numbers aptutude questions

1. Which one of the following is not a prime number?
 A. 31 B. 61 C. 71 D. 91

Explanation:

91 is divisible by 7. So, it is not a prime number.

2. (112 x 54) = ?
 A. 67000 B. 70000 C. 76500 D. 77200

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?
 A. (216 + 1) B. (216 – 1) C. (7 x 223) D. (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)(x2x + 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 ?
 A. 2 B. 3 C. 18 D. 21 E. None of these

5. 1397 x 1397 = ?
 A. 1951609 B. 1981709 C. 18362619 D. 2031719 E. None of these

Explanation:

 1397 x 1397 = (1397)2 = (1400 – 3)2 = (1400)2 + (3)2 – (2 x 1400 x 3) = 1960000 + 9 – 8400 = 1960009 – 8400 = 1951609.

6. How many of the following numbers are divisible by 132 ?
264, 396, 462, 792, 968, 2178, 5184, 6336
 A. 4 B. 5 C. 6 D. 7

Explanation:

132 = 4 x 3 x 11

So, if the number divisible by all the three number 4, 3 and 11, then the number is divisible by 132 also.

264 11,3,4 (/)

396 11,3,4 (/)

462 11,3 (X)

792 11,3,4 (/)

968 11,4 (X)

2178 11,3 (X)

5184 3,4 (X)

6336 11,3,4 (/)

Therefore the following numbers are divisible by 132 : 264, 396, 792 and 6336.

Required number of number = 4.

7. (935421 x 625) = ?
 A. 575648125 B. 584638125 C. 584649125 D. 585628125

Explanation:

 935421 x 625 = 935421 x 54 = 935421 x 10 4 2

 = 935421 x 104 = 9354210000 24 16

= 584638125

8. The largest 4 digit number exactly divisible by 88 is:
 A. 9944 B. 9768 C. 9988 D. 8888 E. None of these

Explanation:

```Largest 4-digit number = 9999

88) 9999 (113
88
----
1199
88
----
319
264
---
55
---

Required number = (9999 - 55)
= 9944.```

9. Which of the following is a prime number ?
 A. 33 B. 81 C. 93 D. 97

Explanation:

Clearly, 97 is a prime number.

10. What is the unit digit in {(6374)1793 x (625)317 x (341491)}?
 A. 0 B. 2 C. 3 D. 5

Explanation:

Unit digit in (6374)1793 = Unit digit in (4)1793

= Unit digit in [(42)896 x 4]

= Unit digit in (6 x 4) = 4

Unit digit in (625)317 = Unit digit in (5)317 = 5

Unit digit in (341)491 = Unit digit in (1)491 = 1

Required digit = Unit digit in (4 x 5 x 1) = 0.