value of the expression logx

(x/y

) + logy (y/x) can never be:

(1) - 1 (2) - 0.5 (3) 0 (4) 1

8. For a positive integer n, let pn denote the product of the digits of n, and sn denote the sum of the digits of n. The

number of integers between 10 and 1000 for which pn + sn = n is: (1) 81 (2) 16 (3) 18 (4) 9

9. Let S be a set of positive integers such that every element n of S satisfies the conditions:

a)1000 <n < 1200

b)every digit in n is odd Then how many elements of S are divisible by 3? (1) 9 (2) 10 (3) 11 (4) 12





CAT - 2004

1. Suppose n is an integer such that the sum of the digits of n is 2, and 1010

<n < 1011

. The number of different values for n

is

1. 11 2. 10 3. 9 4. 8

2. On January 1, 2004 two new societies, S1 and S2, are formed, each with n members. On the first day of each subsequent

month, S1 adds b members while S2 multiplies its current number of members by a constant factor r. Both the societies

have the same number of members on July 2, 2004. If b = 10.5n, what is the value of r?

1. 2.0 2. 9 3. 1.8 4. 1.7

3. If the sum of the first 11 terms of an arithmetic progression equals that of the first 19 terms, then what is the sum of the

first 30 terms?

4. Let f(x) = ax - b x , where a and b are constants. Then at x = 0, f(x) is:

1. maximized whenever a > 0, b > 0 2. minimized whenever a > 0, b > 0 4. 3. maximized whenever a > 0, b < 0 4. minimized whenever a > 0, b < 0

5. If f (x) = x3 - 4x + p, and f(0) and f(1) are of opposite signs, then which of the following is necessarily true?

1.-1 < p < 2 2. 0 < p < 3 3.-2 < p < 1 4. -3 < p < 0

6. N persons stand on the circumference of a circle at 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 total time taken for singing is 28 minutes, what is N?

1. 5 2. 7 3. 9 4. None of the above

7. A new flag is to be designed with six vertical stripes using some or all of the colours yellow, green, blue and red. Then,

the number of ways this can be done such that no two adjacent stripes have the same colour is

1. 12 x 81 2. 16 x 192 3. 20 x 125 4. 24 x 216

Directions for Questions 8 and 9: Answer the questions on the basis of the information given below.

f1 (x) = x 0 < x < 1 = 1 x > 1 = 0 otherwise f2 (x) = f1(-x) for all x f3 (x) = -f2(x) for all x f4 (x) = f3(-x) for all x





8. How many of the following products are necessarily zero for every x:

f1 (x) f2 (x), f2 (x) f3 (x), f2(x) f4 (x)

1. 0 2. 1 3. 2 4.3

9. Which of the following is necessarily true?

1. f4(x) = f1(x) for all x 3. f2(-x) = f4(x) for all x

2. f1(x) = -f3(-x) for all x 4. f1(x) + f3(x) = 0 for all x

10. Consider the sequence of numbers a1, a2, a3 ... to infinity where a1 = 81.33 and a2 = -19 and aj - 1 - a - 2 for j3 3. What is

the sum of the first 6002 terms of this sequence?

1. -100.33 2. -30.00 3. 62.33 4. 119.33





Grand Answer Sheet:

CAT - 2008 Number System Arithmetic Algebra Geometry Modern Math

1-3 1-2 1-2 1-5 1-2

2-3 2-4 2-2 2-3 2-5

3-1 3-3 3-5 3-3

4-1 4-5 4-4

5-4 5-1 5-1

6-4 6-2

7-5

8-4

9-1


1-4 1-3 1-1 1-5

2-1 2-1 2-2 2-3

3-2 3-4 3-3

4-4 4-3

4-1

5-2 5-5

6-2 6-5

7-1 7-3

8-1 8-2

9-3 9-1

10-3


1-2 1-4 1-2 1-5 1-1

2-1 2-4 2-5 2-2 2-2

3-3 3-3 3-2 3-4 3-4

4-2 4-2 4-4

5-5 5-5 5-1

6-5

7-1

8-5






1-4 1-3 1-3 1-4 1-1

2-1 2-4 2-3 2-2 2-4

3-2 3-2 3-2 3-3

4-1 4-2 4-2 4-4

5-4 5-2 5-3

6-3 6-2

7-3 7-4

8-1 8-4

9-1 9-1

10-1


1-3 1-3 1-3 1-4 1-1

2-4 2-3 2-4 2-2 2-1

3-3 3-4 3-2 3-2 3-1

4-1 4-3 4-4

5-2 5-2 5-2

6-2 6-4 6-2

7-3 7-1 7-1

8-1 8-4 8-3

9-3 9-2 9-2

10-4 10-3





Contact Us

Ravi Handa

Phone: +91- 9461 493 393

Email: [email protected]

Facebook: facebook.com/ravihanda

Twitter: twitter.com/ravihanda

Linkedin: in.linkedin.com/in/ravihanda

Avinash Maurya

Phone: +91- 9983 117 978

Email: [email protected]

Facebook: facebook.com/mauryaavinash

Twitter: twitter.com/avinash_maurya



mailto:[email protected]

http://facebook.com/mauryaavinash

http://twitter.com/ravihanda

http://in.linkedin.com/in/ravihanda

mailto:[email protected]

http://facebook.com/mauryaavinash

http://twitter.com/avinash_maurya



Our other free e-books

To download any or all of the free e-books;

Visit: www.handakafunda.com/downloads.php

Trivia about how major Global / Indian companies got their names (250+ company names covered)

Comprehensive

compilation/complete list of

Maths/Quantitative Aptitude

formulas, fundas, tips and tricks

required for CAT, XAT, MAT and

other MBA Entrance examinations.

Collection of selected questions from the Tata Crucible Business Quiz over the years

2006 to 2009. (Best 421 questions)

Collection of 150 questions with answers from previous years CAT papers – Data

Interpretation (DI)+Logical Reasoning(LR). CAT 2008, 2007, 2006, 2005 and 2004

covered.



http://www.handakafunda.com/downloads.php





Date post:	28-Mar-2015
Category:	Documents
Upload:	aayush-mittal
View:	440 times
Download:	2 times

Handa Ka Funda - Old CAT Papers - Maths

Documents