# Aptitude - Numbers

Exercise : Numbers - General Questions
1.
Which one of the following is not a prime number?
31
61
71
91
Explanation:
91 is divisible by 7. So, it is not a prime number.

2.
(112 x 54) = ?
67000
70000
76500
77200
Explanation:
 (112 x 54) = 112 x 10 4 = 112 x 104 = 1120000 = 70000 2 24 16

3.
It is being given that (232 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?
(216 + 1)
(216 - 1)
(7 x 223)
(296 + 1)
Explanation:

Let 232 = x. Then, (232 + 1) = (x + 1).

Let (x + 1) be completely divisible by the natural number N. Then,

(296 + 1) = [(232)3 + 1] = (x3 + 1) = (x + 1)(x2 - x + 1), which is completely divisible by N, since (x + 1) is divisible by N.

4.
What least number must be added to 1056, so that the sum is completely divisible by 23 ?
2
3
18
21
None of these
Explanation:
``` 23) 1056 (45
92
---
136
115
---
21
---

Required number = (23 - 21)
= 2.
```

5.
1397 x 1397 = ?
1951609
1981709
18362619
2031719
None of these