# 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 ?
339
349
369
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) = ?
2525
2975
3225
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) = ?
420
460
500
540
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 ?
8475
8500
8550
8525
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:
4
5
6
7
8 Required value of * is 6.