# numbers aptitude questions

61.

When a number is divided by 13, the remainder is 11. When the same number is divided by 17, then remainder is 9. What is the number ?
A.     339    B.     349

Explanation:

x = 13p + 11 and x = 17q + 9

13p + 11 = 17q + 9

17q – 13p = 2

q =     2 + 13p
17

The least value of p for which q =     2 + 13p     is a whole number is p = 26
17

x = (13 x 26 + 11)

= (338 + 11)

= 349

62.

(51 + 52 + 53 + … + 100) = ?
A.     2525    B.     2975
C.     3225    D.     3775

Explanation:

Sn = (1 + 2 + 3 + … + 50 + 51 + 52 + … + 100) – (1 + 2 + 3 + … + 50)

=     100     x (1 + 100) –     50     x (1 + 50)
2     2

= (50 x 101) – (25 x 51)

= (5050 – 1275)

= 3775.

63.

(800 ÷ 64) x (1296 ÷36) = ?
A.     420    B.     460
C.     500    D.     540
E.     None of these

Explanation:

Given Exp. =     800     x     1296     = 450
64     36

64.

Which natural number is nearest to 8485, which is completely divisible by 75 ?
A.     8475    B.     8500
C.     8550    D.     8525
E.     None of these

65.

If the number 42573 * is exactly divisible by 72, then the minimum value of * is:
A.     4    B.     5
C.     6    D.     7
E.     8

Explanation:

72 = 9 x8, where 9 and 8 are co-prime.

The minimum value of x for which 73x for which 73x is divisible by 8 is, x = 6.

Sum of digits in 425736 = (4 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 9.

Required value of * is 6.

66.

Which of the following numbers is divisible by each one of 3, 7, 9 and 11 ?
A.     639    B.     2079
C.     3791    D.     37911
E.     None of these

67.

Which natural number is nearest to 9217, which is completely divisible by 88 ?
A.     9152    B.     9240
C.     9064    D.     9184
E.     None of these

Explanation:

On dividing we get,

88) 9217 (104
88
—-
417
352
—-
65
—-

Therefore, Required number = 9217 + (88 – 65) // Because (88 – 65) < 65.
= 9217 + 23
= 9240.

68.

(4300731) – ? = 2535618
A.     1865113    B.     1775123
C.     1765113    D.     1675123
E.     None of these

Explanation:

Let 4300731 – x = 2535618

Then x, = 4300731 – 2535618 = 1765113

69.

n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2n is divided by 4 ?
A.     3    B.     2
C.     1    D.     0

Explanation:

Let n = 4q + 3. Then 2n = 8q + 6   = 4(2q + 1 ) + 2.

Thus, when 2n is divided by 4, the remainder is 2.

70.

(489 + 375)2 – (489 – 375)2     = ?
(489 x 375)
A.     144    B.     864
C.     2    D.     4
E.     None of these

Explanation:

Given Exp. =     (a + b)2 – (a – b)2     =     4ab     = 4
ab     ab