# Aptitude - Numbers

### Exercise :: Numbers - General 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 C. 369 D. Data inadequate

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

Explanation:

```On dividing, we get

75) 8485 (113
75
---
98
75
----
235
225
---
10
---

Required number = (8485 - 10) // Because 10 < (75 - 10)
= 8475.
```

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

Explanation:

639 is not divisible by 7

2079 is divisible by each of 3, 7, 9, 11.

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