# numbers aptitude questions

31.

On dividing a number by 5, we get 3 as remainder. What will the remainder when the square of the this number is divided by 5 ?
A.     0    B.     1
C.     2    D.     4

Explanation:

Let the number be x and on dividing x by 5, we get k as quotient and 3 as remainder.

x = 5k + 3

x2 = (5k + 3)2

= (25k2 + 30k + 9)

= 5(5k2 + 6k + 1) + 4

On dividing x2 by 5, we get 4 as remainder.

32.

How many 3-digit numbers are completely divisible 6 ?
A.     149    B.     150
C.     151    D.     166

Explanation:

3-digit number divisible by 6 are: 102, 108, 114,… , 996

This is an A.P. in which a = 102, d = 6 and l = 996

Let the number of terms be n. Then tn = 996.

a + (n – 1)d = 996

102 + (n – 1) x 6 = 996

6 x (n – 1) = 894

(n – 1) = 149

n = 150

Number of terms = 150.

33.

How many natural numbers are there between 23 and 100 which are exactly divisible by 6 ?
A.     8    B.     11
C.     12    D.     13
E.     None of these

Explanation:

Required numbers are 24, 30, 36, 42, …, 96

This is an A.P. in which a = 24, d = 6 and l = 96

Let the number of terms in it be n.

Then tn = 96    a + (n – 1)d = 96

24 + (n – 1) x 6 = 96

(n – 1) x 6 = 72

(n – 1) = 12

n = 13

Required number of numbers = 13.

34.

How many of the following numbers are divisible by 3 but not by 9 ?
2133, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276
A.     5    B.     6
C.     7    D.     None of these

Explanation:

Marking (/) those which are are divisible by 3 by not by 9 and the others by (X), by taking the sum of digits, we get:s

2133 9 (X)

2343 12 (/)

3474 18 (X)

4131 9 (X)

5286 21 (/)

5340 12 (/)

6336 18 (X)

7347 21 (/)

8115 15 (/)

9276 24 (/)

Required number of numbers = 6.

35.

(963 + 476)2 + (963 – 476)2     = ?
(963 x 963 + 476 x 476)
A.     1449    B.     497
C.     2    D.     4
E.     None of these

Explanation:

Given Exp. =     (a + b)2 + (a – b)2     =     2(a2 + b2)     = 2
(a2 + b2)     (a2 + b2)
36.

How many 3 digit numbers are divisible by 6 in all ?
A.     149    B.     150
C.     151    D.     166

Explanation:

Required numbers are 102, 108, 114, … , 996

This is an A.P. in which a = 102, d = 6 and l = 996

Let the number of terms be n. Then,

a + (n – 1)d = 996

102 + (n – 1) x 6 = 996

6 x (n – 1) = 894

(n – 1) = 149

n = 150.

37.

A 3-digit number 4a3 is added to another 3-digit number 984 to give a 4-digit number 13b7, which is divisible by 11. Then, (a + b) = ?
A.     10    B.     11
C.     12    D.     15

Explanation:

4 a 3  |
9 8 4  }  ==> a + 8 = b  ==>  b – a = 8
13 b 7  |

Also, 13 b7 is divisible by 11      (7 + 3) – (b + 1) = (9 – b)

(9 – b) = 0

b = 9

(b = 9 and a = 1)     (a + b) = 10.

38.

8597 – ? = 7429 – 4358
A.     5426    B.     5706
C.     5526    D.     5476
E.     None of these

Explanation:

7429          Let 8597 – x = 3071
-4358          Then,      x = 8597 – 3071
—-                       = 5526
3071
—-

39.

The smallest prime number is:
A.     1    B.     2
C.     3    D.     4

Explanation:

The smallest prime number is 2.
40.

(12345679 x 72) = ?
A.     88888888    B.     888888888
C.     898989898    D.     9999999998