# Aptitude - Numbers

Exercise : Numbers - General Questions
16.
If the number 517*324 is completely divisible by 3, then the smallest whole number in the place of * will be:
1
2
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:
101
103
109
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?
235641
245642
315624
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
63650
53760
59640
61560
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:
1035
1280
2070
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