CAT 1995

Q1.  A person who has a certain amount with him goes to the market. He can buy 50 oranges or40 mangoes. He retains 10% of the amount for taxi fare and buys 20 mangoes, and of the balance he purchases oranges. The number of oranges he can purchase is:

a. 36

b. 40

c. 15

d. 20

 

Q2. Two-fifths of the voters promise to vote for P and the rest promise to vote for Q. Of these, onthe last day, 15% of the voters went back on their promise to vote for P and 25% of voters went back of their promise to vote for Q, and P lost by 2 votes. Then the total number ofvoters is:

a. 100

b. 110

c. 90

d. 95

 

Q3.  One liter of water is poured into each of two containers of equal height. The first containerA has a circular cross section of radius 2 cm and the other B has a square cross section with side of 4 cm. In which container will the water rise to a greater height?

a. Container A

b. Container B

c. Equal in both

d. Depends on the rate at which water ispoured

 

Q4.  ABCD is a square of area 4, which is divided into four non-overlapping triangles as shown in the figure. The sum of the perimeters of the triangles is:

 

 

 

 

 

 

 

Q5. What is the value of m which satisfies

a. m < 2, or m > 5

b. m > 2

c. 2 < m < 5

d. m < 5

 

Q6. The value of

is:

a. 100

b. 105

c. 125

d. 75

 

Q7.  PQRS is a square.  SR is a tangent (at point S) to the circle with centre O and TR = OS. The ratio of the area of the circle to the area of the square is:

 

 

 

 

 

 

 

 

Q8.   is divisible by

a. 13

b. 31

c. 5

d. none of these

 

Q9. The sides of a triangle are 5, 12 and 13 unitsrespectively. A rectangle is constructed whichis equal in area to the triangle and has a widthof 10 units. Then the perimeter of the rectangleis

a. 30

b. 26

c. 13

d. none of these

 

Q10.  Which one of the following cannot be the ratio of angles in a right-angled triangle?

a. 1:2:3

b. 1:1:2

c. 1 :3:6

d. None of these

 

Q11. Three bells chime at an interval of 18, 24 and32 minutes respectively. At a certain time they begin to chime together. What length of time will elapse before they chime together again?

a. 2 hours 24 minutes

b. 4 hours 48 minutes

c. 1 hour 36 minutes

d. 5 hours

 

Q12. A, B, C and D are four towns, any three of which are non-collinear. The number of ways to construct three roads each joining a pair of towns so that the roads do not form a triangle is:

a. 7

b. 8

c. 9

d. more than 9

 

Q13. For the product n(n + 1)(2n + 1), n Î N, which one of the following is necessarily false?

a. It is always even

b. Divisible by3

c. Always divisible by the sum of the squareof first n natural numbers

d. Never divisible by 237

 

Directions Q. 14 to 17, refer to the following data:

le(x, y) = | least of(x, y)

mo(x) = |x|

me(x) (x, y) = maximum of(x, y)

Q14. Find the value of me(a + mo(le(a, b)); mo(a +me(mo(a), mo(b)), at a = -2 and b = – 3

a. 1

b. 0

c. 5

d. 3

 

Q15. Which of the following must be correct?

a.

b. mo(le(a, b)) > (me(mo(a), mo(b))

c. mo(le(a, b)) < (le(mo(a), mo(b))

d. mo(le(a, b)) le(mo(a), mo(b))

 

Q16. For what values of a is

a. a < 3 and a < 1

b. 1 < a < 3

c. a < 3 or a < 1

d. a < 3 or a < 0

 

Q17. For what values of a is

a. 1 < a < 3

b. a < 0 and a < 3

c. a < 0 and a < 3

d. a < 0 or a < 3

 

Q18. Ram purchased a flat at Rs. 1 lakh and Prempurchased a plot of land worth Rs. 1.1 lakh. The respective annual rates at which the pricesof the flat and the plot increased were 10% and5%. After two years they exchanged their belongings and one paid the other the difference. Then:

a. Ram paid Rs. 275 to Prem

b. Ram paid Rs. 475 to Prem

c. Ram paid Rs. 2750 to Prem

d. Prem paid Rs. 475 to Ram

 

Directions Q. 19to 22: Four sisters  Suvarna, Tara, Uma, and Vibha are playing a game such that the loser doubles the money of each of the other players. They played four games and each sister lost one game in the alphabetical order. At the end of fourth game each sister had Rs. 32.

Q19. Who started with the lowest amount?

a. Suvarna

b. Tara.

c. Uma

d. Vibha

 

Q20. Who started with the highest amount?

a. Suvarna

b. Tara

c. Uma

d. Vibha

 

Q21. What was the amount with Uma at the end ofthe second round?

a. 36

b. 72

c. 16

d. None of these

 

Q22. How many rupees did Suvama start with?

a. 60

b. 34

c. 66

d. 28

 

Directions Q. 23 to 28: Choose the correct option:

Q23. The remainder obtained when a prime number greater than 6 is divided by 6 is:

a. 1 or 3

b. 1 or 5

c. 3 or 5

d. 4 or 5

 

Q24. In a race of 200 meters, A beats S by 20 metres and N by 40 metres. If S and N are running a race of 100 metres with exactly the same speed as before, then by how many metres will S beat N?

a. 11.11 metres

b. 10 metres

c. 12 metres

d. 25 metres

 

Q25. In the adjoining figure, AC + AR = 25 AD and AC – AD = 8. The area of the rectangle ABCD is:

a. 36

b. 50

c. 60

d. Cannot be answered.

 

Q16. The rate of inflation was 1000%. What will bethe cost of an article, which costs 6 units of currency now, two years from now?

a. 666

b. 660

c. 720

d. 726

 

Q17. 72 hens cost Rs._96.7_. What does each hen cost, where numbers at “_” are not visible or are written in illegible hand?

a. Rs. 3.23

b. Rs. 5.11

c. Rs. 5.51

d. Rs.7.22

 

Q18. Boxes numbered 1, 2, 3, 4, and 5 are kept in arow, and they are to be filled with either a red or a blue ball, such that no two adjacent boxes can be filled with blue balls. How many different arrangements are possible, given that all balls of a given colour are exactly identical in all respects?

a. 8

b. 10

c. 15

d. 22

 

Directions Q. 29 to 30 are based on the following information: There are three different cable channels namely Ahead, Luck and Bang. In a survey it was found that 85% of viewers respond to Bang, 20% to Luck, and 30% to Ahead. 20% of viewers respond to exactly two channels and 5% to none.

Q29. What percentage of the viewers responded to all three?

a. 10

b. 12

c. 14

d. None of these

 

Q30. Assuming 20% respond to Ahead and Bang, and 16% respond to Bang and Luck, what is the percentage of viewers who watch only Luck?

a. 20

b. 10

c. 16

d. None of these

 

Q31. AB is perpendicular to BC and BD isperpendicular to AC. CE bisects the angle C; <A = 30°. Then, what is <CED?

Q32. One root of is square of the other. Then, the value of k is:

a. 2

b. 8

c. -8

d. -2

 

Q33. AB is diameter of the circle and the points C and D are on the circumference such that<CAD = 30o. What is the measure of <ACD?

Q34. The length of a ladder is exactly equal to the height of the wall it is resting against. If lower end of the ladder is kept on a stool of height 3m and the stool is kept 9 m away from the wall, the upper end of the ladder coincides with the top of the wall. Then, the height ofthe wall is:

a. 12m

b. 15m

c. 18m

d. 11m

 

Q35. The largest value of mm (2 + x2, 6 – 3x) whenx > 0 is

a. 1

b. 2

c. 3

d. 4

 

Q36. A man invests Rs. 3000 at a rate of 5% per annum. How much more should he invest at a rate of 8%, so that he can earn a total of 6% per annum?

a. Rs. 1200

b. Rs. 1300

c. Rs. 1500

d. Rs. 2000

 

Q37.  Three consecutive positive even numbers are such that thrice the first number exceeds double the third by 2;  then the third number is:

a. 10

b. 14

c. 16

d. 12

 

Directions Q. 38 to 41, use the following data: A and B are running along a circular course of radius 7km in opposite directions such that when they meet they reverse their directions and when they meet, A will run at the speed of B and vice-versa. Initially, the speed of A is thrice the speed of B. Assume that they start from M0 and they first meet at M1, then at M2, next at M3, and finally at M4.

 

Q38. What is the shortest distance between M1 andM2?

 

Q39. What is the shortest distance between M1 andM3 along the course?

 

Q40. Which is the point that coincides with M0?

a. M1

b. M2

c. M3

d. M4

 

Q41. What is the distance travelled by A when theymeet at M3?

a. 77km

b. 66km

c. 99km

d. 88km

 

Q42. Directions Q. 42 to 50: Each of these items has question followed by two statements. As the answer, mark

a. if the questions can be answered with the help of both the statements but not with the help of either statement itself.

b. if the question can not be answered even withthe help of both the statements

c. if the question can be answered with the help 0f statement II alone

d. if the question can be answered with the help of statement I alone

 

Q42. What is the number x if

I. The LCM of x and 18 is 36

II. The HCF of x and 18 is 2

a. if the questions can be answered with the help of both the statements but not withthe help of either statement itself

b. if the question can not be answered even with the help of both the statements

c. if the question can be answered with the help 0f statement II alone

d. if the question can be answered with the help of statement I alone

 

Q43. If x, y and z are real numbers, is z – x even or odd?

I. xyz is odd

II. xy + yz + zx is even

a. if the questions can be answered with the help of both the statements but not withthe help of either statement itself

b. if the question can not be answered even with the help of both the statements

c. if the question can be answered with the help 0f statement II alone

d. if the question can be answered with the help of statement I alone

 

Q44. What is value of x, if x and y are consecutive positive even integers?

a. if the questions can be answered with the help of both the statements but not withthe help of either statement itself

b. if the question can not be answered even with the help of both the statements

c. if the question can be answered with the help 0f statement II alone

d. if the question can be answered with the help of statement I alone

 

Q45. What is the profit percent?

I. The cost price is 80% of the selling price

II. The profit is Rs. 50.

a. if the questions can be answered with the help of both the statements but not withthe help of either statement itself

b. if the question can not be answered even with the help of both the statements

c. if the question can be answered with the help 0f statement II alone

d. if the question can be answered with the help of statement I alone

 

Q46. What is the length of the rectangle ABCD?

I. Area of the rectangle is 48 square units

II. Length of the diagonal is 10 units

a. if the questions can be answered with the help of both the statements but not withthe help of either statement itself

b. if the question can not be answered even with the help of both the statements

c. if the question can be answered with the help 0f statement II alone

d. if the question can be answered with the help of statement I alone

 

 

Q47. What is the price of bananas?

I. With Rs. 84, I can buy 14 bananas and 35 oranges

II. If price of bananas if reduced by 50% then we can buy 48 bananas in Rs. 12

a. if the questions can be answered with the help of both the statements but not withthe help of either statement itself

b. if the question can not be answered even with the help of both the statements

c. if the question can be answered with the help 0f statement II alone

d. if the question can be answered with the help of statement I alone

 

 

Q48. What is the first term of an arithmetic progression of positive integers?

I. Sum of the squares of the first and secondterm is 116

II. The fifth term is divisible by 7

a. if the questions can be answered with the help of both the statements but not withthe help of either statement itself

b. if the question can not be answered even with the help of both the statements

c. if the question can be answered with the help 0f statement II alone

d. if the question can be answered with the help of statement I alone

 

Q49. Is x + y – z + t even?

I. x + y + t is even

II. tz is odd

a. if the questions can be answered with the help of both the statements but not withthe help of either statement itself

b. if the question can not be answered even with the help of both the statements

c. if the question can be answered with the help 0f statement II alone

d. if the question can be answered with the help of statement I alone

 

Q50. What is the area of the triangle?

I. Two sides are 41 cm each

II. The altitude to the third side is 9 cm long.

a. if the questions can be answered with the help of both the statements but not withthe help of either statement itself

b. if the question can not be answered even with the help of both the statements

c. if the question can be answered with the help 0f statement II alone

d. if the question can be answered with the help of statement I alone

 

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