CAT 1996

For Q. 1 to 5 use the following data: A manufacturer can choose from any of the three types of tests available for checking the quality of his product. The graph gives the relative costs for each of these tests for a given percentage of defective pieces.

Q1.

 

Q2. If p is equal to 0.2, then which test will be feasible?

a. either 1 or 2

b. 2 only

c. 3 only

d. either 2 or 3

 

Q3. When will Test-3 be feasible?

a. P > 0.2

b. 0.1 < p < 0.2

c. 0.05 < p < 0.1

d. P < 0.05

 

Q4. When is Test-1 feasible?

a. P < 0.05

b. 0.0 < p < 0.2

c. 0.1 < p < 0.2

d. 0.05 to 0.2

 

Q5. If p <0.2, then the best alternative will be:

a. Test-2

b. Test-3

c. Test-1

d. Not Test-3

 

Directions: Q6 to Q15 are independent of each other

Q6. From a circular sheet of paper with a radius of 20 cm, four circles of radius 5cm each are cut out. What is the ratio of the paper left to the area of the circles?

a. 1:3

b. 4:1

c. 3:1

d. 4:3

 

Q7. Two liquids A and B are in the ratio 5: 1 in container 1 and in container 2, they are in the ratio 1: 3. In what ratio should the contents of the two containers be mixed so as to obtain amixture of A and B in the ratio 1 : 1?

a. 2:3

b. 4:3

c. 3:2

d. 3:4

 

Q8. Out of two-thirds of the total number of basket-ball matches, a team has won 17 matches and lost 3 of them. What is the maximum number of matches that the team can lose and still win three-fourths of the total number of matches, if it is true that no match can end in a tie?

a. 4

b. 6

c. 5

d. 3

 

Q9. A closed wooden box of thickness 0.5 cm and length 21 cm, width 11 cm, and height 6 cm, is panted on the inside. The cost of painting is Rs70. What is the rate of painting in rupees per sq. cm?

a. 0.7

b. 0.5

c. 0.1

d. 0.2

 

Q10. If a number 774958A96B is to be divisible by 8 and 9, the values of A and B. respectively, will be:

a. 7,8

b. 8,0

c. 5,8

d. None of these

 

Q11. Once I had been to the post-office to buy stamps of five rupees, two rupees and one rupee. I paid the clerk Rs 20, and since he did not have change, he gave me three more stamps of one rupee. If the number of stamps of each type that I had ordered initially was more than one, what was the total number of stamps that I bought?

a. 10

b. 9

c. 12

d. 8

 

Q12. Given the quadratic equation ,  for what value of A will the sum of the squares of the roots be zero?

a. -2

b. 3

c. 6

d. None of these

 

Q13. I sold two watches for Rs. 300 each, one at a loss of 10% and the other at a profit of 10%. What is the percent loss (–) or the percent profit (+) that resulted from the transaction?

a. (+) 10

b. (–) 1

c. (+) 1

d. 0

 

Q14. The price of a Maruti car rises by 30% while the sales of the car came down by 20%. What is the percent change in the total revenue?

a. –4

b. –2

c. +4

d. 0

 

Q15. In triangle ABC, angle B is a right angle. If AC is 6 cm, and D is the mid-point of side AC, the length of BD is:

a. 4 cm

b. 6 cm

c. 3 cm

d. 3.5 cm

 

Q. 16 and 17: are based on the following information : A, S, M and D are functions of x and y, and they are defined as follows:

A(x, y) + x + y

S(x, y) = x – y

M(x, y) = xy

D(x, y) = x/y, where y=0.1

Q16. What is the value of M(M(A(M(x, y),S(y,x)),x),A(y, x)) for x = 2, y = 3

a. 50

b. 140

c. 25

d. 70

 

Q17. What is the value of S(M(D(A(a, b), 2),D(A(a, b),2)), M(D(S(a, b), 2), D(S(a, b),2)))

 

Q18. The figure shows a rectangle ABCD with a semi-circle and circle inscribed inside it as shown. What is the ratio of the area of the circle to that the semi-circle?

 

Q19. Which of the following values of x do not satisfy the inequality at all?

 

 

Q20. A man travels three-fifths of distance AB at a speed of 3a, and the remaining at a speed of 2b. If he goes from B to A and back at a speed of 5c in the same time, then:

a. 1/a+1/b=1/c

b. a+b=c

c. 1/a + 1/b=2/c

d. None of these

 

Q. 21 to 22 are based on the following data: A salesman enters the quantity sold and the price into the computer. Both the numbers are two-digit numbers. Once, by mistake, both the numbers were entered with their digits interchanged. The total sales value remained the same, i.e. Rs. 1148, but the inventory reduced by 54.

Q21. What is the actual price per piece?

a. 82

b. 28

c. 56

d. 14

 

Q22. What is the actual quantity sold?

a. 28

b. 14

c. 82

d. 41

 

Q. 23 and 24: In a locality, there are five small towns, A, B, C, D and E. The distances of these towns from each other are as follows:

AB=2km

AC=2km

AD>2km

AE>3km

BC=2km

BD=4km

BE=3km

CD=2km

CE=3km

DE>3km

Q23. If a ration shop is to be set up within 2 km of each city, how many ration shops will be required?

a. 2

b. 3

c. 4

d. 5

 

Q24. If a ration shop is to be set up within 3 km of each city, how many ration shops will be required?

a. 1

b. 2

c. 3

d. 4

 

For Q. 25-28, choose the best alternative:

Q25. The cost of a diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ratio 1 : 2 :3 : 4. When the pieces were sold, the merchant got Rs. 70.000 less. Find the original price of the diamond.

a. Rs. 1.4 lakh

b. Rs. 2.0 lakh

c. Rs. 1.0 lakh

d. Rs. 2.1 lakh

 

Q26. A cube of side 12 cm is painted red on all the faces and then cut into smaller cubes, each of side 3 cm. What is the total number of smaller cubes having none of their faces painted?

a. 16

b. 8

c. 12

d. 24

 

Q27. The points of intersection of three lines, 2X +3Y – 5 = 0, 5X – 7Y + 2 = 0, and 9X-5Y-4 =0:

a. form a triangle

b. are on lines perpendicular to each other

c. are on lines parallel to each other

d. are coincident

 

Q28. If n is any odd number greater than 1, then the largest number that divides n(n2 – 1) is:

a. 48

b. 24

c. 6

d. None of these

Q. 29 to 33 are based on the following information: X, Y and Z wish to go from place A to place B, which are separated by a distance of 70 km. All the three persons start off together form A, with X and Y going by Luna at a speed of 20 kmph. X drops V somewhere along the way and returns to pick up Z who has already started walking towards B at a speed of 5kmph. V, after being dropped by X, starts walking towards B at a speed of 5 kmph. In this manner, all three of them reach B at the same time.

Q29. How much distance is covered by Z on foot?

a. 25 km

b. 10 km

c. 20 km

d. 15 km

 

Q30. What is the total distance travelled by X?

a. 130 km

b. 140 km

c. 110 km

d. 90 km

 

Q31. How long does it take them to go from A to B?

a. 6.0 hours

b. 6.5 hours

c. 7.0 hours

d. 14.0 hours

 

Q32. After how much time is Y dropped on the way by X?

a. 2.0 hours

b. 3.0 hours

c. 2.5 hours

d. 1.5 hours

 

Q33. For how long does X travel alone over the entire journey?

a. 2.5 hours

b. 1.0 hour

c. 2.0 hours

d. 1.5 hours

 

Directions Q 34-38: The questions are independent of each other

Q34. The figures shows a circle of diameter AB and radius 6.5 cm. If chord CA is 5 cm long, find the area of triangle ABC.

a. 60 sq.cm

b. 30 sq.cm

c. 40 sq.cm

d. 52 sq.cm

 

Q35. In a locality, two-thirds of the people have cable-TV, one-fifth have VCR, and one-tenth have both, what is the fraction of people having either cable TV or VCR?

a. 19/30

b. 3/5

c. 17/30

d. 23/30

 

Q36. If ABCD is a square and BCE is an equilateral triangle, what is the measure of the angle DEC?

 

Q37. I bought 5 pens, 7 pencils and 4 erasers. Rajan bought 6 pens, 8 erasers and 14 pencils for an amount which was half more than what I had paid. What percent of the total amount paid by me was paid for the pens?

a. 37.5%

b. 625%

c. 50%

d. None of these

 

Q38. If x is a positive integer such that 2x + 12 is perfectly divisible by by x, then the number of possible values of x is:

a. 2

b. 5

c. 6

d. 12

 

For Q. 39 and 40, use the following information:

A watch dealer incurs an expense of Rs 150 for producing every watch. He also incurs an additional expenditure of Rs. 30,000, which is independent of the number of watches produced. If he is able to sell a watch during the season, he sells it for Rs. 250. If he fails to do so, he has to sell each watch for Rs. 100.

Q39. If he is able to sell only 1200 out of the 1500 watches he has made in the season then in the season he has made a profit of

a. Rs. 90,000

b. Rs. 75,000

c. Rs. 45,000

d. Rs. 60,000

 

Q40. If he produces 1500 watches, what is the number of watches that he must sell during the season in order to break even, given that he is able to sell all the watches produced?

a. 500

b. 700

c. 800

d. 1,000

 

Directions Q 41-45: The questions are independent of each other

Q41. A man travels form A to B at a speed of x kmph. He then rests at B or x hours. He then travels from B to C at a speed of 2x kmph and rests at C for 2x hours. He moves further to D at a speed twice as that between B and C. He thus reaches D in 16 hours. If distances A-B,B-C, C-D are all equal to 12 km, the time for which he rested at B could be:

a. 3 hours

b. 6 hours

c. 2 hours

d. 4 hours

 

Q42. Instead of a metre scale, a cloth merchant uses a 120 cm scale while buying, but uses an 80 cm scale while selling the same cloth. If he offers a discount of 20 percent on cash payment, what is his overall percent profit?a. 20%

b. 25%

c. 40%

d. 15%

 

Q43. A man has nine friends, four boys and five girls. In how many ways can he invite them, if there have to be exactly three girls in the invitees?

a. 320

b. 150

c. 80

d. 200

 

Q44. In a watch, the minute hand crosses the hour hand for the third time exactly after every 3hrs 18 mm 15 seconds of watch time. What is the time gained or lost by this watch in one day?

a. 14 mm 10 seconds lost

b. 13 mm 50 seconds lost

c. 13 min 20 second gained

d. 14 mm 40 second gained

 

Q45. In a mile race Akshay can be given a start of128 meters by Balram. If Balram can given Chetan a start of 4 metres in a 100 metres dash, then who out of Akshay and Chetan will win a race of one and half mile, and what will be the final lead given by the winner to the loser? (One mile is. 1600 metres).

a. Akshay, 1/12 miles

b. Chetan, 1/32 miles

c. Akshay, 1/24 miles

d. Chetan, 1/16 miles

 

Q. 46 to 50 are based on the following graph:

Q46. Which year showed the greatest percentage increase in profit as compared to the previous year?

a. 1993

b. 1994

c. 1990

d. 1992

 

Q47. The average revenue collected in the givenseven years is approximately:

a. Rs. 164lakh

b. Rs. 168 lakh

c. Rs. 171 lakh

d. Rs. 175 lakh

 

Q48. In which year was the growth in expenditure greatest as compared to the previous year?

a. 1993

b. 1995

c. 1991

d. 1992

 

Q49. The expenditure for the seven years together forms what percent of the revenues during the same period?

a. 75%

b. 67%

c. 62%

d. 83%

 

Q50. If the profit in 1996 shows the same annual rate of growth as it had shown in 1995 over the previous year, then what approximately will be the profit in 1996?

a. Rs. 72 lakh

b. Rs. 86 lakh

c. Rs. 93 lakh

d. Rs. 78 lakh