CAT 1994

Q1. The number of votes not cast for the Praja Party increased by 25% in the National General Elections over those not cast for it in the previous Assembly Polls, and the Praja Party lost by a majority twice as large as that by which it had won the Assembly Polls. If a total 2,60,000 people voted each time, how many voted for the Praja Party in the Assembly Elections?

a. 1,10,000

b. 1,50,000

c. 1,40,000

d. 1,20,000

 

Directions: Q. 2 to 4 are based on the following information: Ghoshbabu is staying at Ghosh Housing Society, Aghosh Colony, Dighoshpur, Calcutta. In Ghosh Housing Society 6 persons read daily Ganshakit and 4 read Anand Bazar Patrika: in his colony there is no person who reads both. The total number of persons who read these two newspapers in Aghosh Colony and Dighoshpur is 52 and 200 respectively. The number of persons who read Ganashakti in Aghosh Colony and Dighoshpur is33 and 121 respectively; while the persons who read Anand Bazar Patrika in Aghosh Colony and Dighoshpurare32 and 117 respectively.

Q2. Number of persons in Dighoshpur who read only Ganashakti is:

a. 121

b. 83

c. 79

d. 127

 

Q3. Number of persons in Aghosh Colony who read both these newspapers is:

a. 13

b. 20

c. 19

d. 14

 

Q4. Number of persons in Aghosh Colony who read only one newspaper is:

a. 29

b. 19

c. 39

d. 20

 

Directions Q. 5 to 12: Choose the best alternative.

Q5. If   find the value of x.

a. 1

b. 0

c. 2

d. None of these

 

Q6. A right circular cone, a right circular cylinder and a hemisphere, all have the same radius,and the heights of the cone and cylinder equal their diameters. Then their volumes are proportional, respectively to:

a. 1:3:1

b. 2:1:3

c. 3:2:1

d. 1:2:3

 

Q7. Two towns A and B are 100 km apart. A school is to be built for 100 students of Town B and 30 students of Town A. Expenditure on transport is Rs 1.20 per km. If the total expenditure on transport by all 130 students is to be as small as possible, then the school should be built at:

a. 33 km from Town A

b. 33 km from town B

c. Town A

d. Town B

 

Q8. One man can do as much work in one day as a woman can do in 2 days A child does one third the work in a day as a woman. If an estate-owner hires 39 pairs of hands, men,woman and children in the ratio 6 : 5 :2 and pays them in all Rs 1113 at the end of the day’s work. What must the daily wages of a child be, if the wages are proportional to the amount of work done?

a. Rs. 14

b. Rs. 5

c. Rs. 20

d. Rs. 7

 

Q9. A right circular cone of height h’ is cut by a plane parallel to the base and at a distance h/3 from  the vertex, then the volumes of the resulting cone and frustum are in the ratio:

a. 1 : 3

b. 8 : 19

c. 1 : 4

d. 1 : 7

 

Q10. If a + b + c = 0, where , then what is the value of:

a. zero

b. 1

c. -1

d. abc

 

Q11. If the harmonic mean between two positive numbers is to their geometric mean as 12 : 13, then the numbers could be in the ratio:

a. 12: 13

b. 1/12: 1/13

c. 4:9

d. 2:3

 

Q12. If one root of is 4, while the equation has equal roots, then the value of q is:

a. 49/4

b. 4/49

c. 4

d.14

 

Directions: Q. 13 and 14 are based on the following information.

If md(x) = |x|,

mn(x, y) = minimum of x and y, and

ma(a, b, c,) = maximum of a, b, c

Q13. The value of ma(a)[md(a), mn(md(b), a),mn(ab, md(ac))] where a = -2,b = -3, c = 4 is:

a. 2

b. 6

c. 8

d. -2

 

Q14. Given that a > b, then the relation ma[md(a),mn(a, b)] = mn[a, md(ma(a, b))] does not hold if:

a. a < 0, b < 0

b. a > 0, b > 0

c. a > 0, b < 0, |a| < |b|

d. a > 0, b < 0, |a| > |b|

 

Directions for questions 15 to 23: Choose the best alternative

Q15. A water tank has three taps A, B, and C. A fills four buckets in 24 mm, B fills 8 buckets in 1 hour and C fills 2 buckets in 20 minutes. If all the taps are opened together, a full tank is emptied in 2 hours. If a bucket can hold 5 litres of water, what is the capacity of the tank?

a. 120 litres

b. 240 litres

c. 180 litres

d. 60 litres

 

Q16. Shyam went from Delhi to Simla via Chandigarh by car. The distance from Delhi to Chandigarh is 3/4 times the distance from Chandigarh to Simla. The average speed from Delhi to Chandigarh was half as much again as that from Chandigarh to Simla. If the averages peed for the entire journey was 49 kmph,what was the average speed from Chandigarh to Simla?

a. 39.2 kmph

b. 63 kmph

c. 42 kmph

d. None of these

 

Q17. The fourth term of an arithmetic progression is 8. What is the sum of the first 7 terms of the arithmetic progression?

a. 7

b. 64

c. 56

d. cannot be determined

 

Q18. It takes a pendulum of a clock 7 seconds to strike 4 o’clock. How much time will it take to strike 11 o’clock?

a. 18 seconds

b. 20 seconds

c. 19.25 seconds

d. 23.33 seconds

 

Q19. Along a road lie an odd number of stones placed at intervals of 10 m. These stones have to be assembled around the middle stone. A person can carry only one stone at a time. Aman carried out the job starting with the stone in the middle, carrying stones in succession, thereby covering a distance of 4.8 km. Then the number of stones is:

a. 35

b. 15

c. 29

d. 31

 

Q20. What is the smallest number, which when increased by 5 is completely divisible by 8, 11 and 24?

a. 264

b. 259

c. 269

d. None of these

 

Q21. A man buys spirit at Rs. 60 per litre, adds water to it and then sells it at Rs. 75 per litre. What is the ratio of spirit to water if his profit in the deal is 37.5%?

a. 9 : 1

b. 10 : 1

c. 11 : 1

d. None of these

 

Q22. Four friends start from four towns, which are at the four corners of an imaginary rectangle. They meet at a point which falls inside the rectangle, after travelling distances of 4O, 50 and 60 metres. The maximum distance that the fourth could have travelled is (approximately):

a. 67 metres

b. 52 metres

c. 22.5 metres

d. Cannot be determined

 

Q23. A and B walk from X to Y, a distance of27 km at 5 kmph and 7 kmph respectively. B reaches Y and immediately turns back meeting A at Z. What is the distance from X to Z?

a. 25 km

b. 22.5 km

c. 24 km

d. 20 km

 

Direction: Q. 24 to 26, reefer to the following information:

Alphonso, on his death bed, keeps half his property for his wife and divides the rest equally among his three sons Ben, Carl and Dave. Some years later Ben dies leaving half his property to his widow and half to his brothers Carl and Dave together, shared equally. When Carl makes his will he keeps half his property for his widow and the rest he bequeaths to his younger brother Dave. When Dave dies some years later, he keeps half his property for his widow and the remaining for his mother. The mother now has Rs 1,575,000.74. What was the worth of the total property?

a. Rs. 30 lakh

b. Rs. 8 lakh

c. Rs. 18 lakh

d. Rs. 24 lakh

 

Q25. What was Carl’s original share?

a. Rs. 4 lakh

b. Rs. 12 lakh

c. Rs. 6 lakh

d. Rs. 5 lakh

 

Q26. What was the ratio of the property owned by the widows of the three sons, in the end?

a. 7 : 9 : 13

b. 8 : 10 : 15

c. 5 : 7 : 9

d. 9 : 12 : 13

 

Directions: Q. 27 to 30, choose the best alternative:

Q27. log to the base 6 is:

a. 3

b. 3/2

c. 7/2

d. None of these

 

Q28. There is leak in the bottom of a tank. This leak can empty a full tank in 8 hours. When the tank is full, a tap is opened into the tank which admits 6 litres per hour and the tank is now emptied in 12 hours. What is the capacity of the tank?

a. 28.8 litres

b. 36 litres

c. 144 litres

d. Cannot be determined

 

Q29. Which is the least number that must be subtracted from 1856, so that the remainder, when divided by 7, 12, and 16, will leave the same remainder 4.

a. 137

b. 1361

c. 140

d. 172

 

Q30. A dealer offers a cash discount of 20% and still makes a profit of 20%, when he further allows 16, articles to a dozen to a particularly sticky bargainer. How much percent above the cost price were his wares listed?

a. 100%

b. 80%

c. 75%

d. 66.667%

 

Directions: Q 31 to 35, data is a provided followed by two statements – I and II – both resulting in a value, I and II.

Mark a if I > II

Mark b if I < II

Mark c if I = II

Mark d if nothing can be said

Q31. Nineteen years from now Jackson will be 3 times as old as Joseph is now. Johnson is three years younger than Jackson.

1. Johnson’s age now.

2. Joseph’s age now.

a. Mark a if I > II

b. Mark b if I < II

c. Mark c if I = II

d. Mark d if nothing can be said.

 

Q32. In triangle ACD, AD = AC and <C = 2<E. Thedistance between the parallel lines AB and CD is h. <CAE = 150° and <DEA= 30°. Then:

1. Area of parallelogram ABCD

2. Area of triangle ADE.

a. Mark a if I > II

b. Mark b if I < II

c. Mark c if I = II

d. Mark d if nothing can be said.

 

Q33. Last week Manoj received Rs 10 in commission for selling 100 copies of a magazine. Last week Manu sold 100 copies of this magazine. He received his salary of Rs 5 prweek plus a commission of 2 paise for each of the first 25 copies sold, 3 paise for each of next 25 copies sold and 4 paise for each copy thereafter.

1. Manoj’s commission in the last week

2. Manu’s total income for last week.

a. Mark a if I > II

b. Mark b if I < II

c. Mark c if I = II

d. Mark d if nothing can be said.

 

Q34. k1, k2, k3 are parallel lines. AD = 2cm. BE = 8cm and CF = 32 cm.

1. (AB x (EF)

2. (BC) x (DE)

a. Mark a if I > II

b. Mark b if I < II

c. Mark c if I = II

d. Mark d if nothing can be said.

 

Q35.1. The probability of encountering 54 Sundays in a leap year

2. The probability of encountering 53 Sundays in a non-leap year

a. Mark a if I > II

b. Mark b if I < II

c. Mark c if I = II

d. Mark d if nothing can be said.

 

Directions: Choose the best option

Q36. The winning relay team in a high school sports competition clocked 4-8 minutes for a distance of 13.2 km. Its runners A, B, C and D maintained speeds of 15 kmph, 16 kmph, 17kmph and 18 kmph respectively. What is the ratio of the time taken by B to that taken by D?

a. 5 : 16

b. 5 : 17

c. 9 : 8

d. 8 : 9

 

Directions: Q. 37 to 40: If f(x) = 2x + 3 and g(x) = (x-3)/2, then

Q37. Then f(g(x)) =

a. 1

b. g(f(x)

c. (15x + 9)/(16x -5)

d. 1/x

 

Q38. For what value of x; f(x) = g(x-3)

a. -3

b. 1/4

c. -4

d. None of these

 

Q39. What is value of (g0f0g0g0f) (x) f0g0f0g)(x)

a. x

b. 

c. (5x +3) / (4x – 1)

d. [(x + 3) (5x + 3)] / [4x – 5) (4x – 1)]

 

Q40. What is the value of f0(f0g) (g0f)(x)

a. x

b. 

c. 2x +3

d. (x + 3) / (4x – 5)

 

Directions Q. 41 to 50: Each item has a question followed by two statements Mark a, if the question can be answered with the help of I alone.

Mark b, if the question can be answered with the help of II alone.

Mark c, if the question can be answered only with the help of both I and II

Mark d, if the question cannot be answered even with the help of both statements

Q41. Is the distance from the office to home less than the distance from the cinema hall to home?

1. The time taken to travel from home to office is as much as the time taken from home to the cinema hall, both distances being covered without stopping.

2. The road from the cinema hall to home is bad and speed reduces, as compared to that one the road from home to the office.

a. Mark a, if the question can be answered with the help of I alone

b. Mark b, if the question can be answered with the help of II alone

c. Mark c, if the question can be answered only with the help of both I and II

d. Mark d, if the question cannot be answered even with the help of both the statements.

 

Q42. A and B work at digging a ditch alternately for a day each. If A can dig a ditch in ‘a’ days andB can dig it in ‘b’ days, will work get done faster if A begins the work?

1. n is a positive integer such that n(1/a + 1/b) = 1

2.b > a

a. Mark a, if the question can be answered with the help of I alone

b. Mark b, if the question can be answered with the help of II alone

c. Mark c, if the question can be answered only with the help of both I and II

d. Mark d, if the question cannot be answered even with the help of both the statements.

 

Q43. If twenty sweets are distributed among some boys and girls such that each girl gets two sweets and each boys gets three sweets, what is the number of boys and girls?

1. The number of girls is not more than five

2. If each girl gets 3 sweets and each boy gets 2 sweets, the number of sweets required for the children will still be the same.

a. Mark a, if the question can be answered with the help of I alone

b. Mark b, if the question can be answered with the help of II alone

c. Mark c, if the question can be answered only with the help of both I and II

d. Mark d, if the question cannot be answered even with the help of both the statements.

 

Q44. If the selling price were to be increased by10%, the sales would reduce by 10%. In what ratio would profits change?

1. The cost price remains constant

2. The cost price increased by 10%.

a. Mark a, if the question can be answered with the help of I alone

b. Mark b, if the question can be answered with the help of II alone

c. Mark c, if the question can be answered only with the help of both I and II

d. Mark d, if the question cannot be answered even with the help of both the statements.

 

Q45. What is the average weight of the 3 new team members who are recently included into the team?

1. The average weight of the team increasesby 20 kg

2. The 3 new men substitute 3 earlier members whose weights are 64 kg, 75 kg,and 66 kg.

a. Mark a, if the question can be answered with the help of I alone

b. Mark b, if the question can be answered with the help of II alone

c. Mark c, if the question can be answered only with the help of both I and II

d. Mark d, if the question cannot be answered even with the help of both the statements.

 

Q46. Is segment PQ greater than segment RS?

1. PB > RE, BQ = ES

2. B is a point on PQ, E is a point on RS.

a. Mark a, if the question can be answered with the help of I alone

b. Mark b, if the question can be answered with the help of II alone

c. Mark c, if the question can be answered only with the help of both I and II

d. Mark d, if the question cannot be answered even with the help of both the statements.

 

Q47. Three boys had a few Coffee Bite toffees with them. The number of toffees with the second were four more than those with the first and the number of toffees with the third were four more than those with the second. How many toffees were there in all?

1. The number of toffees with each of them is a multiple of 2

2. The first boy ate up four toffees from what he had and the second boy ate up six toffees from what he had and the third boy gave them two toffees each from what he had, and the number of toffees remaining with each of them formed a geometric progression.

a. Mark a, if the question can be answered with the help of I alone

b. Mark b, if the question can be answered with the help of II alone

c. Mark c, if the question can be answered only with the help of both I and II

d. Mark d, if the question cannot be answered even with the help of both the statements.

 

Q48. Little Beau Peep lost her sheep, she couldn’t remember how many were there. She knew she would have 400 more next year, than the number of sheep she had last year. How many sheep were there?

1. The number of sheep last year was 20% more than the year before that and this simple rate of increase continues to be the same for the next 10 years

2. The increase is compounded annually.

a. Mark a, if the question can be answered with the help of I alone

b. Mark b, if the question can be answered with the help of II alone

c. Mark c, if the question can be answered only with the help of both I and II

d. Mark d, if the question cannot be answered even with the help of both the statements.

 

Q49. What will be the total cost of creating a I-foot border of tiles along the inside edges of a room?

1. The room is 48 feet in length and 50 feet in breadth.

2. Every tile costs Rs. 10.

a. Mark a, if the question can be answered with the help of I alone

b. Mark b, if the question can be answered with the help of II alone

c. Mark c, if the question can be answered only with the help of both I and II

d. Mark d, if the question cannot be answered even with the help of both the statements.

 

Q50. Ten boys go to a neighbouring orchard. Each boy steals a few mangoes. What is the total number of mangoes they steal?

1. The first boy steals 4 mangoes, the fourth boy steals 16 mangoes, the eight boy 32 mangoes and the tenth boy steals 40 mangoes.

2. The first boy stole the minimum number of mangoes and the tenth boy stole the maximum number of mangoes.

a. Mark a, if the question can be answered with the help of I alone

b. Mark b, if the question can be answered with the help of II alone

c. Mark c, if the question can be answered only with the help of both I and II

d. Mark d, if the question cannot be answered even with the help of both the statements.

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