# Numbers Questions

Q:

A number when divided by 779 gives a remainder 47. By dividing the same number by 19, what would be the remainder?

Number = ( 779 x a) + 47, where "a" is the quotient

= (19 x 41 x a) + (19 x 2) + 9

= 19 x (41a + 2) + 9

= 19 x (New quotient) + 9

$\inline&space;\fn_jvn&space;\therefore$  Required remainder = 9

4219
Q:

Which one of the following cannot be the square of a natural number?

 A) 32761 B) 42437 C) 81225 D) 20164

Explanation:

The square of a natural number never ends in 7.
42437 is not the square of a natural number

5 4053
Q:

What smallest number should be added to 4456 so that the sum is completely divisible by 6 ?

 A) 4 B) 3 C) 2 D) 1

Explanation:

6)4456(742
42
--------
25
24
-------
16
12
-----
4
------
Required number = (6-4) = 2.

3 3860
Q:

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 is divisible by all three numbers 4,3 and 11,then the number is divisible by 132 also.
264   => 4,3,11(/)
396   => 4,3,11(/)
462   => 11,3
792   => 4,3,11(/)
968   => 11,4
2178 => 11,3
5184 => 3,4
6336 => 4,3,11(/)
Required number of numbers=4.

9 3605
Q:

What smallest number of 6 digit is divisible by 111?

Smallest number of 6 digits is 100000

on dividing 100000 by 111 we get 100 as remainder

$\inline&space;\fn_jvn&space;\therefore$ Number to be added = (111 -100) = 11

$\inline&space;\fn_jvn&space;\therefore$ Required Number  = 100011