Mathematical Aptitude Test

1. One hundred Students took math and physics tests. 25 students got scores higher than or equal to 80 for both tests. 42 students’ math score was higher than or equal to 80. The numbers of the students whose scores of both tests were less than 80 is 48. Let x and y be the numbers of the students with only math score higher than or equal to 80, and with physics score higher than or equal to 80, respectively. What are x and y?

(A) x = 17, y = 35 (B) x = 10, y = 17 (C) x = 10, y = 23 (D) x = 23, y = 10 (E) x = 35, y = 17

2. Three lottery winners, X, Y, and Z share the lottery jackpot. X’s share equals to 1/5 of Y’s share, and also equals to 1/7 of Z’s share. If the total jackpot is 195,000 Rs., What is the amount of Z’s share?

(A) 15,000 Rs. (B) 35,000 Rs.

(C) 75,000 Rs. (D)105,000 Rs.

(E) 115,000 Rs.

3. A farmer uses 140 meter fencing to enclose a rectangular field. The ratio of the two different sides is 3:4. What is the distance between the two corners diagonally apart from each other?

(A) 40m (B) 253m (C) 45m (D) 50m (E)(653)/2 cm

4. Two types of notebooks are sold. The price of type A is 12 Rs. and that of type B is 15 Rs. for each. John bought 10 notebooks in mixture of both types, and paid 126 Rs.. How many notebooks of type A did he buy?

(A) 5 (B) 6 (C) 7 (D) 8 (E) 9

5. If -1 <>

(A) X square (B)X cube (C) 1 (D) -x (E)1/x

6. Suppose x^2 – y^2 = 155 ( x square minus y square is equal to 155) and x - y = 5. What is the value of x + y?

(A) 15 (B) 31 (C) 35 (D) 100 (E) 150

7. One printer prints a sheet in 0.5 seconds, and the other does it in 0.75 seconds. If we use both printers simultaneously, what is the minimum time to print 200 sheets?

(A) 40 sec. (B) 45 sec. (C) 50 sec. (D) 55 sec. (E) 60 sec

8. Let series an =n^2 – 2n (n = 0, 1, 2,   ). What is the value of (a100 - a99 - a98 + a97)?

(A) 2 (B) 4 (C) 10 (D) 40 (E) 400

9. How many 3-digit positive odd integers that do not contain 5 in any places exist?

(A) 256 (B) 288 (C) 320 (D) 324 (E) 360

10. Darsh and Tathya independently try to decode a coded message. The probabilities that Darsh and Tathya are successfull are 0.8 and 0.7, respectively. What is the probability that at least one of them decodes the message?

(A) 0.10 (B) 0.47

(C) 0.56 (D) 0.80 (E) 0.94

11. When throwing two fair dice, what is the probability that the sum of their numbers is equal to or greater then 11?

(A) 1/18 (B) 1/12

(C) 1/8 (D) 1/6

(E) 1/3

12. Let gcd(m, n) be the greatest common divisor of integers m and n. Which of the following is the largest?

(A) gcd(14, 144) (B) gcd(24, 144) (C) gcd(49, 144) (D) gcd(70, 144) (E) gcd(91, 144)

13. The price of a Seiko watch is 1/3 the price of Omega watch. The shop sold 45 Seiko watches and 60 Omega watches, and the total receipt is 90,000 Rs. What is the price of one Omega watch?

(A) 1200 Rs (B) 1500 Rs(C) 1850 Rs(D) 2000 Rs (E) 2200 Rs

14. There is a circular railroad track for miniature train models. The space between the two rails is

3cm. How much longer is the outer rail than the inner rail?

(A) 2p cm (B) 3p cm (C) 4p cm (D) 6p cm (E) 8p cm

15. Let S = {a, b, c, d, e}. What is the number of subsets with two elements of set S?

(A) 4 (B) 8 (C) 10 (D) 16 (E) 20

16. Let f(x) = x^2 - 1. Which of the following satisfies equation f(f(x)) = 0?

(A) 1 (B) 2 (C) 2 (D) 3 (E) 3

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Answers

1. B

2. D

3. D

4. D

5. B

6. B

7. E

8. B

9. B

10. E

11. B

12. B

13. A

14. D

15. C

16. B

{2006/11/15}