# Numbers Questions

Q:

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

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

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

= It is in the form of

= n1 = 100 , n2 = 50

=

=  (5050 - 1275) = 3775

24339
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.

98 25318
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

44 15685
Q:

The difference between the place value and the face value of 7 in the numeral 967452 is

 A) 6393 B) 5831 C) 6993 D) 6339

Explanation:

(Place value of 7)-(face value of 7)
=7000-7=6993.

42 11664
Q:

The sum of first 45 natural numbers is:

The sum of n natural numbers $\inline \frac{n(n+1)}{2}=\frac{45\times 46}{2}=1035$

6185
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

5346
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.

$\inline \fn_jvn \left [ \frac{2^{n}+2^{n-1}}{2^{n+1}-2^{n}} \right ]$ is: