# Numbers Questions

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

10979
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.

52 10918
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

23 7950
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.

18 7417
Q:

The difference between a positive proper fraction and its reciprocal is 9 / 20. Then the fraction is :

 A) 3/5 B) 3/10 C) 4/5 D) 5/4