Student@ competition

Mathematical Aptitude Test

1. The inequality (x+1)/(x-1)< 1 is true &

a. for no values of x,

b. whenever -1 < x < 1

c. whenever x < -2,

d. for all values of x.

2. The function f is defined for whole positive numbers and satisfies f (1) = 1 and also the rules

f (2n) = f (n),

f (2n + 1) = f (n) + 1

for all values of n. It follows that f (9) equals

a. 1 b. 2

c. 4 d. 3

3. The fact that 6 x 7 = 42, is a counter-example to which of the following statements ?

a. the product of any two odd integers is odd

b. if the product of two integers is not a multiple of 4 then the integers are not consecutive

c. if the product of two integers is a multiple of 4 then the integers are not consecutive

d. any even integer can be written as the product of two even integers

4. The point lying between P (2, 3) and Q (8, -3) which divides the line P Q in the ratio 1 & 2 has co-ordinates

a. (4, -1) b. (6, -2)

c. (14/3, 2) d. (4, 1)

5. The numbers x and y satisfy the following inequalities

2x + 3y < = 23,

x + 2 < = 3y,

3y + 1 < = 4x.

The largest possible value of x is

a. 6 b. 7

c. 8 d. 9

6. In the range 0<=x < 2TT the equation cos (sin x) = 1/2 has

a. no solutions

b. one solutions

c. two solutions

d. three solutions

7. The four digit number 2652 is such that any two consecutive digits from it make a

multiple of 13. Another number N has this same property, is 100 digits long, and begins in a 9. What is the last digit of N ?

a. 2 b. 3

c. 6 d. 9

8. The cubic equation x3 (x cube) + ax + b has both (x -1) and (x -2) as factors. Then

a. a = -7 and b = 6

b. a = -3 and b = 3

c. a = 0 and b = -2

d. a = 5 and b = 4

9. The inequality (x ^ 2 + 1) / (x 2-1) < 1 is true &

a. for no values of x

b. whenever -1 < x < 1

c. whenever x > 1

d. for all values of x

10. The equation | x | + |x-1| = 0 has

a. no solutions

b. one solutions

c. two solutions

d. thre solutions

11. The function S (n) is defined for positive integers n by S(n) = sum of the digits of n.

For example, S (723) = 7 + 2 + 3 = 12

The sum S(1) + S(2) + S(3) + ... + S(99) equals

a. 746 b. 862

c. 900 d. 924

12. Let g (n) be a function, defined for all integers n > 0, as follows &

g (n) = 0 if n = 0,

g(n) = 1 + g (n/2) if n > 0 and n is even,

g(n) = 1 +g (n-1) if n > 0 and n is odd.

What is g (5) ?

a. 5 b. 0

c. 1 d. 4

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Answers:

1. c

2. b

3. b

4. d

5. b

6. a

7. d

8. a

9. b

10. a

11. c

12. d