# Aptitude - Numbers

### Exercise :: Numbers - General Questions

11.

5358 x 51 = ?

 A. 273258 B. 273268 C. 273348 D. 273358

Explanation:

 5358 x 51 = 5358 x (50 + 1) = 5358 x 50 + 5358 x 1 = 267900 + 5358 = 273258.

12.

The sum of first five prime numbers is:

 A. 11 B. 18 C. 26 D. 28

Explanation:

Required sum = (2 + 3 + 5 + 7 + 11) = 28.

Note: 1 is not a prime number.

Definition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself.

13.

The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?

 A. 240 B. 270 C. 295 D. 360

Explanation:

Let the smaller number be x. Then larger number = (x + 1365). x + 1365 = 6x + 15 5x = 1350 x = 270 Smaller number = 270.

14.

(12)3 x 64 ÷ 432 = ?

 A. 5184 B. 5060 C. 5148 D. 5084 E. None of these

Explanation:

 Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184 432 12 x 62

15.

72519 x 9999 = ?

 A. 725117481 B. 674217481 C. 685126481 D. 696217481 E. None of these

Explanation:

 72519 x 9999 = 72519 x (10000 - 1) = 72519 x 10000 - 72519 x 1 = 725190000 - 72519 = 725117481.

16.

If the number 517*324 is completely divisible by 3, then the smallest whole number in the place of * will be:

 A. 0 B. 1 C. 2 D. None of these

Explanation:

Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x), which must be divisible by 3. x = 2.

17.

The smallest 3 digit prime number is:

 A. 101 B. 103 C. 109 D. 113

Explanation:

The smallest 3-digit number is 100, which is divisible by 2. 100 is not a prime number.

101 < 11 and 101 is not divisible by any of the prime numbers 2, 3, 5, 7, 11. 101 is a prime number.

Hence 101 is the smallest 3-digit prime number.

18.

Which one of the following numbers is exactly divisible by 11?

 A. 235641 B. 245642 C. 315624 D. 415624

Explanation:

(4 + 5 + 2) - (1 + 6 + 3) = 1, not divisible by 11.

(2 + 6 + 4) - (4 + 5 + 2) = 1, not divisible by 11.

(4 + 6 + 1) - (2 + 5 + 3) = 1, not divisible by 11.

(4 + 6 + 1) - (2 + 5 + 4) = 0, So, 415624 is divisible by 11.

19.

(?) - 19657 - 33994 = 9999

 A. 63650 B. 53760 C. 59640 D. 61560 E. None of these

Explanation:

``` 19657         Let x - 53651  = 9999
33994         Then, x = 9999 + 53651 = 63650
-----
53651
-----
```

20.

The sum of first 45 natural numbers is:

 A. 1035 B. 1280 C. 2070 D. 2140

Explanation:

Let Sn =(1 + 2 + 3 + ... + 45). This is an A.P. in which a =1, d =1, n = 45.

 Sn = n [2a + (n - 1)d] = 45 x [2 x 1 + (45 - 1) x 1] = 45 x 46 = (45 x 23) 2 2 2

= 45 x (20 + 3)

= 45 x 20 + 45 x 3

= 900 + 135

= 1035.

Shorcut Method:

 Sn = n(n + 1) = 45(45 + 1) = 1035. 2 2