# Numbers Questions

Q:

What least number must be subtracted from 13601, so that the remainder is divisible by 87 ?

 A) 23 B) 31 C) 29 D) 37

Explanation:

87)13601(156
87
-----
490
435
-----
551
522
-----
29
-----
Required number is 29.

80 19944
Q:

(51 + 52 + 53 + .........+100) is equal to

51 + 52 + 53 + ...........+ 100

= (1 + 2 + 3 + .... + 100) - (! + 2 + 3 + ...... + 50)

=$\inline \fn_jvn \left ( \frac{100\times 101}{2}-\frac{50\times 51}{2} \right )$

=  (5050 - 1275) = 3775

18181
Q:

A number when divided by 296 leaves 75 as remainder.When the same number is divided by 37,the remainder will be:

 A) 1 B) 3 C) 5 D) 2

Explanation:

Let the Number be Y.

Then  Y = 296 q + 75

= (37 x 8)q +( 37 x 2) + 1

= 37 (8q + 2) + 1

Thus, when the number is divided by 37, the remainder is 1

32 12500
Q:

The sum of all two digit numbers divisible by 5 is

 A) 945 B) 678 C) 439 D) 568

Explanation:

Required numbers are 10,15,20,25,...,95
This is an A.P. in which a=10,d=5 and l=95.
Let the number of terms in it be n.Then t=95
So a+(n-1)d=95.
10+(n-1)*5=95,then n=18.
Required sum=n/2(a+l)=18/2(10+95)=945.

23 12158
Q:

476 ** 0 is divisible by both 3 and 11.The non zero digits in the hundred's and ten's places are respectively:

 A) 6 and 2 B) 8 and 2 C) 6 and 5 D) 8 and 5

Explanation:

Let the number  be 476ab0

476ab0 is divisible by 3

=> 4 + 7 + 6 + a + b + 0 is divisible by 3

=> 17 + a + b is divisible by 3 ------------------------(i)

476ab0 is divisible by 11

[(4 + 6 + b) -(7 + a + 0)] is 0 or divisible by 11

=> [3 + (b - a)] is 0 or divisible by 11  --------------(ii)

Substitute the values of a and b with the values given in the choices and select the values which satisfies both Equation 1 and Equation 2.

if a=6 and b=2,

17 + a + b = 17 + 6 + 2 = 25 which is not divisible by 3 --- Does not meet equation(i).Hence this is not the answer

if a=8 and b=2,

17 + a + b = 17 + 8 + 2 = 27 which is divisible by 3 --- Meet equation(i)

[3 + (b - a)] = [3 + (2 - 8)] = -3 which is neither 0 nor divisible by 11---Does not meet equation(ii).Hence this is not the answer

if a=6 and b=5,

17 + a + b = 17 + 6 + 5 = 28 which is not divisible by 3 --- Does not meet equation (i) .Hence this is not the answer

if a=8 and b=5,

17 + a + b = 17 + 8 + 5 = 30 which is divisible by 3 --- Meet equation 1

[3 + (b - a)] = [3 + (5 - 8)] = 0 ---Meet equation 2

Since these values satisfies both equation 1 and equation 2, this is the answer