CAT 2001

Directions from questions 1 to 5: Each question is independent of each other.

1. A ladder leans against a vertical wall. The top of the ladder is 3m above the ground. When the bottom of the ladder is moved 2m farther away from the wall, the top of the ladder rests against the foot of the wall. What is the length of the ladder?

a. 10m

b. 15m

c. 20m

d. 17m

 

2. Ujakar and Keshav attempted to solve a quadratic equation. Ujakar made a mistake in writing down the constant term. He ended up with the roots (4,3). Keshav made a mistake in writing down the coefficient of x. He got the roots as (3,2). What will be the exact roots of the original quadratic equation? a. (6,1)

b. (–3,–4)

c. (4,3)

d. (–4,–3)

 

3. A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6:7:8:9:10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than 50% marks is:

a. 2

b. 3

c. 4

d. 5

 

4. A certain city has a circular wall around it, and the wall has four gates pointing north, south, east and west. A house stands outside the city, three kms north of the north gate, and it can just be seen from a point nine kms east of the South Gate. What is the diameter of the wall that surrounds the city?

a. 6 km

b. 9 km

c. 12 km

d. None of these

 

5. Let x, y and z be distinct integers, x and y are odd and positive, and z is even and positive. Which one of the following statements can not be true?

a. (x–z)2y is even

b. (x–z)y2 is odd

c. (x–z)y is odd

d. (x–y)2z is even

 

6. A square, whose side is 2 meters, has its corners cut away so as to form an octagon with all sides equal. Then the length of each side of the octagon, in meters is:

a.  (sq root 2) /  ((sq root 2) + 1)

b. 2 /  ((sq root 2) + 1)

c. 2 /  ((sq root 2) – 1)

d.  (sq root 2) / ((sq root 2) -1)

 

7. All the page numbers from a book are added, beginning at page 1. However, one page number was mistakenly added twice. The sum obtained was 1000. Which page number was added twice?

a. 44

b. 45

c. 10

d. 12

 

8. x and y are real numbers satisfying the conditions 2< x < 3 and –8 < y < –7. Which of the following expressions will have the least value?

a. x2y

b. xy2

c. 5xy

d. None of these

 

9. In a number system the product of 44 and 11 is 1034. The number 3111 of this system, when converted to the decimal number system, becomes

a. 406

b. 1086

c. 213

d. 691

 

10. Based on the figure below, what is the value of x, if y=10? It is given that AD=y, AB=z, DC=x–3, BC=x+4. If AE is the perpendicular on BD, then AE = x –3.

a. 10

b. 11

c. 12

d. None of these

 

Directions for questions 11 to 12:

The petrol consumption rate of a new car ‘Palto’ depends on its speed and nay be described by the graph below :

 

11. Manisha makes the 200 km trip from Mumbai in Pune at a steady speed of 60 km per hour. What is the amount of petrol consumed for the journey?

a. 12.5 litres

b. 13.33 litres

c. 16 litres

d. 19.75 litres

 

12. Manisha would like to minimise the fuel consumption for the trip by driving at the appropriate speed. How should she change the speed?

a. Increase the speed

b. Decrease the Speed

c. Maintain the speed at 60 km/hour

d. Cannot be determined

 

DIRECTIONS for questions 13 and 14:

The batting average (BA) of a test batsman is computed from runs scored and innings played-completed innings and incomplete innings (not out) in the following manner:

r1 = number of runs scored in completed innings

n1 = number of completed innings

r2 = number of runs scored in incomplete innings

n2 = number of incomplete innings

BA = (r1 + r2)/n1s To better assess a batsman’s accomplishments, the ICC is considering two other measures MBA1 and MBA2 defined as follows: MBA1 = r1/n1 + n2/n1 + max [0, (r2/n2 – r1/n1)]

MBA2 = (r1 + r2)/(n1 + n2)

 

13. Based on the information provided which of the following is true?

a. MBA1 £ BA £ MBA2

b. BA £ MBA2 £ MBA1

c. MBA2 £ BA £ MBA1

d. None of these 14.

 

An experienced cricketer with no incomplete innings has a BA of 50, The next time he bats, the innings is incomplete and he scores 45 runs. In can be inferred that

a. BA and MBA1 will both increase

b. BA well increase and MBA2 will decrease.

c. BA will increase and not enough data is available to assess change in MBA1 and MBA2

d. None of these

 

DIRECTIONS for questions 15 to 50:

Answer the questions independent of each other.

 

15. Raju has 128 boxes with him. He has to put at least 120 oranges in one box and 144 at the most. Then the least number of boxes which will have the same number of oranges is:

a. 5

b. 103

c. 3

d. 6

 

16. Every ten years the Indian government counts all the people living in the country. Suppose that the director of he census has reported the following data on two neighboring villages Chota hazri and Mota bazri. Chota hazri has 4,522 fewer males than Mota hazri. Mota hazri has 4,020 more females than males. Chota hazri has twice as many females as males. Chota hazri has 2,910 fewer females than Mota hazri. What is the total number of males in Chota hazri?

a. 11264

b. 14174

c. 5632

d. 10154

 

17. If x > 5 and y <–1, then which of the following statements is true?

a. (x+4y) > 1

b. x > –4y

c. –4x < 5y

d. None of these

 

18. The figure below shows the network connecting cities A, B, C, D, E and F. The arrows indicate permissible direction of travel. What is the number of distinct paths from A to F? a. 9

b. 10

c. 11

d. None of these

 

19. Three runners A, B and C run a race, with runner A finishing 12 meters ahead of runner B and 18 meters ahead of runner C, while runner B finishes 8 meters ahead of runner C. Each runner travels the entire distance at a constant speed. What was the length of the race?

a. 36 meters

b. 48 meters

c. 60 meters

d. 72 meters

 

20. Consider a triangle. Its longest side has length 20 and another of its sides has length 10. Its area is 80. What is the exact length of its third side?

a. sq root (260)

b. sq root (250)

c. sq root (240)

d. sq root (270)

 

21. A train X departs from station A at 11.00 a.m. for station B, which is 1110 km away. Another train Y departs from station B at the same time. Train X travels at an average speed of 70 km/hr and does not stop anywhere until it arrives at station B. Train Y travels at an average speed of 50 km/hr, but has to stop for 15 minutes at station C, which is 60 km away from station B enroute to station A. At what distance from A would they meet?

a. 112

b. 118

c. 120

d. None of these

 

 

22. Three friends, returning from a movie, stopped to eat at a restaurant. After dinner, they paid their bill and noticed mints at the front counter. Sita took 1/3 of the mints, but returned four because she had a momentary pang of guilt. Fatima then took 1/4 of what was left but returned three for similar reasons. Eswari then took half of the reminder but threw two back into the bowl. The bowl had only 17 mints left when the raid was over. How many mints were originally in the bowl?

a. 38

b. 31

c. 41

d. None of these

 

23. Shyam and Vyom walk up an escalator (moving stairway). The escalator moves at a constant speed. Shyam takes three steps for every two of Vyom’s steps. Shyam gets to the top of the escalator after having taken 25 steps, while Vyom (because her slower pace lets the escalator do a little more of the work) takes only 20 steps to reach the top. If the escalator were turned off, how many steps would they have to take to walk up?

a. 40

b. 50

c. 60

d. 80

 

24. If a, b, c and d are four positive real numbers such that abcd = 1, what is the minimum value of (1+a) (1+b) (1+c) (1+d)

a. 4

b. 1

c. 16

d. 18

 

25. Anita had to do a multiplication. Instead of taking 35 as one of the multipliers, she took 53. As a result, the product went up by 540. What is the new product?

a. 1050

b. 540

c. 1440

d. 1590

 

26. The owner of apart shop conducts his business in the following manner: Every once in a while he raises his prices by X%, then a while later he reduces all the new prices by X%. After one such up-down cycle, the price of a painting decreased by Rs 441. After a second up- down cycle the painting was sold for Rs 1944.81. What was the original price of the painting?

a. 2756.25

b. 2256.25

c. 2500

d. 2000

 

27. A set of consecutive positive integers beginning with 1 is written on the blackboard. A student came along and erased one number. The average of the remaining numbers is 357/17. What was the number erased?

a. 7

b. 8

c. 9

d. None of these

 

28. Let n be the number of different 5 digit numbers, divisible by 4 that can be formed with the digits 1,2,3,4,5 and 6, with no digit being repeated What is the value of n?

a. 144

b. 168

c. 192

d. None of these

 

29. Three math classes: X, Y, and Z, take an algebra test. The average score in class X is 83. The average score in class Y is 76. The average score in class Z is 85. The average score of all students in classes X and Y together is 79. The average score of all student in classes Y and Z together is 81. What is the average for all the ice classes?

a. 81

b. 81.5

c. 82

d. 84.5

 

30. In the diagram, ABCD is a rectangle with AE = EF = FB. What is the ratio of the area of the triangle CFF and that of the rectangle?

a. 1/6

b. 1/8

c. 1/9

d. None of these

 

31. At a certain fast food restaurant, Bakshi can buy 3 burgers, 7 shakes, and one order of fries for Rs. 120. At the same place it would cost Rs. 164.50 for 4 burgers, 10 shakes, and one order of fries. How much would it cost for a meal of one burger, one shake, and one order of fries?

a. Rs 31

b. Rs 41

c. Rs 21

d. Cannot be determined.

 

32. A can complete a piece of work in 4 days. B takes double the time taken by A. C takes double that of B, and D takes double that of C to complete the same task. They are paired in groups of two each One pair takes two- thirds the time needed by the second pair to complete the work. Which is the first pair?

a. A,B

b. A,C

c. B,C

d. A,D

 

33. In a 4-digit number, the sum of the first two digits is equal to that of the last two digits. The sum of the first and last digits is equal to the third digit. Finally, the sum of the second and fourth digits is twice the sum of the other two digits. What is the third digit of the number?

a. 5

b. 8

c. 1

d. 4

 

34. A college has raised 75% of the amount it needs for a new building by receiving an average donation of Rs. 600 from the people already solicited. The people already solicited represent 60% of the total people the college will ask for donations. If the college is to raise exactly the amount needed for the new building, what should be the average donation from the remaining people to he solicited?

a. Rs 300

b. Rs 250

c. Rs 400

d. Rs 500

 

35. There’s a lot of work in preparing a birthday dinner. Even after the turkey s in the oven, there’s still the potatoes and gravy, salad, and cranberries, not to mention setting the table. Three friends, Asit, Arnold, and Afzal work together to get all of these chores done, The time it takes them to do the work together is six hours less than Asit would have taken working alone, one hour less than Arnold would have taken alone, and half the time Afzal would have taken working alone.

How long did it take them to do these chores working together?

a. 20 minutes
b. 30 minutes
c. 40 minutes
d. 50 minutes

 

36. A red light flashes 3 times per minute and a green light flashes 5 times in two minutes at regular intervals. If both lights start flashing at the same time, how many times do they flash together in each hour?
a. 30
b. 24
c. 20
d. 60
37. Two sides of a plot measure 32 meters and 24 meters and the angle between them is a right angle. The other two sides measure 25 meters each and the other three angles are not right angles.

What is the area of the plot?
a. 768
b. 534
c. 676.5
d. 684

 

38. Ashish is given Rs. 158 in one rupee denominations. He has been asked to allocate them into a number of bags such that any amount required between Re. 1 and Rs. 158 can be given by handing out a certain number of bags without opening them. What is the minimum number of bags required?
a. 11
b. 12
c. 13
d. None of these
39. In the given figure BC = AC, angle AFD = 40° and CE = CD. The value of angle BCE =?

a. 140
b. 70
c. 100
d. None of these

 

40. For a Fibonacci sequence, from the third term onwards, each term in the sequence is the sum of the previous two terms in that sequence. If the difference of squares of seventh and sixth terms of this sequence is 517, what is the tenth term of this sequence?
a. 147
b. 76
c. 123
d. Cannot be determined
41. In some code, letters a, b, c, d and e represents numbers 2, 4, 5, and 10. We don’t know which letter represents which number. Consider the
following relationships:
1. a+c = e
2. b–d = d and
3. e+a = b
Which statement below is true?
a. b=4, d=2
b. b=4, e=6
c. b=6, e=2
d. a=4, c=6
42. At his usual rowing rate, Rohit can travel 12 miles downstream in a certain river in six hours less than it takes him to travel the same distance upstream. But if he could double his usual rowing rate for this 24 mile round trip, the downstream 12 miles would then take only one hour less than the upstream 12 miles.
What is the speed of the current in miles per
hour?
a. 7/3
b. 4/3
c. 5/3
d. 8/3
43. Two men X and Y started working for a certain company at similar jobs on January 1,1950. X asked for an initial salary of Rs. 300 with an annual increment of Rs. 30. Y asked for an initial salary of Rs. 200 with a rise of Rs. 15 every six months. Assume that the arrangements remained unaltered till
December 31,1959. Salary is paid on the last day of the month. What is the total amount paid to them as salary during the period?
a. Rs. 93,300
b. Rs. 93,200
c. Rs. 93,100
d. None of these
44. m is the smallest positive integer such that n >m. also it is known that n3 – 7n2 ± 11n – 5 is positive. Then the possible value form is:
a. 5
b. 8
c. 4
d. None of these
45. A rectangular pool 20 meters wide and 60 metres long is surrounded by a walkway of uniform width. If the total area of the walkway is 516 square meters, how wide, in metres, is the walkway?

a. 43
b. 4.3
c. 3
d. 3.5

 

46. December 9, 2001 is Sunday. What was the day on December 9, 1971?
a. Thursday
b. Wednesday
c. Saturday
d. Sunday
47. Let b be a positive integer and a = b2–b. If b=4, then a2–a is divisible by
a. 15
b. 20
c. 24
d. None of these
48. Fresh grapes contain 90% water by weight while dried grapes contain 20% water by weight. What is the weight of dry grapes available from 20 kg of fresh grapes?
a. 2 Kg
b. 2.4 Kg
c. 2.5 Kg
d. None of these
49. A change making machine contains 1 rupee, 2 rupee and 5 rupee coins. The total number of coins is 300. The amount is Rs. 960. If the number of 1 rupee coins and the number of 2 rupee coins are interchanged, the value comes down by Rs. 40. The total number of 5 rupee coins is:
a. 100
b. 140
c. 60
d. 150
50. Let x, y he two positive numbers such that x + y = 1. Then, the minimum value of (x+1/x)2 + (y+1/y)2 is…
a. 12
b. 20
c. 12.5
d. 13.3

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