1.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

Explanation: Required no. = LCM of ( 8, 11, 24 ) –5 = 264 – 5 = 259

2. 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) 1367

c) 140

d) 172

Explanation: Suppose least no. be x

1856 - x = n (LCM of 7,12,16) + 4

or 1856 – x = n (336)+ 4

we should take n = 5 so that n(336) is nearest to 1856

and n (336) < 1856

1856 – x = 1680 + 4 = 1684

x = 1856 – 1684 = 172

3. Two positive integers differ by 4 and sum of their reciprocals is 10/21. Then one of the number is

a) 3

b) 1

c) 5

d) 21

Explanation:

4. Three bells chime at an interval of 18, 24 and 32 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 8 minutes

c) 1 hours 36 minutes

d) 5 hours

Explanation: L.C.M of 18, 24 and 32 = 288

Hence they would chime together after every 288 min.

or 4 hrs. 8 min

5. For the product n(n+1)(2n+1), n \[ \epsilon \] N, which one of the following is not necessarily true?

a) It is always even

b) Divisible by 3.

c) Always divisible by the sum of the square of first n natural numbers

d) Never divisible by 237.

Explanation: It is clear that for n = 237 the expression n(n + 1) (2n + 1) is divisible by 237.

Hence option (d) is not necessarily true

6. 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

Explanation: It is clearly 1 or 5

Example : 7 divided by 6 leaves remainder 1

11 divided by 6 leaves remainder 5

13 divided by 6 leaves remainder 1

7. Cost of 72 hens is Rs .....96.7..... Then, what will be the cost of hen, where two digits in place of “ ....... ” are not visible or are written
in illegible hand-writing?

a) Rs. 3.23

b) Rs. 5.11

c) Rs. 5.51

d) Rs. 7.22

Explanation: Multiply each option by 72 and find out the result which matches the visible digits.

Clearly we see 72 * 5.51 = 396.72

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

a) 10

b) 14

c) 16

d) 12

Explanation: Let x - 2, x, x + 2 be the 3 consecutive numbers

then, 3 (x – 2) = 2 (x + 2) + 2 (according to the question)

or 3x - 6 = 2x + 6

or x = 12

Hence, the 3rd no. is 14

9. \[5^{6}-1\] is divisible by

a) 13

b) 31

c) 3

d) None of these

Explanation:

10. 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

Explanation: