CAT 1998

Q1. You have reached Utopia where you find two kinds of precious stones, rubies and emeralds.The worth of a ruby and that of an emerald are Rs. 4 crores and Rs. 5 crores respectively while their weights are 0.3 kg and 0.4 kg respectively. You have a bag that can carry a maximum of 12 kgs. How many rubies and emeralds would you carry such that their total value is maximised?

a. 20 rubies and 15 emeralds

b. 8 rubies and 24 emeralds

c. 0 rubies and 30 emeralds

d. None of the above

 

Q2. A colony of bacteria is a container grows by each bacterium splitting into eight next generation bacteria. However, because of environmental conditions only 50% of the bacteria in a generation can split as above. A colony of first generation bacteria was put in the container and it was found that the numberof seventh generation bacteria was 4096 million. What was the size of the first generation population initially put in the container?a. 2 million

b. 8 million

c. 1 million

d. 4 million

 

DIRECTIONS for Q3 and 4: A factory produces a product (measured in cubic feet) over seven days as per the following schedule:

The finished goods are to be transported to the market by a truck having a capacity of 200 cubic feet. Any finished goods (ready at the end of the day) retained overnight at the factory will incur a storage cost of Rs. 5 per cubic foot for each night of storage. The hiring cost for the truck is Rs. 100 per day.

Q3. If the total cost of transportation and storage is to be minimized, the truck should operate on

a. 2nd, 4th, 6th and 7th days

b. only the 7th day

c. 2nd, 4th, 5th and 7th days

d. None of the above

 

Q4. If the storage cost reduces to Rs. 0.80 per cubic foot per night, the truck should operate on

a. 2nd, 4th, 6th and 7th days

b. only the 7th day

c. 2nd, 4th, 5th and 7th days

d. None of the above

 

Directions: each of the following should be solved independently

Q5. A company has a job to prepare certain number of cans and there are three machines A, B, C for this job. A can complete the job in3 days, B can complete the job in 4 days and C can complete the job in 6 days. How many days the company will take to complete the job if all the machines are used simultaneously?

a. 4 days

b. 4/3 days

c. 3 days

d. 12 days

 

Q6. If n3 is odd, which of the following statement(s)is/are true.

a. A only

b. B only

c. A and B only

d. A and C only

 

Q7. In the following figure, there are three circles, each of radius 20 and centres at P, Q, R. Further, AB=5, CD=10 and EF=12. What is the perimeter of the triangle PQR?

 

a. 60 cm

b. 81 cm

c. 93 cm

d. 87 cm

 

Directions for Q. 8 to 10. The following operations are defined for real numbers:

a # b = a + b if a and b both are positive else a # b = 1

Q58. The value  of is

a. 2/3

b. 1/2

c. 1/3

d. None of these

 

Q9. The value of

 

Q10. Given that is equal to 3/8, for two integers x and y, which of the following statements is true:

a. Both x and y are negative

b. x = 1 and y =2

c. x<0, y>0

d. x>0, y<0

 

Directions: Each of the following should be solved independently

Q11. If , where B, E, M & P are distinct integers, then what is the value of M ?

a. 2

b. 3

c. 9

d. None of these

 

Q12. Five digit numbers are formed using only 0, 1,2, 3, 4 exactly once. What is the difference between the maximum and minimum number that can be formed?

a. 19800

b. 41976

c. 32976

d. None of these

 

Q13. How many numbers can be formed from 1, 2,3, 4, 5 (without repetition), when the digit at the units place must be greater than that in the tenth place?

a. 54

b. 60

c. 5!/3

d. 2 × 4!

 

Q14. Distance between two places A and B is 72 km. Two men started walking from A and B at the same time towards each other. The person who started from A travelled uniformly with average speed4 kmph. While the other man travelled with varying speeds as follows:

In first hour his speed was 2 kmph, in the second hour it was 2.5 kmph, in the third hour it was 3 kmph, and so on. When will they meet each other?

a. 7 hours

b. 10 hours

c. 35 km from A

d. midway between A & B

 

Q15. P, Q, R, S are four statements. Relation between these statements is as follows:

If P is true then Q must be true.

If Q is true then R must be true.

If S is true then either Q is false or R is false.

Then which of the following must be true?

a. If P is true then S is false

b. If S is false then Q must be true

c. If Q is true then P must be true

d. If R is true then Q must be true

 

Directions for Q. No. 16 & 17: A cow is tethered at A by a rope. Neither the rope nor the cow is allowed to enter the triangle ABC.

m<A=30°

l(AB)=l(AC)= 10m

l(BC)=6m

Q16. What is the area that can be grazed by the cow if the length of the rope is 8 m?

a. 133 (1/6)(pi) sq m

b. 121(pi) sq m

c. 132(pi) sq m

d. 176/3(pi) sq m

 

Q17. What is the area that can be grazed by the cow if the length of the rope is 12 m?

a. 133(1/6)( pi) sq m

b. 121(pi) sq m

c. 132(pi) sq m

d. 176/3(pi) sq m

 

Directions for Q. No. 18 to 20: A, B, C, D are to be seated in a row. But C and D cannot be together. Also B cannot be at the third place.

Q18. Which of the following must be false?

a. A is at the first place

b. A is at the second place

c. A is at the third place

d. A is at the fourth place

 

Q19. If A is not at the third place, then C has which of the following options?

a. the first place only

b. the third place only

c. the first and the third place only

d. any of the places

 

Q20. If A and B are together then which of the following must be necessarily false?

a. C is not at the first place

b. A is at the second place

c. D is at the first place

d. C is at the first place

 

Directions : Each of the following should be solved independently

Q21. A man engaged a servant on the condition that he would pay him Rs. 90 and also give him a turban after service of one year. The servant served only for nine months and received a turban and Rs. 65. Find the value of the turban in rupees.

a. 10

b. 9

c. 0

d. 2.50

 

Q22. Four identical circular coins are placed inside the square ABCD as in the following diagram:

If for each coin, (area/circumference) =(circumference/ area) then the area not occupied by the coins in ABCD is

a. 8(4-pi)

b. 16(8-pi)

c. 16(4-pi)

d. None of these

 

Q23. Three wheels can complete respectively 60, 36, 24 revolutions per minute. There is a red spot on each wheel that touches the ground at time zero. After how much time all these spots will simultaneously touch the ground again?

a. 5/2 seconds

b. 5/3 seconds

c. 5 seconds

d. 7.5 seconds

 

Q24. A certain number when divided by 899 leaves the remainder 63. Find the remainder when the same number is divided by 29.

a. 5

b. 4

c. 1

d. Cannot be determined.

 

Q25. A is the set of positive integers such that when divided by 2,3,4,5,6 leaves the remainders 1,2,3,4,5 respectively. How many integers between 0 and 100 belong to set A?

a. 0

b. 1

c. 2

d. None of these

 

Directions for Q. 26 to 28: Ramesh, Ram, Kareem and Mohan collected coins of different countries.

A. They collected 100 altogether.

B. None collected less than 10.

C. Each collected an even number.

D. Each collected a different number.

76. Based on the above, we can say that the number of coins collected by the boy who collected the most could not have exceeded

a. 64

b. 2154

c. 60

d. 58

 

Q27. If Ramesh collected 54 coins, we can say (on the basis of information obtained so far) that the difference in numbers collected by the boy who collected the most and the boy who collected the second most should he at least.

a. 30

b. 18

c. 26

d. 12

 

Q28. Ramesh collected 54 coins. If Kareem collected two more than double the number collected by Mohan, the number collected by Kareem was

a. 10

b. 30

c. 22

d. 26

 

Directions Q 29-80: Suppose shirts of only three colours, namely, red, blue and green are available. Further suppose Amar does not wear a red shirt. Akbar does not wear a green shirt and Anthony does not wear a blue shirt.

Q29. If Akbar and Anthony wear shirts of the same colour then which of the following is necessarily true?

a. The colour of Amar’s shirt is not blue

b. The colour of Amar’s shirt is definitely blue

c. The colour of Amar’s shirt is not green

d. None of the above is necessarily true

 

Q30. If any two of them wear shirts of the same colour then how many of the following statements are definitely false?

A. The colour of Anthony’s shirt is red and that of Akbar’s shirt is green.

B. The colour of Anthony’s shirt is red and that of Amar’s shirt is blue.

C. The colour of Akbar’s shirt is blue and that of Anthony’s shirt is red.

D. The colour of Amar’s shirt is blue and that of Akbar’s shirt is red.

a. 0

b. 2

c. 1

d. 3

 

Directions: Each of the following should be solved independently.

Q31. The number of students who have opted for the subjects A, B, C are 60, 84, 108 respectively. The examination is to be conducted for these students such that only the students of the same subject are allowed in one room. Also the number of students in each room must be same. What is the minimum number of rooms that should be arranged to meet all these conditions?

a. 28

b. 60

c. 12

d. 21

 

Q32. How many five digit numbers can be formed using 2, 3, 8, 7, 5 exactly once such that the number is divisible by 125?

a. 0

b. 1

c. 4

d. 4

 

Q33. I have one rupee coins, fifty paise coins and twenty five paise coins. The number of coins are in the ratio 2.5 : 3: 4. If the total amount with me is Rs. 210, find the number of one rupee coins:

a. 90

b. 85

c. 100

d. 105

 

Q34. My ten year old nephew Debu adores chocolates, likes biscuits, and hates apples. One evening I took him to a super market and told him that he could buy as many chocolates as he wanted, but then he should have twice that number of biscuits and finally buy more apples than the total number of chocolates and biscuits. The chocolates cost Re. 1 per piece and apples are twice as expensive; the price of four biscuits matches the price of one apple. Which of the following can possibly be the amount spent by me on Debu’s evening snacks?

a. Rs. 34

b. Rs. 16

c. Rs. 25

d. None of these

 

Directions for Q. 35 & 36: A company imports component A from Germany and component B from USA. It then assembles them along with other components to produce a machine used in a chemical process. Component A contributes 30% to the production cost and component B contributes 50% to the production cost. The current practice is to sell the machine at a price that is 20% over the production cost. Due to foreign exchange fluctuations the German Mark has become costlier by 30% and the US Dollar by 22%. But the company is unable to increase the selling price by more than 10%.

Q35. The current margin of profit is:

a. 10%

b. 15%

c. 12%

d. 8%

 

Q36. Suppose the US dollar becomes cheaper by 12% of its original value, and the German Mark becomes costlier by 20% of its original value. To achieve a profit margin of 10%, the selling price must exceed the production cost by

a. 10%

b. 20%

c. 12%

d. 15%

 

Directions for Q. 37 to 40: Kamal Babu came home just after judging a beauty contest where there were four semi-finalists, Ms.Andhra Pradesh, Ms. Uttar Pradesh, Ms. Maharashtra and Ms. West Bengal. His wife was very keen on knowing who the winner was and Kamal Babu replied immediately that it was the one wearing the yellow saree. When his wife asked for more details, he gave the following information:

 The four girls were wearing sarees of different colours (yellow, red green, white) and the runner- up was wearing green.

 The four girls were sitting in a row, and Ms.West Bengal was not sitting at either end.

 There was only one runner-up and she was sitting next to Ms. Maharashtra.

 The girls wearing yellow and white sarees occupied the seats at either end.

 Ms. West Bengal was neither the winner nor the runner-up.

 Ms. Maharashtra was wearing white.

 The winner and the runner-up were not sitting next to each other.

 The girls wearing the green saree was not Ms.Andhra Pradesh.

Answer the following questions based on the above information:

Q37. What was the colour of the saree that Ms. Andhra Pradesh was wearing?

a. White

b. Yellow

c. Red

d. Cannot be determined

 

Q38. Between which two was Ms. West Bengal sitting?

a. Ms. Andhra Pradesh and Ms. Maharashtra

b. Ms. Andhra Pradesh and Ms. UttarPradesh

c. Ms. Uttar Pradesh and Maharashtra

d. Cannot be uniquely determined

 

Q39. Who was wearing the red saree?

a. Ms. Andhra Pradesh

b. Ms. Uttar Pradesh

c. Ms. West Bengal

d. Cannot be uniquely determined

 

Q40. What was the colour of the saree that Ms. Uttar Pradesh was wearing?

a. White

b. Green

c. Red

d. Yellow

 

Directions: Each of the following should be solved independently:

Q41. I started climbing up the hill at 6 a.m. and reached the temple at the top at 6 p.m. Next day I started coming down at 6 a.m. and reached the foothill at 6 p.m. I walked on the same road. The road is so narrow that only one person can walk on it. Although I varied my pace, I never stopped on my way. Then which of the following must be true?

a. My average speed downhill was greater than that uphill.

b. At noon, I was at the same spot on both the days.

c. There must be a point where I reached at the same time on both the days.

d. There cannot be a spot where I reached at the same time on both the days.

 

Q42. What is the digit in the unit place of 251?

a. 2

b. 8

c. 1

d. 4

 

Q43. From a barrel containing 500ml of alcohol, 3 cups of alcohol are poured into a barrel containing 500ml of water. After mixing the contests well, 3 cups of the mixture are poured into the barrel of alcohol. The percentage of water into the barrel of alcohol andthe percentage of alcohol in the barrel of water are then compared. Which one of the following is true?

a. the former is greater than the latter

b. The two are equal

c. The latter is greater than the former

d. Cannot be determined

 

Q44. Consider a 99 digit number created by writing side by side the first fifty four natural number as follows:12345678910111213…….5354The above number when divided by 8 will leave a remainder of

a. 6

b. 4

c. 2

d. 0

 

Q45. A, B, C, D, ………., X, Y, Z are the players who participated in a tournament. Everyone played with every other player exactly once. A win scores 2 points, a draw scores 1 point and a lose scores 0 points. None of the matches ended in a draw. No two players scored the same score. At the end of the tournament, the ranking list is published which is in accordance with the alphabetical order. Then,

a. M wins over N

b. N wins over M

c. M does not play with N

d. None of these

Be a Maths & Reasoning Genius..Beauty Simplified !!!

error:
Skip to toolbar