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CAT 2005 Quant Paper

Sub-section I-A: Number of Questions = 10

Note: Questions 1 to 10 carry one mark each.

Directions for Questions 1 to 5: Answer the questions independently of each other.

1. If x = (16³ + 17³+ 18³+ 19³), then x divided by 70 leaves a remainder of

1. 0 2. 1 3. 69 4. 35

2. 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

4. 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%

5. 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

Directions for Questions 6 and 7: 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.

6. 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.

7. 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.

9. 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

Sub-section I-B: Number of Questions = 20

Note: Questions 11 to 30 carry two marks each.

Directions for Questions 11 to 30: Answer the questions independently of each other.

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

1. 10 2. 0 3. 7 4. 1

12. 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

13. 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

14. If a = 1 and a_n+1 – 3a_n+ 2 = 4n for every positive integer n, then a₁₀₀ equals

1. 3⁹⁹- 200 2. 3⁹⁹+ 200 3. 3¹⁰⁰- 200 4. 3¹⁰⁰ + 200

15. 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

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

1. 1 2. 3 3. 7 4. 9

19. For a positive integer n, let p_n denotes the product of the digits of n, and s denotes the sum of the digits of n. The number of integers between 10 and 1000 for which p_n + s_n = n is

1. 81 2. 16 3. 18 4. 9

20. Rectangular tiles each of size 70 cm by 30 cm must be laid horizontally on a rectangular floor of size 110 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

27. 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

28. 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

29. 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

30. 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

CAT 2006 Quant Paper

51. 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

53. Consider a sequence where the n^th term, t_n = n/(n + 2), n = 1, 2, …. The value of t₃ × t₄ × t₅ × … × t₅₃ equals:

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

54. Which among 2^1/2, 3^1/3, 4^1/4, 6^1/6 and 12^1/12 is the largest?

(1) 2^1/2 (2) 3^1/3 (3) 4^1/4 (4) 6^1/6 (5) 12^1/12

55. 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%

56. 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; September and July; 8; September: 28;

July: 48; July and August: 10; 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

57. 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) 32p (2) 50p (3) 40.5p (4) 81p (5) CBD

Answer Questions 58 and 59 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 charges 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.

58. What is the weight of Praja’s luggage?

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

59. What is the free luggage allowance?

(1) 10 kg (2) 15 kg (3) 20 kg (4) 25 kg (5) 30 kg

60. 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 61 and 62 on the basis of the information given below:

63. What values of x satisfy x ^2/3 + x^1/3 – 2 ≤ 0?

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

64. 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

65. 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.)

66. 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

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

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

68. 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

69. 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

70. 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) (p, 1/p) (5) (2,2)

72. 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

73. 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

74. 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

75. 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 Kiramala start?

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

CAT 2007 Quant Paper

2. 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 family is nearest to

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

3. A function f(x) is given as f(1) + f(2) + f(3) +………+ f(n) = n²f(n), for all positive integers n > 1. If f(1) = 3600, find the value of f(9)?

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

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

5. A confused bank teller transposed the rupees and paise when he cashed a cheque for Shailaja, giving her rupees instead of 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 13 but less than Rupees 14 (2) Over Rupees 7 but less than Rupees 8

(3) Over Rupees 22 but less than Rupees 23 (4) Over Rupees 18 but less than Rupees 19

(5) Over Rupees 4 but less than Rupees 5

Directions for Questions 7 to 10: 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.

7. 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, W_I, of Section I is smaller than the average weight, W_II, 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 Section I becomes W_II and that of Section II becomes W_I. What is the weight of Poonam?

A: W_II – W_I =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.

8. ABC Corporation is required to maintain at least 400 Kilolitres 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 weight 30,000 kg when empty, and is made of a material with density of 3 gm/cc

9. Consider integers x, y and z. What is the minimum possible value of x²+y²+z²?

A: x + y + z = 89

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

10. 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.

Directions for Questions 11 and 12:

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.

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.

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

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

(4) 1 hour (5) Cannot be determined

12. What is the plane’s cruising speed in km per hour?

(1) 700 (2) 550 (3) 600 (4) 500 (5) CBD

Directions for Questions 13 and 14:

Shabnam is considering three alternatives to invest her surplus cash for a week. She wishes to guarantee maximum returns on her investment. She has three options, 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%.

13. The maximum guaranteed return to Shabnam is

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

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

(1) 100% in option A

(2) 36% in option B and 64% in option C

(3) 64% in option B and 36% in option C

(4) 1/3 in each of the three options

(5) 30% in option A, 32% in option B and 38% in option C

Directions for Question 15 and 16:

Let S be the set of all the 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.

18. 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 prefect squares?

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

Directions for Questions 19 and 20:

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 66.66%. 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.

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

(1) 130 (2) 100 (3) 70 (4) 150 (5) CBD

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

(1) 620 (2) 920 (3) 840 (4) 760 (5) CBD

21. The price of Darjeeling tea (in rupees per kilogram) is 100 + 0.10n, on the n^th day of 2007 (n = 1, 2, ….., 100), and then remains constant. On the other day, the price of Ooty tea (in rupees per kilograms) is 89 + 0.15n, on n^th day of 2007 (n = 1, 2, 3, 4,…….,365). On which date in 2007 will the prices of these two varieties of tea be equal?

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

22. Two circles with centres P and Q cut each other at two distinct points 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 90 (2) Between 0 and 30 (3) Between 0 and 60 (4) Between 0 and 75 (5) Between 0 and 45

23. 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) –119 (2) –159 (3) –110 (4) –180 (5) –105

CAT 2008 Quant Paper

1. The integers 1, 2……, 40 are written on a black board. The following operation is then repeated 39 times: In each repetition, any two numbers, say a and b, currently on the blackboard are 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 7²⁰⁰⁸?

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

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

Directions for Questions 5 and 6:

Let f(x) = ax² + bx + c, where a, b and c are certain constants and a ≠ 0. It is known that f(5) = -3f(2) and that 3 is a root of f(x) = 0

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

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

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

(1) 9 (2) 14 (3) 13 (4) 37 (5) CBD

7. 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

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) 373 (4) 376 (5) 501

Directions for Questions 9 and 10:

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.

9. Neelam rides her bicycle form 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

10. 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

11. 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(0.5)?

(1) 0 (2) 0.25 (3) 0.5 (4) 1 (5) Cannot be determined

13. 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

14. Consider obtuse-angles triangles with sides 8 cm, 15cm and x cm. If x is an integer, then how many such triangles exist?

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

16. 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

Directions for Questions 17 and 18:

Five horses, Red, White, Grey, Black and Spotted participated in a race. As per the rules of the race, the persons betting on the wining 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 and Rs.1000 on Red, White and Black horses respectively and ends up with no profit and no loss.

17. 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

18. 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

Directions for Questions 19 and 20:

Mark (1) if Q can be answered from A alone but not from B alone.

Mark (2) if Q can be answered from B alone but not from A alone.

Mark (3) if Q can be answered from A alone as well as from B alone.

Mark (4) if Q can be answered A and B together but not from any of them alone.

Mark (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, 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.

(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 winner 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.

19. 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.

20. 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 the third round.

22. 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^o to AB. Also, C is located between south and southwest of A with AC at 30^oto 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

23. 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

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

CAT 2003 DI Paper

Directions for questions 51 to 53: Answer the questions on the basis of the information given below.

One of the functions of the Reserve Bank of India is to mobilize funds for the Government of India by issuing securities. The following table shows the details of funds mobilized during the period of July 2002-July 2003. Notice that on each date there were two rounds of issues, each with a different maturity.

51. How many times was the issue of securities under-subscribed, i.e., how often did the total amount mobilized fall short of the amount notified?

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

52. Which of the following is true?

(1) The second round issues have a higher maturity than the first round for all dates.

(2) The second round issue of any date has a lower maturity only when the first round’s notified amount exceeds that of the second round.

(3) On at least one occasion, the second round issue having lower maturity, received a higher number of competitive bids.

(4) None of the above three statements is true.

53. Which of the following statements is NOT true?

(1) Competitive bids received always exceed non-competitive bids received.

(2) The number of competitive bids accepted does not always exceed the number of non-competitive bids accepted.

(3) The value of competitive bids accepted on any particular date is never higher for higher maturity.

(4) The value of non-competitive bids accepted in the first round is always greater than that in the second round.

Directions for questions 54 to 56: In each question there are two statements: A and B, either of which can be true or false on the basis of the information given below.

A research agency collected the following data regarding the admission process of a reputed management school in India.

Choose 1 if only A is true

Choose 2 if only B is true

Choose 3 if both A and B are true

Choose 4 if neither A nor B is true

54. Statement A: The success rate of moving from written test to interview stage for males was worse than for females in 2003.

Statement B: The success rate of moving from written test to interview stage for females was better in 2002 than in 2003

55. Statement A: In 2002, the number of females selected for the course as a proportion of the number of females who bought application forms, was higher than the corresponding proportion for males.

Statement B: In 2002, among those called for interview, males had a greater success rate than females.

56. Statement A: The percentage of absentees in the written test among females decreased from 2002 to 2003.

Statement B: The percentage of absentees in the written test among males was larger than among females in 2003.

Directions for questions 57 to 59: Answer the questions on the basis of the information given below

Table A below provides data about ages of children in a school. For the age given in the first column, the second column gives the number of children not exceeding that age. For example, first entry indicates that there are 9 children aged 4 years or less. Tables B and C provide data on the heights and weights respectively of the same group of children in a similar format. Assuming that an older child is always taller and weighs more than a younger child, answer the following questions.

57. What is the number of children of age 9 years or less whose height does not exceed 135 cm?

(1) 48 (2) 45 (3) 3 (4) Cannot be determined

58. How many children of age more than10 years are taller than 150 cm and do not weigh more than 48 kg?

(1) 16 (2) 40 (3) 9 (4) Cannot be determined

59. Among the children older than 6 years but not exceeding 12 years, how many weigh more than 38 kg?

(1) 34 (2) 52 (3) 44 (4) Cannot be determined

Directions for questions 60 and 61: Answer the questions on the basis of the information given below.

An industry comprises four firms (A, B, C and D), Financial details of these firms and of the industry as a whole for a particular year are given below. Profitability of a firm is defined as profit as a percentage of sales.

60. Which firm has the highest profitability?

(1) A (2) B (3) C (4) D

61. If Firm A acquires Firm B, approximately what percentage of the total market (total sales) will they corner together?

(1) 55% (2) 45% (3) 35% (4) 50%

Directions for questions 62 to 64: Answer the question on the basis of the information given below.

Each point in the graph below shows the profit and turnover data for a company. Each company belongs to one of the three industries: textiles, cement and steel.

62. For how many companies does the profit exceed 10% of turnover?

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

63. For how many steel companies with a turnover of more than 2000 is the profit less than 300?

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

64. An investor wants to buy stock of only steel or cement companies with a turnover more than 1000 and profit exceeding 10% of turnover. How many choices are available to the investor?

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

Directions for questions 65 to 67: Answer the questions on the basis of the information given below. Details of the top 20 MBA schools in the US as ranked by US News and World Report, 1997 are given below.

65. Madhu has received admission in all schools listed above. She wishes to select the highest overall ranked school whose a) annual tuition fee does not exceed $ 23,000 and b) median starting salary is at least $70,000. Which school will she select?

(1) University of Virginia (2) University of Pennsylvania (3) North western University (4) University of California – Berkeley

66. In terms of starting salary and tuition fee, how many schools are uniformly better (higher median starting salary AND lower annual tuition fee) than Dartmouth College?

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

67. How many schools in the list above have single digit rankings on at least 3 of the 4 parameters (overall ranking, ranking by academics, ranking by recruiters and ranking by placement)?

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

Directions for questions 68 to 71: Answer the questions on the basis of the information given below.

The length of an infant is one of the measures of his / her development in the early stages of his / her life. The figure below shows the growth chart of four infants in the first five months of life.

68. After which month did Seeta’s rate of growth start to decline?

(1) Second month (2) Third month (3) Fourth month (4) Never

69. Who grew at the fastest rate in the first two months of life?

(1) Geeta (2) Seeta (3) Ram (4) Shyam

70. The rate of growth during the third month was the lowest for

(1) Geeta. (2) Seeta. (3) Ram. (4) Shyam.

71. Among the four infants, who grew the least in the first five months of life?

(1) Geeta (2) Seeta (3) Ram (4) Shyam

Directions for questions 72 to 74: Answer the questions on the basis of the information given below.

The table below provides certain demographic details of 30 respondents who were part of a survey. The demographic characteristics are: gender, number of children, and age of respondent. The first number in each cell is the number of respondents in that group. The minimum and maximum age of respondents in each group is given in brackets. For example, there are five female respondents with no children and among these five, the youngest is 34 years old, while the oldest is 49.

72. The percentage of respondents aged less than 40 years is at least

(1) 10% (2) 16.67% (3) 20.0% (4) 30%

73. Given the information above, the percentage of respondents older than 35 can be at most

(1) 30% (2) 73.33% (3) 76.67% (4) 90%

74. The percentage of respondents that fall into the 35 to 40 years age group (both inclusive) is at least

(1) 6.67% (2) 10% (3) 13.33% (4) 26.67%

Directions for questions 75 to 77: Answer the questions on the basis of the information given below.

Spam that enters our electronic mailboxes can be classified under several spam heads. The following table shows the distribution of such spam worldwide over time. The total number of spam emails received during December 2002 was larger than the number received in June 2003. The total number of spam emails received during September 2002 was larger than the number received in March 2003. The figures in the table represent the percentage of all spam emails received during that period, falling into those respective categories.

75. In which category was the percentage of spam emails increasing but at a decreasing rate?

(1) Financial (2) Scams (3) Products (4) None of the above

76. In the health category, the number of spam emails received in December 2002 as compared to June 2003

(1) was larger. (2) was smaller. (3) was equal. (4) Cannot be determined.

77. In the financial category, the number of spam emails received in September 2002 as compared to March 2003

(1) was larger. (2) was smaller. (3) was equal. (4) Cannot be determined

Directions for questions 78 to 81: In each question there are two statements A and B.

Choice 1, if the question can be answered by one of the statements alone but not by the other.

Choice 2, if the question can be answered by using either statement alone.

Choice 3, if the question can be answered by using both the statements together but cannot be answered using either statement alone.

Choice 4, if the question cannot be answered even by using both the statements A and B.

78. F and M are father and mother of S, respectively. S has four uncles and three aunts. F has two siblings. The siblings of F and M are unmarried. How many brothers does M have?

A. F has two brothers.

B. M has five siblings.

79. A game consists of tossing a coin successively. There is an entry fee of Rs.10 and an additional fee of Re.1 for each toss of the coin. The game is considered to have ended normally when the coin turns heads on two consecutive throws. In this case the player is paid Rs.100. Alternatively, the player can choose to terminate the game prematurely after any of the tosses. Ram has incurred a loss of Rs.50 by playing this game. How many times did he toss the coin?

A. The game ended normally.

B. The total number of tails obtained in the game was 138.

80. Each packet of SOAP costs Rs.10. Inside each packet is a gift coupon labelled with one of the letters S, O, A and P. If a customer submits four such coupons that make up the word SOAP, the customer gets a free SOAP packet. Ms. X kept buying packet after packet of SOAP till she could get one set of coupons that formed the word SOAP. How many coupons with label P did she get in the above process?

A. The last label obtained by her was S and the total amount spent was Rs.210

B. The total number of vowels obtained was 18.

81. If A and B run a race, then A wins by 60 seconds. If B and C run the same race, then B wins by 30 seconds. Assuming that C maintains a uniform speed what is the time taken by C to finish the race?

A. A and C run the same race and A wins by 375 metres

B. The length of the race is 1 km.

Directions for questions 82 and 83: Answer the questions on the basis of the information given below.

Some children were taking free throws at the basketball court in school during lunch break. Below are some facts about how many baskets these children shot.

i. Ganesh shot 8 baskets less than Ashish

ii. Dhanraj and Ramesh together shot 37 baskets

iii. Jugraj shot 8 baskets more than Dhanraj

iv. Ashish shot 5 baskets more than Dhanraj

v. Ashish and Ganesh together shot 40 baskets.

82. Which of the following statements is true?

(1) Ramesh shot 18 baskets and Dhanraj shot 19 baskets.

(2) Ganesh shot 24 baskets and Ashish shot 16 baskets.

(3) Jugraj shot 19 baskets and Dhanraj shot 27 baskets.

(4) Dhanraj shot 11 baskets and Ashish shot 16 baskets.

83. Which of the following statements is true?

(1) Dhanraj and Jugraj together shot 46 baskets.

(2) Ganesh shot 18 baskets and Ramesh shot 21 baskets.

(3) Dhanraj shot 3 more baskets than Ramesh.

(4) Ramesh and Jugraj together shot 29 baskets.

Directions for questions 84 to 86: Answer the questions on the basis of the information given below.

Seven varsity basketball players (A, B, C, D, E, F and G) are to be honoured at a special luncheon. The players will be seated on the dais in a row. A and G have to leave the luncheon early and so must be seated at the extreme right. B will receive the most valuable player’s trophy and so must be in the centre to facilitate presentation. C and D are bitter rivals and therefore must be seated as far apart as possible.

84. Which of the following cannot be seated at either end?

(1) C (2) D (3) F (4) G

85. Which of the following pairs cannot be seated together?

(1) B & D (2) C & F (3) D & G (4) E & A

86. Which of the following pairs cannot occupy the seats on either side of B?

(1) F & D (2) D & E (3) E & G (4) C & F

Directions for questions 87 to 89: Answer the questions on the basis of the information given below.

A, B, C, D, E and F are a group of friends. There are two housewives, one professor, one engineer, one accountant and one lawyer in the group. There are only two married couples in the group. The lawyer is married to D, who is a housewife. No woman in the group is either an engineer or an accountant. C, the accountant, is married to F, who is a professor. A is married to a housewife. E is not a housewife.

87. Which of the following is one of the married couples?

(1) A & B (2) B & E (3) D & E (4) A & D

88. What is E’s profession?

(1) Engineer (2) Lawyer (3) Professor (4) Accountant

89. How many members of the group are males?

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

Directions for questions 90 to 92: Answer the questions on the basis of the information given below.

Rang Barsey Paint Company (RBPC) is in the business of manufacturing paints. RBPC buys RED, YELLOW, WHITE, ORANGE, and PINK paints. ORANGE paint can also be produced by mixing RED and YELLOW paints in equal proportions. Similarly, PINK paint can also be produced by mixing equal amounts of RED and WHITE paints. Among other paints, RBPC sells CREAM paint, (formed by mixing WHITE and YELLOW in the ratio 70 : 30) AVOCADO paint (formed by mixing equal amounts of ORANGE and PINK paint) and WASHEDORANGE paint (formed by mixing equal amounts of ORANGE and WHITE paint). The following table provides the prices at which RBPC buys paints.

90. The cheapest way to manufacture AVOCADO paint would cost

(1) Rs.19.50 per litre. (2) Rs.19.75 per litre. (3) Rs.20.00 per litre. (4) Rs.20.25 per litre.

91. WASHEDORANGE can be manufactured by mixing

(1) CREAM and RED in the ratio 14 : 10. (2) CREAM and RED in the ratio 3 : 1.

(3) YELLOW and PINK in the ratio 1 : 1. (4) RED, YELLOW, and WHITE in the ratio 1 : 1 : 2.

92. Assume the AVOCADO, CREAM, and WASHEDORANGE each sells for the same price. Which of the three is the most profitable to manufacture?

(1) AVOCADO. (2) CREAM. (3) WASHEDORANGE. (4) Sufficient data is not available.

Directions for questions 93 and 94: Answer the questions on the basis of the information given below.

The Head of a newly formed government desires to appoint five of the six elected members A, B, C, D, E and F to portfolios of Home, Power, Defence, Telecom and Finance. F does not want any portfolio if D gets one of the five. C wants either Home or Finance or no portfolio. B says that if D gets either Power or Telecom then she must get the other one. E insists on a portfolio if A gets one.

93. Which is a valid assignment?

(1) A-Home, B-Power, C-Defence, D-Telecom, E-Finance. (2) C-Home, D-Power, A-Defence, B-Telecom, E-Finance.

(3) A-Home, B-Power, E-Defence, D-Telecom, F-Finance. (4) B-Home, F-Power, E-Defence, C-Telecom, A-Finance.

94. If A gets Home and C gets Finance, then which is NOT A valid assignment for Defence and Telecom?

(1) D-Defence, B-Telecom. (2) F-Defence, B-Telecom. (3) B-Defence, E-Telecom. (4) B-Defence, D-Telecom.

Directions for questions 95 to 97: Answer the questions on the basis of the information given below.

Five friends meet every morning at Sree Sagar restaurant for an idli-vada breakfast. Each consumes a different number of idlis and vadas. The number of idlis consumed are 1, 4, 5, 6 and 8, while the number of vadas consumed are 0, 1, 2, 4 and 6. Below are some more facts about who eats what and how much.

i. The number of vadas eaten by Ignesh is three times the number of vadas consumed by the person who eats four idlis.

ii. Three persons, including the one who eats four vadas, eat without chutney.

iii. Sandeep does not take any chutney.

iv. The one who eats one idli a day does not eat any vadas or chutney. Further, he is not Mukesh.

v. Daljit eats idli with chutney and also eats vada.

vi. Mukesh, who does not take chutey, eats half as many vadas as the person who eats twice as many idlis as he does.

vii. Bimal eats two more idlis than Ignesh, but Ignesh eats two more vadas than Bimal.

95. Which one of the following statements is true?

(1) Daljit eats 5 idlis. (2) Ignesh eats 8 idlis. (3) Bimal eats 1 idli. (4) Bimal eats 6 idlis.

96. Which of the following statements is true?

(1) Sandeep eats 2 vadas. (2) Mukesh eats 4 vadas. (3) Ignesh eats 6 vadas. (4) Bimal eats 4 vadas.

97. Which of the following statements is true?

(1) Mukesh eats 8 idlis and 4 vadas but no chutney.

(2) The person who eats 5 idlis and 1 vada does not take chutney.

(3) The person who eats equal number of vadas and idlis also takes chutney.

(4) The person who eats 4 idlis and 2 vadas also takes chutney.

Directions for questions 98 to 100: Answer the questions on the basis of the information given below.

Five women decided to go shopping to M.G. Road, Bangalore. They arrived at the designated meeting place in the following order: 1. Archana, 2. Chellamma, 3. Dhenuka, 4. Helen and5. Shahnaz. Each woman spent at least Rs.1000. Below are some additional facts about how much they spent during their shopping spree.

i. The woman who spent Rs.2234 arrived before the lady who spent Rs.1193.

ii. One woman spent Rs.1340 and she was not Dhenuka.

iii. One woman spent Rs.1378 more than Chellamma.

iv. One woman spent Rs.2517 and she was not Archana.

v. Helen spent more than Dhenuka.

vi. Shahnaz spent the largest amount and Chellamma the smallest.

98. What was the amount spent by Helen?

(1) Rs.1193. (2) Rs.1340. (3) Rs.2234. (4) Rs.2517.

99. Which of the following amounts was spent by one of them?

(1) Rs.1139. (2) Rs.1378. (3) Rs.2571. (4) Rs.2718.

100. The woman who spent Rs.1193 is

(1) Archana. (2) Chellamma. (3) Dhenuka. (4) Helen.

CAT 2004 DI Paper

Directions for Questions 1 to 4: Answer the questions on the basis of the information given below.

1. Which family has the lowest average income?

1. Ahuja 2. Bose 3. Coomar 4. Dubey

2. Which family has the highest average expenditure?

1. Ahuja 2. Bose 3. Coomar 4. Dubey

3. The highest amount of savings accrues to a member of which family?

1. Ahuja 2. Bose 3. Coomar 4. Dubey

4. Which family has the lowest average savings?

1. Ahuja 2. Bose 3. Coomar 4. Dubey

Directions for Questions 5 to 8: Answer the questions on the basis of the information given below.

The Dean’s office recently scanned student results into the central computer system. When their character reading software cannot read something, it leaves that space blank. The scanner output reads as follows:

In the grading system, A, B, C, D, and F grades fetch 6, 4, 3, 2 and 0 grade points respectively. The Grade Point Average (GPA) is the arithmetic mean of the grade points obtained in the five subjects. For example Nisha’s GPA is (6 + 2 + 4 + 6 + 0)/5 = 3.6.

Some additional facts are also known about the students’ grades. These are

(a) Vipul obtained the same grade in Marketing as Aparna obtained in Finance and Strategy.

(b) Fazal obtained the same grade in Strategy as Utkarsh did in Marketing.

5. What grade did Preeti obtain in Statistics?

1. A 2. B 3. C 4. D

6. In Operations, Tara could have received the same grade as

1. Ismet 2. Hari 3. Jagdeep 4. Manab

7. What grade did Utkarsh obtain Finance?

1. B 2. C 3. D 4. F

8. In Strategy, Gowri’s grade point was higher than that obtained by

1. Fazal 2. Hari 3. Nisha 4. Rahul

Directions for Questions 9 to 12: Answer the questions on the basis of the information given below.

Purana and Naya are two brands of kitchen mixer-grinder available in the local market. Purana is an old brand that was introduced in 1990, while Naya was introduced in 1997. 20% of the mixer-grinders bought in a particular year are disposed off as junk exactly two years later. It is known that 10 Purana mixer-grinders were disposed off in 1997. The following figures show the number of Purana and Naya mixer-grinders in operation from 1995 to 2000, as at the end of the year.

9. How many Naya mixer-grinders were purchased in 1999?

1. 44 2. 50 3. 55 4. 64

10. How many Naya mixer-grinders were disposed off by the end of 2000?

1. 10 2. 16

3. 22 4. Cannot be determined from the data

11. How many Purana mixer-grinders were purchased in 1999?

1. 20 2. 23

3. 50 4. Cannot be determined from the data

12. How many Purana mixer-grinders were disposed off in 2000?

1. 0 2. 5

3. 6 4. Cannot be determined from the data

Directions for Questions 13 to 16: Answer the question on the basis of the information given below.

Prof. Singh has been tracking the number of visitors to his homepage. His services provider has provided him with the following data on the country of origin of the visitors and the university they belong to

13. To which country does University 5 belong?

1. India or Netherlands but not USA 2. India or USA but not Netherlands

3. Netherlands or USA but not India 4. India or USA but not UK

14. University 1 can belong to

1. UK 2. Canada

3. Netherlands 4. USA

15. Visitors from how many universities from UK visited Prof.Singh’s homepage in the three days?

1. 1 2. 2

3. 3 4. 4

16. Which among the listed countries can possibly host three of the eight listed universities?

1. None 2. Only UK

3. Only India 4. Both India and UK

Directions for Questions 17 to 20: Answer the questions on the basis of the information given below.

A study was conducted to ascertain the relative importance that employees in five different countries assigned to five different traits in their Chief Executive Officers. The traits were Compassion (C), Decisiveness (D), Negotiation skills (N), Public Visibility (P), and Vision (V). The level of dissimilarity between two countries is the maximum difference in the ranks allotted by the two countries to any of the five traits. The following table indicates the rank order of the five traits for each country.

17. Which of the following countries is least dissimilar to India?

1. China 2. Japan

3. Malaysia 4. Thailand

18. Which amongst the following countries is most dissimilar to India?

1. China 2. Japan

3. Malaysia 4. Thailand

19. Which of the following pairs of countries are most dissimilar?

1. China & Japan 2. India & China

3. Malaysia & Japan 4. Thailand & Japan

20. Three of the following four pairs of countries have identical levels of dissimilarity. Which pair is the odd one out?

1. Malaysia & China 2. China & Thailand

3. Thailand& Japan 4. Japan & Malaysia

Directions for Questions 21 to 26: Each question is followed by two statements, A and B. Answer each question using the following instructions:

Choose 1 if the question can be answered by using one of the statements alone but not by using the other statement alone.

Choose 2 if the question can be answered by using either of the statements alone.

Choose 3 if the question can be answered by using both statements together but not by either statement alone.

Choose 4 if the question cannot be answered on the basis of the two statements.

21. Four candidates for an award obtain distinct scores in a test. Each of the four casts a vote to choose the winner of the award. The candidate who gets the largest number of votes wins the award. In case of a tie in the voting process, the candidate with the highest score wins the award. Who wins the award?

A: The candidates with top three scores each vote for the top scorer amongst the other three.

B: The candidate with the lowest score votes for the player with the second highest score.

22. Zakib spends 30% of his income on his children’s education, 20% on recreation and 10% on healthcare. The corresponding percentages for Supriyo are 40%, 25%, and 13%. Who spends more on children’s education?

A: Zakib spends more on recreation than Supriyo.

B: Supriyo spends more on healthcare than Zakib.

23. Tarak is standing 2 steps to the left of a red mark and 3 steps to the right of a blue mark. He tosses a coin. If it comes up heads, he moves one step to the right; otherwise he moves one step to the left. He keeps doing this until he reaches one of the two marks, and then he stops. At which mark does he stop?

A: He stops after 21 coins tosses.

B: He obtains three more tails than heads.

24. In a class of 30 students, Rashmi secured the third rank among the girls, while her brother Kumar studying in the same class secured the sixth rank in the whole class. Between the two, who had a better overall rank?

A: Kumar was among the top 25% of the boys merit list in the class in which 60% were boys.

B: There were three boys among the top five rank holders, and three girls among the top ten rank holders.

25. Nandini paid for an article using currency notes of denominations Re.1, Rs.2, Rs.5 and Rs.10 using at least one note of each denomination. The total number of five and ten rupee notes used was one more than the total number of one and two rupee notes used. What was the price of the article?

A: Nandini used a total of 13 currency notes.

B: The price of the article was a multiple of Rs.10.

26. Ravi spent less than Rs.75 to buy one kilogram each of potato, onion, and gourd. Which one of the three vegetables bought was the costliest?

A: 2 kg potato and 1 kg gourd cost less than 1 kg potato and 2 kg gourd.

B: 1 kg potato and 2 kg onion together cost the same as 1 kg onion and 2 kg gourd.

Directions for Questions 27 to 30: Answer the questions on the basis of the information given below.

Coach John sat with the score cards of Indian players from the 3 games in a one-day cricket tournament where same set of players played for India and all the major batsmen got out. John summarized the batting performance through three diagrams, one for each game. In each diagram, the three outer triangles communicate the number of runs scored by the three top scorers from India, where K, R, S, V, and Y represent kaif, Rahul, Saurav, Virender and Yuvraj respectively. The middle triangle in each diagram denotes the percentage of total score that was scored by the top three Indian scorers in that game. No two players score the same number of runs in the same game. John also calculated two batting indices for each player based on his scores in the tournament; the R-index of a batsman is the difference between his highest and lowest scores in the 3 games while the M-index is the middle number, if his scores are arranged in a non-increasing order.

27. How many players among those listed definitely scored less than Yuvraj in the tournament?

1. 0 2. 1

3. 2 4. More than 2

28. Which of the players had the best M-index from the tournament?

1. Rahul 2. Saurav

3. Virender 4. Yuvraj

29. For how many Indian players is it possible to calculate the exact M-index?

1. 0 2. 1

3. 2 4. More than 2

30. Among the players mentioned, who can have the lowest R-index from the tournament?

1. Only Kaif, Rahul or Yuvraj 2. Only Kaif or Rahul

3. Only Kaif or Yuvraj 4. Only Kaif

Sub-section I – B: Number of Questions = 12

Directions for Questions 31 to 34: Answer the questions on the basis of the information given below.

Twenty-one participants from four continents (Africa, Americas, Australasia, and Europe) attended a United Nations conference. Each participant was an expert in one of four fields, labour, health, population studies, and refugee relocation. The following five facts about the participants are given.

(a) The number of labour experts in the camp was exactly half the number of experts in each of the three other categories.

(b) Africa did not send any labour expert. Otherwise, every continent, including Africa, sent at least one expert for each category.

(d) If there had been one less Australasian expert, then the America would have had twice as many experts as each of the other continents.

(e) Mike and Alfanso are leading experts of population studies who attended the conference. They are from Australasia.

31. Alex, an American expert in refugee relocation, was the first keynote speaker in the conference. What can be inferred about the number of American experts in refugee relocation in the conference, excluding Alex?

i. At must one

ii. At least two

1. Only i and not ii 2. Only ii and not i

3. Both i and ii 4. Neither i nor ii

32. Which of the following numbers cannot be determined from the information given?

1. Number of labour experts from Americas

2. Number of health experts from Europe

3. Number of health experts from Australasia

4. Number of experts in refugee relocation from Africa.

33. Which of the following combinations is NOT possible?

1. 2 experts in population studies from the Americas and 2 health experts from Africa attended the conference.

2. 2 experts in population studies from the Americas and 1 health expert from Africa attended the conference.

3. 3 experts in refugee relocation from the Americas and 1 health expert from Africa attended the conference.

4. Africa and America each had 1 expert in population studies attending the conference.

34. If Ramos is the lone American expert in population studies, which of the following is NOT true about the numbers of experts in the conference from the four continents?

1. There is one expert in health from Africa.

2. There is one expert in refugee relocation from Africa.

3. There are two experts in health from the Americas.

4. There are three experts in refugee relocation from the Americas.

Directions for Questions 35 to 38: Answer the questions on the basis of the information given below.

The year was 2006. All six teams in pool A of World Cup hockey, play each other only once. Each win earns a team three points, a draw earns one point and loss earns zero points. The two teams with the highest points qualify for the semi-finals. In case of a tie, the team with highest goal difference (Goal For- Goals Against) qualifies.

In the opening match, Spain lost to Germany. After the second round (after each team played two matches), the pool table looked as shown below.

In third round. Spain played Pakistan, Argentina played Germany, and New Zealand played South Africa. All the third round matches were drawn. The following are some results from the fourth and fifth round matches.

(a) Spain won both the fourth and fifth round matches.

(b) Both Argentina and Germany won their fifth round matches by 3 goals to 0.

35. Which one of the following statements is true about matches played in the first two rounds?

1. Germany beat New Zealand by 1 goal to 0.

2. Spain beat New Zealand by 4 goals to 0.

3. Spain beat South Africa by 2 goals to 0.

4. Germany beat South Africa by 2 goals to 1.

36. Which one of the following statements is true about matches played in the first two rounds?

1. Pakistan beat South Africa by 2 goals to 1.

2. Argentina beat Pakistan by 1 goal to 0.

3. Germany beat Pakistan by 2 goals to 1.

4. Germany beat Spain by 2 goals to 1.

37. Which team finished at the top of the pool after five rounds of matches?

1. Argentina 2. Germany

3. Spain 4. Cannot be determined

38. If Pakistan qualified as one of the two teams from Pool A, which was the other team that qualified?

1. Argentina 2. Germany

3. Spain 4. Cannot be determined

Directions for Questions 1 to 4: Answer the questions on the basis of the information given below.

The data points in the figure below represent monthly income and expenditure data of individual members of the Ahuja family (), the Bose family (), the Coomar family () and the Dubey family ().

For these questions savings is defined as Savings = Income – Expenditure.

CAT 2005 DI Paper

Answer Questions 61 to 64 on the basis of the information given below:

A management institute was established on January 1, 2000 with 3, 4, 5 and 6 faculty members in the Marketing, Organisational Behaviour (OB), Finance, and Operations Management (OM) areas respectively, to start with. No faculty member retired or joined the institute in the first three months of the year 2000. In the next four years, the institute recruited one faculty member in each of the four areas. All these new faculty members, who joined the institute subsequently over the years, were 25 years old at the time of their joining the institute. All of them joined the institute on April 1. During these four years, one of the faculty members retired at the age of 60. The following diagram gives the area-wise average age (in terms of number of completed years) of faculty members as on April 1 of 2000, 2001, 2002, and 2003.

61. From which area did the faculty member retire?

(1) Finance (2) Marketing (3) OB (4) OM

62. Professors Naresh and Devesh, two faculty members in the Marketing area, who have been with the Institute since its inception, share a birthday, which falls on 20^th November. One was born in 1947 and the other one in 1950. On April 1 2005, what was the age of the third faculty member, who has been in the same area since inception?

(1) 47 (2) 50 (3) 51 (4) 52

63. In which year did the new faculty member join the Finance area?

(1) 2000 (2) 2001 (3) 2002 (4) 2003

64. What was the age of the new faculty member, who joined the OM area, as on April 1, 2003?

(1) 25 (2) 26 (3) 27 (4) 28

Answer Questions 65 to 67 on the basis of the information given below:

The table below reports annual statistics related to rice production in select states of India for a particular year.

65. Which two states account for the highest productivity of rice (tons produced per hectare of rice cultivation)?

(1) Haryana and Punjab (2) Punjab and Andhra Pradesh

(3) Andhra Pradesh and Haryana (4) Uttar Pradesh and Haryana

66. How many states have a per capita production of rice (defined as total rice production divided by its population) greater than Gujarat?

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

67. An intensive rice producing state is defined as one whose annual rice production per million of population is at least 400,000 tons. How many states are intensive rice producing states?

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

Answer Questions 68 to 70 on the basis of the information given below:

The table below reports the gender, designation and age-group of the employees in an organization. It also provides information on their commitment to projects coming up in the months of January (Jan), February (Feb), March (Mar) and April (Apr), as well as their interest in attending workshops on: Business Opportunities (BO), Communication Skills (CS), and E-Government (EG).

M – Male, F = Female, Exe = Executive, Mgr = Manager, Dir = Director, Y = Young, I = In-between, O = Old

For each workshop, exactly four employees are to be sent, of which at least two should be Females and at least one should be Young. No employee can be sent to a workshop in which he/she is not interested in. An employee cannot attend the workshop on.

Communication Skills, if he/she is committed to internal projects in the month of January;
Business Opportunities, if he/she is committed to internal projects in the month of February;
E-governance, if he/she is committed to internal projects in the month of March.

68. Assuming that Parul and Hari are attending the workshop on Communication Skills (CS), then which of the following employees can possibly attend the CS workshop?

(1) Rahul and Yamini (2) Dinesh and Lavanya

(3) Anshul and Yamini (4) Fatima and Zeena

69. How many Executives (Exe) cannot attend more than one workshop?

(1) 2 (2) 3 (3) 15 (4) 16

70. Which set of employees cannot attend any of the workshops?

(1) Anshul, Charu, Eashwaran and Lavanya

(2) Anshul, Bushkant, Gayatri and Urvashi

(3) Charu, Urvashi, Bushkant and Mandeep

(4) Anshul, Gayatri, Eashwaran and Mandeep

Answer Questions 71 to 74 on the basis of the information given below:

In the table below is the listing of players, seeded from highest (#1) to lowest (#32), who are due to play in an Association of Tennis Players (ATP) tournament for women. This tournament has four knockout rounds before the final, i.e., first round, second round, quarterfinals, and semi-finals. In the first round, the highest seeded player plays the lowest seeded player (seed # 32) which is designated match No.1 of first round; the 2^nd seeded player plays the 31^st seeded player which is designated match No.2 of the first round, and so on. Thus, for instance, match No. 16 of first round is to be played between 16^th seeded player and the 17^th seeded player. In the second round, the winner of match No. 1 of first round plays the winner of match No.16 of first round and is designated match No. 1 of second round. Similarly, the winner of match No. 2 of first round plays the winner of match No. 15 of first round, and is designated match No. 2 of second round. Thus, for instance, match No. 8 of the second round is to be played between the winner of match No. 8 of first round and the winner of match No. 9 of first round. The same pattern is followed for alter rounds as well.

71. If there are no upsets (a lower seeded player beating a higher seeded player) in the first round, and only match Nos. 6, 7 and 8 of the second round result in upsets, then who would meet Lindsay Davenport in quarter finals, in case Devenport reaches quarter finals?

(1) Justine Henin (2) Nadia Petrova (3) Patty Schnyder (4) Venus Williams

72. If Elena Dementieva and Serena William lose in the second round, while Justine Henin and Nadia Petrova make it to the semi-finals, then who would play Maria Sharapova in the quarterfinals, in the event Sharapova reaches quarterfinals?

(1) Dinara Safina (2) Justine Henin (3) Nadia Petrova (4) Patty Schnyder

73. If, in the first round, all even numbered matches (and none of the odd numbered ones) result in upsets, and there are no upsets in the second round, then who could be the lowest seeded player facing Maria Sharapova in semi-finals?

(1) Anastasia Myskina (2) Flavia Pennetta (3) Nadia Petrova (4) Svetlana Kuznetsova

74. If the top eight seeds make it to the quarterfinals, then who, amongst the players listed below, would definitely not play against Maria Sharapova in the final, in case Sharapova reaches the final?

(1) Amelie Mauresmo (2) Elena Dementieva (3) Kim Clijsters (4) Lindsay Davenport

Answer Questions 75 to 78 on the basis of the information given below:

Venkat, a stockbroker, invested a part of his money in the stock of four companies — A, B, C and D. Each of these companies belonged to different industries, viz., Cement, Information Technology (IT), Auto, and Steel, in no particular order. At the time of investment, the price of each stock was Rs.100. Venkat purchased only one stock of each of these companies. He was expecting returns of 20%, 10%, 30%, and 40% from the stock of companies A, B, C and D, respectively. Returns are defined as the change in the value of the stock after one year, expressed as a percentage of the initial value. During the year, two of these companies announced extraordinarily good results. One of these two companies belonged to the Cement or the IT industry, while the other one belonged to either the Steel or the Auto industry. As a result, the returns on the stocks of these two companies were higher than the initially expected returns. For the company belonging to the Cement or IT industry with extraordinarily good results, the returns were twice that of the initially expected returns. For the company belonging to the Steel or the Auto industry, the returns on announcement of extraordinarily good results were only one and a half times that of the initially expected returns. For the remaining two companies, which did not announce extraordinarily good results, the returns realized during the year were the same as initially expected.

75. What is the minimum average return Venkat would have earned during the year?

(1) 30% (2) 31 ¹/₄% (3) 32 ¹/₂% (4) Cannot be determined

76. If Venkat earned a 35% return on average during the year, then which of these statements would necessarily be true?

I. Company A belonged either to Auto or to Steel Industry.

II. Company B did not announce extraordinarily good results.

III. Company A announced extraordinarily good results.

IV. Company D did not announce extraordinarily good results.

(1) I and II only (2) II and III only (3) III and IV only (4) II and IV only

77. If Venkat earned a 38.75% return on average during the year, then which of these statement(s) would necessarily be true?

I. Company C belonged either to Auto or to Steel Industry.

II. Company D belonged either to Auto or to Steel Industry.

III. Company A announced extraordinarily good results.

IV. Company B did not announce extraordinarily good result.

(1) I and II only (2) II and III only (3) I and IV only (4) II and IV only

78. If Company C belonged to the Cement or the IT industry and did announce extraordinarily good results, then which of these statement(s) would necessarily be true?

I. Venkat earned not more than 36.25% return on average.

II. Venkat earned not less than 33.75% return on average.

III. If Venkat earned 33.75% return on average, Company A announced extraordinarily good results.

IV. If Venkat earned 33.75% return on average, Company B belonged either to Auto or to Steel Industry.

(1) I and II only (2) II and IV only (3) II and III only (4) III and IV only

Answer Questions 79 to 82 on the basis of the information given below:

The year is 2089. Beijing, London, New York, and Paris are in contention to host the 2096 Olympics. The eventual winner is determined through several rounds of voting by members of the IOC with each member representing a different city. All the four cities in contention are also represented in IOC.

In any round of voting, the city receiving the lowest number of votes in that round gets eliminated. The survivor after the last round of voting gets to host the event.
A member is allowed to cast votes for at most two different cities in all rounds of voting combined. (Hence, a member becomes ineligible to cast a vote in a given round if both the cities (s)he voted for in the earlier rounds are out of contention in that round of voting.)
A member is also ineligible to cast a vote in a round if the city (s)he represents is in contention in that round of voting.
As long as the member is eligible, (s)he must vote and vote for only one candidate city in any round of voting.

The following incomplete table shows the information on cities that received the maximum and minimum votes in different rounds, the number of votes cast in their favour, and the total votes that were cast in those rounds.

It is also known that:

All those who voted for London and Paris in round 1, continued to vote for the same cities in subsequent rounds as long as these cities were in contention. 75% of those who voted for Beijing in round 1, voted for Beijing in round 2 as well.
Those who voted for New York in round 1, voted either for Beijing or Paris in round 2.
The difference in votes cast for the two contending cities in the last round was 1.
50% of those who voted for Beijing in round 1, voted for Paris in round 3.

79. What percentage of members from among those who voted for New York in round 1, voted for Beijing in round 2?

(1) 33.33 (2) 50 (3) 66.67 (4) 75

80. What is the number of votes cast for Paris in round 1?

(1) 16 (2) 18 (3) 22 (4) 24

81. What percentage of members from among those who voted for Beijing in round 2 and were eligible to vote in round 3, voted for London?

(1) 33.33 (2) 38.10 (3) 50 (4) 66.67

82. Which of the following statements must be true?

a. IOC member from New York must have voted for Paris in round 2.

b. IOC member from Beijing voted for London in round 3.

(1) Only a (2) Only b (3) Both a and b (4) Neither a nor b

Answer Questions 83 to 86 on the basis of the information given below:

The table below presents the revenue (in million rupees) of four in three states. These firms, Honest Ltd., Aggressive Ltd., Truthful Ltd. And Profitable Ltd. are disguised in the table as A, B, C and D, in no particular order.

Further, it is know that:

In the state of MP, Truthful Ltd. has the highest market share.
Aggressive Ltd.’s aggregate revenue differs from Honest Ltd.’s by Rs.5 million.

83. What can be said regarding the following two statements?

Statement 1: Profitable Ltd. has the lowest share in MP market.

Statement 2: Honest Ltd.’s total revenue is more than Profitable Ltd.

(1) If statement 1 is true then statement 2 is necessarily true.

(2) If statement 1 is true then statement 2 is necessarily false.

(3) Both statement 1 and statement 2 are true.

(4) Neither statement 1 nor statement 2 is true.

84. What can be said regarding the following two statements?

Statement 1: Aggressive Ltd.’s lowest revenues are from MP.

Statement 2: Honest Ltd.’s lowest revenues are from Bihar.

(1) If statement 2 is true then statement 1 is necessarily false.

(2) If statement 1 is false then statement 2 is necessarily true.

(3) If statement 1 is true then statement 2 is necessarily true.

(4) None of the above.

85. What can be said regarding the following two statements?

Statement 1: Honest Ltd. has the highest share in the UP market.

Statement 2: Aggressive Ltd. has the highest share in the Bihar market.

(1) Both statements could be true. (2) At least one of the statements must be true.

(3) At most one of the statements is true. (4) None of the above.

86. If Profitable Ltd.’s lowest revenue is from UP, then which of the following is true?

(1) Truthful Ltd.’s lowest revenues are from MP.

(2) Truthful Ltd.’s lowest revenues are from Bihar.

(3) Truthful Ltd.’s lowest revenues are from UP.

(4) No definite conclusion is possible.

Answer Questions 87 to 90 on the basis of the information given below:

Help Distress (HD) is an NGO involved in providing assistance to people suffering from natural disasters. Currently, it has 37 volunteers. They are involved in three projects: Tsunami Relief (TR) in Tamil Nadu, Flood Relief (FR) in Maharashtra, and Earthquake (ER) in Gujarat. Each volunteer working with Help Distress has to be involved in at least one relief work project.

A Maximum number of volunteers are involved in the FR project. Among them, the number of volunteers involved in FR project alone is equal to the volunteers having additional involvement in the ER project.
The number of volunteers involved in the ER project alone is double the number of volunteers involved in all the three projects.
17 volunteers are involved in the TR project.
The number of volunteers involved in the TR project alone is one less than the number of volunteers involved in ER project alone.
Ten volunteers involved in the TR project are also involved in at least one more project.

87. Based on the information given above, the minimum number of volunteers involved in both FR and TR projects, but not in the ER project is:

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

88. Which of the following additional information would enable to find the exact number of volunteers involved in various projects?

(1) Twenty volunteers are involved in FR.

(2) Four volunteers are involved in all the three projects.

(3) Twenty three volunteers are involved in exactly one project.

(4) No need for any additional information.

89. After some time, the volunteers who were involved in all the three projects were asked to withdraw from one project. As a result, one of the volunteers opted out of the TR project, and one opted out of the ER project, while the remaining ones involved in all the three projects opted out of the FR project. Which of the following statements, then, necessarily follows?

(1) The lowest number of volunteers is now in TR project.

(2) More volunteers are now in FR project as compared to ER project.

(3) More volunteers are now in TR project as compared to ER project.

(4) None of the above.

90. After the withdrawal of volunteers, as indicated in Question 89, some new volunteers joined the NGO. Each one of them was allotted only one project in a manner such that, the number of volunteers working in one project alone for each of the three projects became identical. At that point, it was also found that the number of volunteers involved in FR and ER projects was the same as the number of volunteers involved in TR and ER projects. Which of the projects now has the highest number of volunteers?

(1) ER (2) FR (3) TR (4) Cannot be determined

Word Smyths

English is mostly Latin and Greek in its origins. The fact you must have encountered while studying the etymological approach to building vocabulary. And when people make language their words come from their stories from the world around them. Greek and Latin mythologies with their heroes , gods and a plethora of villains has left an indelible mark on the English language. In this Article we look at spectactular stories of Some of these Heroes and Gods and beautiful women and the modern day word.

Words Explored: Trojan horse , Achilles heel , Hector , Odyssey , Pandora’s Box , Medusa, Narcissism , Herculean , Erotic, Aphrodaisac, Cupid , Ambrosia , Mentor , Cyclopes , Odyssey , Jovial , Mercurial , Janus Faced , Hydra Headed , Sirens, lotus eater ,Scylla ,Calypso

The World of Greek/Roman Mythology :

From Iliad and Odyssey

Trojan Horse:

a hollow wooden statue of a horse in which the Greeks concealed themselves in order to enter Troy.
figurative a person or thing intended secretly to undermine or bring about the downfall of an enemy or opponent : the rebels may use this peace accord as a Trojan horse to try and take over.
Computing a program designed to breach the security of a computer system while ostensibly performing some innocuous function.

Now you might wonder why the Greeks were trying to enter Troy. Primarily because a very beautiful woman name Helen who was the wife of the Greek king of Sparta , was according to Greeks was abducted by a Trojan prince named Paris Paris was the son of King Priam and brother of Prince Hector. Offended by this treachery the Greeks got into a thousand ships and Attacked Troy . The war went on for 40 years but the walls of TROY were strong and both side had a set of Gods favoring them so it wasn’t heading anywhere. So the Greeks Pretended to left and left a wooden horse behind looking like a gift to the god Apollo. The wooden horse was not a gift. See the picture to guess what happened.

Yes you are right. The Greeks Hid in the Horse and Attacked from inside the city of Troy and opened the gates of the city for the army waiting outside. Troy fell that day. This Most famous of Greek Mythological Tales has left tons of words behind.

Achilles Vs Hector

Achilles heel
noun
a weakness or vulnerable point. If there are terrorists seeking to do damage, Birmingham looks like a bit of an Achilles heel from a security perspective.

Achilles : One of the major Greek heroes of the Trojan War and the central figure in Homer’s epic poem the Iliad.Achilles was the son of a sea nymph,Thetis, and a mortal man, Peleus,king of Phthia (in Thessaly). According to legend,Thetis dipped the infant Achilles into the River Styx,which made him invulnerable to wounds,except in the heel by which she held him. Later,when he was a young man and the Greek forces were gathering to attack Troy,she hid her son to keep him from going to Troy because an oracle had predicted that he would die on the expedition. However,the Greek hero Odysseus discovered Achilles’hidingplace and convinced him to go to Troy. Achilles sailed for Troy at the head of acontingent of fifty ships and a group of loyal followers called the Myrmidons. According to the Iliad,in the ninth year of the siege,Achilles quarreled with the leader of the Greek forces,Agamemnon,then retired to his tent,refusing to fight. But when the Trojan champion Hector killed Achilles’ close friend Patroclus,Achilles reentered the fray and slew Hector. Later,an arrow shot by Troy’s Prince Paris struck Achilles’ vulnerable heel,killing him. So i guess you can easily make sense of the word and the meaning.

hector
verb [ trans. ]
talk to (someone) in a bullying way : she doesn’t hector us about giving up things | [as adj. ] ( hectoring) a brusque, hectoring manner.

ORIGIN late Middle English : from the Greek name Hector . Originally denoting a hero, the sense later became [braggart or bully] (applied in the late 17th cent. to a member of a gang of youths in London, England), hence [talk to in a bullying way.]

Story of Hector: 2. The eldest son of Priam and Hecuba,king and queen of Troy,and the mightiest of the Trojan warriors during the famous war with the Greeks. As Homer tells it in his Iliad, Hector played a major role in the early phases of the fighting. Later,after bidding farewell to his wife,Andromache, and small son,Astyanax (one of the most touching and memorable scenes in Western literature),Hector led several offensives against the enemy. These climaxed in his killing of Patroclus,the close friend of the great warrior Achilles. In retaliation,Achilles entered the fray,led a Greek offensive that pushed the Trojans back,and met Hector in single combat outside the city walls. Achilles managed to slay Hector,then dragged the corpse behind his chariot. (The death of Troy’s greatest champion foreshadowed the city’s eventual fall.) Later,Achilles released Hector’s body to King Priam; the Trojans gave the fallen hero a funeral fitting his stature. Hector was a noble prince and was defending his kingdom but since history is written by the survivors of the war the greeks gave hector a bad name relgating him to a status of bully possibly because of the way he treated them in the war.

odyssey
noun
a long and eventful or adventurous journey figurative : his odyssey from military man to politician.

Mentor , comes from a character called Mentor (one of the Greek kings in the trojan war) , who Ulysses trusted with his son’s education , now means a teacher or a wise counselor

Odysseus

A king of the island kingdom of Ithaca,one of the principal leaders of the Greek expedition to Troy,and the central character of Homer’s epic poem the Odyssey. Odysseus (whom the Romans called Ulysses) was one of the cleverest of the Greek leaders. He devised the plan for getting Greek troops into Troy by hiding them inside the hollow Wooden Horse,for example. After the city fell,Odysseus’s ships were blown off course and he wandered for ten years,encountering numerous adventures and crises,until finally returning home to his wife,Penelope,and son,Telemachus.The poems name became the standard for any adventurous eventful Journey.

in his journey Odysseus came across many wonders and beings and aventures each of them leaving a word behind

“For nine days I was chased by those accursed winds across the fish-infested seas,”Odysseus began,as Homer tells it in theOdyssey. “But on the tenth day we made it to the country of the Lotus-eaters, a race that live on vegetable foods.”The local inhabitants, he went on, gave some of his men some potent flower food,which made them feel lazy and forgetful and lose their desire to continue homeward. “I had to use force to bring them back to the ships,” Odysseus recalled,

lotus-eater
noun
a person who spends time indulging in pleasure and luxury rather than dealing with practical concerns.

Next,Odysseus recalled,“we came to the land of the Cyclopes,a fierce,uncivilized people, one eyed people who never lift a hand to plant or plow,but put their trust in Providence.”The Cyclopes’society is very different from that of civilized peoples, the storyteller explained. They “have no assemblies for the making of laws,nor any settled customs,but live in hollow caverns in the mountain heights,where each man is lawgiver to his children and his wives,and nobody cares a jot for his neighbors.”(Odyssey 9.94–105)

Cyclopean:

1. Vast , Gigantic

2. Architecture, Building Trades. formed with or containing large, undressed stones fitted closely together without the use of mortar: a cyclopean wall.

“They soon had to sail past the island of the Sirens, women whose seemingly beautiful songs lured sailors to their deaths. Odysseus told his men that
Circe had warned him about the Sirens and had advised him on the best way to avoid their deadly trap. As they neared the island,the men should stuff their ears with beeswax; that way they would not be able to hear the Sirens’song. Meanwhile,they must tie Odysseus to one of the ship’smasts to keep him from being bewitched and swimming to the island.”

siren
noun
1 a device that makes a loud prolonged sound as a signal or warning : ambulance sirens.
2.a woman who is considered to be alluring or fascinating but also dangerous in some way.

The plan worked and the ship made it past the Sirens’lair. However,the Greeks next had to face the perils of Scylla and Charybdis,a fearsome monster and a giant whirlpool infesting the shores of Sicily’s Strait of Messina. “My men turned pale with fear,”Odysseus recalled. .

PHRASE

between Scylla and Charybdis used to refer to a situation involving two dangers in which an attempt to avoid one increases the risk from the other.

Although they survived Scylla and Charybdis because of an offence against the Sun God Helios , Zeus destroys Odysseus’s remaining ships and he alone survives. After clinging to a broken mast and drifting for nine days, Odysseus washed ashore in Ogygia,a remote island ruled by the nymph Calypso. She fell in love with him and made him stay with her for seven years. Eventually,however,Zeus sent his swift-footed messenger, Hermes, to tell

Calypso that she must let her captive go. Reluctantly, she helped Odysseus construct a small boat,stocked the vessel with food,and sent him on his way.

calypso
noun ( pl. -sos)
a kind of West Indian (originally Trinidadian) music in syncopated African rhythm, typically with words improvised on a topical theme.
• a song in this style.

Odysseus finally reached home to Ithaca to his wife and son and killed his wife suitors and lived happily after.

Other mortals , heroes and Gods

Pandora’s box
noun
a process that generates many complicated problems as the result of unwise interference in something. “Reform is a Pandora’s box; opening up the system can lead to a loss of economic and political control” (Russell Watson).

Pandora:

In Greek legend,the first human woman. At the order of Zeus (who wanted to punish the Titan Prometheus),Hephaestos (god of the forge) fashioned Pandora from clay,and various gods endowed her with physical and mental gifts (hence her name,meaning “All Gifts”). Zeus sent her to Prometheus’s slow-witted brother,Epimetheus,who took her into his home,even though Prometheus had warned him not to accept any gifts from Zeus. Once inside, she unwittingly opened a jar (or in some accounts a box), unleashing all of the evils that still plague the human race.

According to author Willem Verdenius, the myth is not intended to imply that Pandora acted out of malice in opening the jar as she quickly closed the jar immediately after opening it. Rather her curiosity is said to have been the cause of her actions.

narcissism
noun
excessive or erotic interest in oneself and one’s physical appearance.
• Psychology extreme selfishness, with a grandiose view of one’s own talents and a craving for admiration, as characterizing a personality type.
• Psychoanalysis self-centeredness arising from failure to distinguish the self from external objects, either in very young babies or as a feature of mental disorder.

Narciss

The son of the Boeotian river god Cephisus and a nymph,Liriope. Narcissus was so handsome that he attracted many lovers,both male and female. But he was vain and eventually rejected them all. Then a nymph named Echo fell in love with him. The goddess Hera had earlier robbed her of speech,except for the ability to repeat the last syllables of words she heard. Narcissus callously ignored her advances, as he had those of so many others,and she was so crushed that she wasted away until only her voice was left (the origin of the phenomenon known as an echo,named after her). Appalled at Narcissus’s cruelty,Aphrodite (or, in an alternate account, Nemesis) caused the young man to fall in ove with his own image reflected in a pool of water. Day after day he reclined beside the pool,enamored of what he saw, until he,like Echo,wasted away and perished. Today, people who are overly impressed with themselves are called narcissists,after Narcissus.

Herculean :
adjective
requiring great strength or effort : a Herculean task.
• (of a person) muscular and strong.

Heracles : Romanised as Hercules

The most famous of all Greek heroes and a legendary strongman whose deeds figure
in dozens of Greek and Roman myths.(The Romans called him Hercules.) He was one of many illegitimate children of Zeus and Hera wife of Zeus in a rage of jealousy made Heracles mad and he ended up killing his family. To atone for his crime Heracles undertakes 12 labors given to him by Eurtheys The 12 tasks of Hercules is a major Greek Myth and quite and interesting one at that. The 12 tasks in Short are

1.   Slay the Nemean Lion.
2.   Slay the 9-headed Lernaean Hydra.
3.   Capture the Golden Hind of Artemis.
4.   Capture the Erymanthian Boar.
5.   Clean the Augean stables in a single day.
6.   Slay the Stymphalian Birds.
7.   Capture the Cretan Bull.
8.   Steal the Mares of Diomedes.
9.   Obtain the Girdle of the Amazon Queen.
10.   Obtain the Cattle of the Monster Geryon.
11.   Steal the Apples of the Hesperides.
12.   Capture Cerberus.

Hydra

1 Greek Mythology a many-headed snake whose heads grew again as they were cut off, killed by Hercules.
• [as n. ] ( hydra) a thing that is hard to overcome or resist because of its pervasive or enduring quality or its many aspects.

” But the Guerrilla movement is hydra-headed as regards reinforcements both from inside the country and outside. ” The Hydra was a water monster with 9 heads , and as soon as you cut-off one two new heads would emerge. Modern day meaning of Hydra headed is hard to eliminate or destroy . Killing the Hydra was one of the 12 tasks given to Hercules.
The Hydra had an enormous body and nine heads,one of which was immortal. Heracles went to Lerna . . . and found the Hydra on the brow of a hill . . . where it had its den. Shooting at it with flaming arrows Heracles drove the creature out,and then, when it came close,he grabbed it and held it tight. But the Hydra wrapped itself around his foot,and he was not able to get
free by striking off its heads with his club, for as soon as one head was cut off, two grew in its place. In addition,a huge crab came to the aid of the Hydra and kept biting Heracles’foot. He therefore killed the crab and . . . set fire to the woods nearby and,by burning the stumps of the Hydra’s heads with firebrands, kept them from growing out again. Then Heracles cut off the immortal head,and when he had buried it in the ground,he put a heavy rock over it.

Amazon

noun
1 a member of a legendary race of female warriors believed by the ancient Greeks to exist in Scythia (near the Black Sea in modern Russia) or elsewhere on the edge of the known world.

Watch Xena The Warrior Princess for the unadulterated Amazonian culture experiece. All hokum of course. !

erotic
adjective
of, relating to, or tending to arouse sexual desire or excitement

From Eros
1 Greek Mythology the god of love, son of Aphrodite. Roman equivalent Cupid .
• sexual love or desire.
• (in Freudian theory) the life instinct. Often contrasted with Thanatos .
• (in Jungian psychology) the principle of personal relatedness in human activities, associated with the anima. Often contrasted with Logos .

Cupid |ˈkyoōpəd| Roman Mythology
the god of love. He is represented as a naked, winged boy with a bow and arrows, with which he wounds his victims. Greek equivalent Eros .
• [as n. ] (also cupid) a representation of a naked winged child, typically carrying a bow.

Eros :

The Greek god of love (and fertility, particularly of a sexual nature),whom the Romans called Cupid (meaning “Desire”).Two versions of Eros’s origins were known in ancient times. In the first and oldest (described by the poet Hesiod), he was one of the first beings (or perhaps natural forces) born out of Chaos at the beginning of time. In this version, Eros arranged the union between Gaia (the earth) and Uranus (the sky), who subsequently gave rise to the first race of gods, the Titans. The second and later tradition about Eros made him the son of the Greek love goddess, Aphrodite, and the war god, Ares. In this more familiar role,Eros was an extremely handsome and athletic young deity whose symbols were his bow and arrows and a torch. In the HellenisticAge (the last three centuries B.C.), when romantic love came into fashion in Greek art and literature, the image of Eros/Cupid changed accordingly with the times;in his myths he became increasingly involved in making people fall into or out of love (by shooting his arrows at their hearts).

Aphrodisiac
noun
a food, drink, or drug that stimulates sexual desire : the Romans worshiped the apple as an aphrodisiac | [ as adj. ] aphrodisiac powers.
• a thing that causes excitement : for a few seconds she’d fallen for the powerful aphrodisiac of music | power is an aphrodisiac.

Aphrodite:

The Greek goddess of love and beauty and one of the twelve Olympians. Among her many symbols were dolphins, rams, doves,and roses. According to the Greek poet Hesiod, she was born out of sea foam, an image captured in numerous artistic representations through the ages.. Homer claimed that Aphrodite was the child of Zeus and Dione (a minor earth goddess). Though married to the god of the forge, Hephaestos,Aphrodite secretly loved the war god,Ares (with whom she had a son Eros, a love god often depicted in Greek art as her companion).

ambrosia
noun
the food of the gods.
• something very pleasing to taste or smell : the tea was ambrosia after the slop I’d been drinking.
• a fungal product used as food by ambrosia beetles.
• another term for beebread .
• a dessert made with oranges and shredded coconut.

Ambrosia :

A mythical, sweet-smelling food consumed by the Greek gods. According to tradition, ambrosia (along with nectar, a liquid) maintained these deities’immortality; and when a human ate it,he or she became immortal,too.

Janus-Faced come from Janus, god of beginnings and doors , now means two-faced

Mercurial , comes from Mercury the messenger of gods , who flew with the aid of his winged sandals , now means swift or active , or changing rapidly.

CAT 2006 DI Paper

Answer Questions 1 to 5 on the basis of the information given below:

K, L, M, N, P, Q, R, S, U and W are the only ten members in a department. There is a proposal to form a team from within the members of the department, subject to the following conditions:

A team must include exactly one among P, R, and S.
A team must include either M or Q, but not both.
If a team includes K, then it must also include L, and vice versa.
If a team includes one among S, U, and W, then it must also include the other two.
L and N cannot be members of the same team.
L and U cannot be members of the same team.

The size of a team is defined as the number of members in the team.

1. Who cannot be a member of a team of size 3?

(1) L (2) M (3) N (4) P (5) Q

2. Who can be a member of a team of size 5?

(1) K (2) L (3) M (4) P (5) R

3. What would be the size of the largest possible team?

(1) 8 (2) 7 (3) 6 (4) 5 (5) Cannot be determined

4. What could be the size of a team that includes K?

(1) 2 or 3 (2) 2 or 4 (3) 3 or 4 (4) Only 2 (5) Only 4

5. In how many ways a team can be constituted so that the team includes N?

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

Answer Questions 6 to 10 on the basis of the information given below:

In a Class X Board examination, ten papers are distributed over five Groups – PCB, Mathematics, Social Science, Vernacular and English. Each of the ten papers is evaluated out of 100. The final score of a student is calculated in the following manner. First, the Group Scores are obtained by averaging marks in the papers within the Group. The final score is the simple average of the Group Scores. The data for the top ten students are presented below. (Dipan’s score in English Paper II has been intentionally removed in the table.)

Note: B or G against the name of a student respectively indicates whether the student is a boy or a girl.

6. How much did Dipan get in English Paper II?

(1) 94 (2) 96.5 (3) 97 (4) 98 (5) 99

7. Among the top ten students, how many boys scored at least 95 in at least one paper from each of the groups?

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

8. Had Joseph, Agni, Pritam and Tirna each obtained Group Score of 100 in the Social Science Group, then their standing in decreasing order of final score would be:

(1) Pritam, Joseph, Tirna, Agni (2) Joseph, Tirna, Agni, Pritam (3) Pritam, Agni, Tirna, Joseph

(4) Joseph, Tirna, Pritam, Agni (5) Pritam, Tirna, Agni, Joseph

9. Students who obtained Group Scores of at least 95 in every group are eligible to apply for a prize. Among those who are eligible, the student obtaining the highest Group Score in Social Science Group is awarded this prize. The prize was awarded to:

(1) Shreya (2) Ram (3) Ayesha (4) Dipan (5) No one from the top ten

10. Each of the ten students was allowed to improve his/her score in exactly one paper of choice with the objective of maximizing his/her final score. Everyone scored 100 in the paper in which he or she chose to improve. After that, the topper among the ten students was:

(1) Ram (2) Agni (3) Pritam (4) Ayesha (5) Dipan

Answer Questions 11 to 15 on the basis of the information given below:

Mathematicians are assigned a number called Erdӧs number (named after the famous mathematician, Paul Erdӧs). Only Paul Erdӧs himself has an Erdӧs number of zero. Any mathematician who has written a research paper with Erdӧs has an Erdӧs number of 1. For other mathematicians, the calculation of his/her Erdӧs number is illustrated below:

Suppose that a mathematician X has co-authored papers with several other mathematicians. From among them, mathematician Y has the smallest Erdӧs number. Let the Erdӧs number of Y be y. Then X has an Erdӧs number of y+1. Hence any mathematician with no co-authorship chain connected to Erdӧs has an Erdӧs number of infinity.

In a seven day long mini-conference orgainzed in memory of Paul Erdӧs, a close group of eight mathematicians, call them A, B, C, D, E, F, G and H, discussed some research problems. At the beginning of the conference, A was the only participant who had an infinite Erdӧs number. Nobody had an Erdӧs number less than that of F.

On the third day of the conference F co-authored a paper jointly with A and C. This reduced the average Erdӧs number of the group of eight mathematicians to 3. The Erdӧs numbers of B, D, E G and H remained unchanged with the writing of this paper. Further, no other co-authorship among any three members would have reduced the average Erdӧs number of the group of eight to as low as 3.
At the end of the third day, five members of this group had identical Erdӧs numbers while the other three had Erdӧs numbers distinct from each other.
On the fifth day, E co-authored a paper with F which reduced the group’s average Erdӧs number by 0.5. The Erdӧs numbers of the remaining six were unchanged with the writing of this paper.
No other paper was written during the conference.

11. How many participants in the conference did not change their Erdӧs number during the conference?

(1) 2 (2) 3 (3) 4 (4) 5 (5) Cannot be determined

12. The person having the largest Erdӧs number at the end of the conference must have had Erdӧs number (at that time):

(1) 5 (2) 7 (3) 9 (4) 14 (5) 15

13. How many participants had the same Erdӧs number at the beginning of the conference?

(1) 2 (2) 3 (3) 4 (4) 5 (5) Cannot be determined

14. The Erdӧs number of C at the end of the conference was:

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

15. The Erdӧs number of E at the beginning of the conference was:

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

Answer Questions 16 to 20 on the basis of the information given below:

Two traders, Chetan and Michael, were involved in the buying and selling of MCS shares over five trading days. At the beginning of the first day, the MCS share was priced at Rs.100, while at the end of the fifth day it was priced at Rs.110. At the end of each day, the MCS share price either went up by Rs.10, or else, it came down by Rs.10. Both Chetan and Michael took buying and selling decisions at the end of each trading day. The beginning price of MCS share on a given day was the same as the ending price of the previous day. Chetan and Michael started with the same number of shares and amount of cash, and had enough of both. Below are some additional facts about how Chetan and Michael traded over the five trading days.

Each day if the price went up, Chetan sold 10 shares of MCS at the closing price. On the other hand, each day if the price went down, he bought 10 shares at the closing price.
If on any day, the closing price was above Rs.110, then Michael sold 10 shares of MCS, while if it was below Rs.90, he bought 10 shares, all at the closing price.

16. If Chetan sold 10 shares of MCS on three consecutive days, while Michael sold 10 shares only once during the five days, what was the price of MCS at the end of day 3?

(1) Rs.90 (2) Rs.100 (3) Rs.110 (4) Rs.120 (5) Rs.130

17. If Chetan ended up with Rs.1300 more cash than Michael at the end of day 5, what was the price of MCS share at the end of day 4?

(1) Rs.90 (2) Rs.100 (3) Rs.110 (4) Rs.120 (5) Not uniquely determinable

18. If Michael ended up with 20 more shares than Chetan at the end of day 5, what was the price of the share at the end of day 3?

(1) Rs.90 (2) Rs.100 (3) Rs.110 (4) Rs.120 (5) Rs.130

19. If Michael ended up with Rs.100 less cash than Chetan at the end of day 5, what was the difference in the number of shares possessed by Michael and Chetan (at the end of day 5)?

(1) Michael had 10 less shares than Chetan.

(2) Michael had 10 more shares than Chetan.

(3) Chetan had 10 more shares than Michael.

(4) Chetan had 20 more shares than Michael.

(5) Both had the same number of shares.

20. What could have been the maximum possible increase in combined cash balance of Chetan and Michael at the end of the fifth day?

(1) Rs.3700 (2) Rs.4000 (3) Rs.4700 (4) Rs.5000 (5) Rs.6000

Answer Questions 21 to 25 on the basis of the information given below :

A significant amount of traffic flows from point S to point T in the one-way street network shown below. Points A, B, C and D are junctions in the network, and the arrows mark the direction of traffic flow. The fuel cost in rupees for travelling along a street is indicated by the number adjacent to the arrow representing the street.

Motorists travelling from point S to point T would obviously take the route for which the total cost of travelling is the minimum. If two or more routes have the same least travel cost, then motorists are indifferent between them. Hence, the traffic gets evenly distributed among all the least cost routes.

The government can control the flow of traffic only by levying appropriate toll at each junction. For example, if a motorist takes the route S-A-T (using junction A alone), then the total cost of travel would be Rs.14 (i.e., Rs.9 + Rs.5) plus the toll charged at junction A.

21. If the government wants to ensure that no traffic flows on the street from D to T, while equal amount of traffic flows through junctions A and C, then a feasible set of toll charged (in rupees) at junctions A, B, C and D respectively to achieve this goal is:

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

22. If the government wants to ensure that all motorists travelling from S to T pay the same amount (fuel costs and toll combined) regardless of the route they choose and the street from B to C is under repairs ( and hence unusable), then a feasible set of toll charged (in rupees) at junctions A, B, C and D respectively to achieve this goal is:

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

23. If the government wants to ensure that the traffic at S gets evenly distributed along streets from S to A, from S to B, and from S to D, then a feasible set of toll charged (in rupees) at junctions A, B, C and D respectively to achieve this goal is:

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

24. If the government wants to ensure that all routes from S to T get the same amount of traffic, then a feasible set of toll charged (in rupees) at junctions A, B, C and D respectively to achieve this goal is:

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

25. The government wants to devise a toll policy such that the total cost to the commuters per trip is minimized. The policy should also ensure that not more than 70 per cent of the total traffic passes through junction B. The cost incurred by the commuter travelling from point S to point T under this policy will be:

(1) Rs.7 (2) Rs.9 (3) Rs.10 (4) Rs.13 (5) Rs.14

CAT 2007 DI Paper

Directions for Questions 26 to 29: Answer the following questions based on the information given below:

A health-drink company’s R and D department is trying to make various diet formulations, which can be used for certain specific purposes. It is considering a choice of 5 alternative ingredients (O, P, Q, R and S), which can be used in different proportions in the formulations. The table below gives the composition of these ingredients. The cost per unit of each of these ingredients is O : 150, P : 50, Q : 200, R : 500, S : 100.

26. For a recuperating patient, the doctor recommended a diet containing 10% minerals and at least 30% protein. In how many different ways can we prepare this diet by mixing at least two ingredients?

(1) One (2) Two (3) Three (4) Four (5) None

27. Which among the following is the formulation having the lowest cost per unit for a diet having 10% fat and at least 30% protein? The diet has to be formed by mixing two ingredients.

(1) P and Q (2) P and S (3) P and R (4) Q and S (5) R and S

28. In what proportion P, Q and S should be mixed to make a diet having at least 60% carbohydrate at the lowest per unit cost?

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

29. The company is planning to launch a balanced diet required for growth needs of adolescent children. This diet must contain at least 30% each of carbohydrate and protein, no more than 25% fat and at least 5% minerals. Which one of the following combinations of equally mixed ingredients is feasible?

(1) O and P (2) R and S (3) P and S (4) Q and R (5) O and S

Directions for questions 30 to 33: Each question is followed by two statements, A and B. Answer each question using the following instructions:

Mark (1) If the question can be answered by using the statement A alone but not by using the statement B alone

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

Mark (3) If the question can be answered by using either of the statements alone.

Mark (4) If the question can be answered by using both the statements together but not by either of the statements alone.

Mark (5) If the question cannot be answered on the basis of the two statements.

30. In a particular school, sixty students were athletes. Ten among them were also among the top academic performers. How many top academic performers were in the school?

A. Sixty per cent of the top academic performers were not athletes

B. All the top academic performers were not necessarily athletes.

31. Five students Atul, Bala, Chetan, Dev and Ernesto were the only ones who participated in a quiz contest. They were ranked based on their scores in the contest. Dev got a higher rank as compared to Ernesto, while Bala got a higher rank as compared to Chetan. Chetan’s rank was lower than the median. Who among the five got the highest rank?

A. Atul was the last rank holder.

B. Bala was not among the top two rank holders.

32. Thirty per cent of the employees of a call centre are males. Ten per cent of the female employees have an engineering background. What is the percentage of male employees with engineering background?

A. Twenty five per cent of the employees have engineering background.

B. Number of male employees having an engineering background is 20% more than the number of female employees having an engineering background.

33. In a football match, at the half-time, Mahindra and Mahindra Club was trailing by three goals. Did it win the match?

A. In the second-half Mahindra and Mahindra Club scored four goals.

B. The opponent scored four goals in the match.

Directions for questions 34 to 37: Answer the following questions based on the information given below:

The following table shows the break-up of actual costs incurred by a company in last five years (year 2002 to year 2006) to produce a particular product:

The production capacity of the company is 2000 units. The selling price for the year 2006 was Rs.125 per unit. Some costs change almost in direct proportion to the change in volume of production, while others do not follow any obvious pattern of change with respect to the volume of production and hence are considered fixed. Using the information provided for the year 2006 as the basis for projecting the figures for the year 2007, answer the following questions:

34. What is the approximate cost per unit in rupees, if the company produces and sells 1400 units in the year 2007?

(1) 104 (2) 107 (3) 110 (4) 115 (5) 116

35. What is the minimum number of units that the company needs to produce and sell to avoid any loss?

(1) 313 (2) 350 (3) 384 (4) 747 (5) 928

36. If the company reduces the price by 5%, it can produce and sell as many units as it desires. How many units the company should produce to maximize its profit?

(1) 1400 (2) 1600 (3) 1800 (4) 1900 (5) 2000

37. Given that the company cannot sell more than 1700 units, and it will have to reduce the price by Rs.5 for all units, if it wants to sell more than 1400 units what is the maximum profit, in rupees, that the company can earn?

(1) 25,400 (2) 24,400 (3) 31,400 (4) 32,900 (5) 32,000

Directions for Questions 38 to 41: Answer the following questions based on the information given below:

The proportion of male students and the proportion of vegetarian students in a school are given below. The school has a total of 800 students, 80% of whom are in the Secondary Section and rest equally divided between Class 11 and 12.

38. What is the percentage of male students in the secondary section?

(1) 40 (2) 45 (3) 50 (4) 55 (5) 60

39. In Class 12, twenty five per cent of the vegetarians are male. What is the difference between the number of female vegetarians and male non-vegetarians?

(1) less than 8 (2) 10 (3) 12 (4) 14 (5) 16

40. What is the percentage of vegetarian students in Class 12?

(1) 40 (2) 45 (3) 50 (4) 55 (5) 60

41. In the Secondary Section, 50% of the students are vegetarian males. Which of the following statements is correct?

(1) Except vegetarian males, all other groups have same number of students.

(2) Except non-vegetarian males, all other groups have same number of students.

(3) Except vegetarian females, all other groups have same number of students.

(4) Except non-vegetarian females, all other groups have same number of students.

(5) All of the above groups have the same number of students.

Directions for Questions 42 to 45: Answer the following questions based on the information given below:

The Table below shows the comparative costs, in US Dollars, of major surgeries in USA and a select few Asian countries.

The equivalent of one US Dollar in the local currencies is given below:

A consulting firm found that the quality of the health services were not the same in all the countries above. A poor quality of a surgery may have significant repercussions in future, resulting in more cost in correcting mistakes. The cost of poor quality of surgery is given in the table below:

42. A US citizen is hurt in an accident and requires an angioplasty, hip replacement and a knee replacement. Cost of foreign travel and stay is not a consideration since the government will take care of it. Which country will result in the cheapest package, taking cost of poor quality into account?

(1) India (2) Thailand (3) Malaysia (4) Singapore (5) USA

43. Taking the cost of poor quality into account, which country/countries will be the most expensive for knee replacement?

(1) India (2) Thailand (3) Malaysia (4) Singapore (5) India and Singapore

44. Approximately, what difference in amount in Bahts will it make to a Thai citizen if she were to get a hysterectomy done in India instead of in her native country, taking into account the cost of poor quality? It costs 7500 Bahts for one-way travel between Thailand and India.

(1) 23500 (2) 40500 (3) 57500 (4) 67500 (5) 75000

45. The rupee value increases to Rs.35 for a US Dollar, and all other things including quality, remain the same. What is the approximate difference in cost, in US Dollars, between Singapore and India for a Spinal Fusion, taking this change into account?

(1) 700 (2) 2500 (3) 4500 (4) 8000 (5) No difference

Directions for Questions 46 to 50: Answer the following questions based on the information given below:

A low-cost airline company connects ten Indian cities, A to J. The table below gives the distance between a pair of airports and the corresponding price charged by the company. Travel is permitted only from a departure airport to an arrival airport. The customers do not travel by a route where they have to stop at more than two intermediate airports.

46. What is the lowest price, in rupees, a passenger has to pay for travelling by the shortest route from A to J?

(1) 2275 (2) 2850 (3) 2890 (4) 2930 (5) 3340

47. The company plans to introduce a direct flight between A and J. The market research results indicate that all its existing passengers travelling between A and J will use this direct flight if it is priced 5% below the minimum price that they pay at present. What should the company charge approximately, in rupees, for this direct flight?

(1) 1991 (2) 2161 (3) 2707 (4) 2745 (5) 2783

48. If the airports C, D and H are closed down owing to security reasons, what would be the minimum price, in rupees, to be paid by a passenger travelling from A to J?

(1) 2275 (2) 2615 (3) 2850 (4) 2945 (5) 3190

49. If the prices include a margin of 10% over the total cost that the company incurs, what is the minimum cost per kilometre that the company incurs in flying from A to J?

(1) 0.77 (2) 0.88 (3) 0.99 (4) 1.06 (5) 1.08

50. If the prices include a margin of 15% over the total cost that the company incurs, which among the following is the distance to be covered in flying from A and J that minimizes the total cost per kilometer for the company?

(1) 2170 (2) 2180 (3) 2315 (4) 2350 (5) 2390

CAT 2005 Quant Paper

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CAT 2006 Quant Paper

CAT 2007 Quant Paper

CAT 2008 Quant Paper

CAT 2003 DI Paper

CAT 2004 DI Paper

CAT 2005 DI Paper

Word Smyths

The World of Greek/Roman Mythology :

From Iliad and Odyssey

Other mortals , heroes and Gods

CAT 2006 DI Paper

CAT 2007 DI Paper

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