# Number System

Pratice Number System Questions and answers.

Rule Description
1

If the sum of digits of two digit number is ‘a’ and if the digits or the number are reversed, such that number reduces by ‘b’, then,

Original Number $=\frac{11a+b}{2}$

2

If the sum of digits of two digit number is ‘a’ and if the digits of the number are reversed, such that number increases by ‘b’, then,

Original Number $=\frac{11a-b}{2}$

3

If the difference between a number and formed by number reversing digit is x, then the difference between both the digits of the number is

$\frac{x}{9}$

4

If the sum of a number and the number formed by reversing the digits is x, then the sum of digits of the number is

$\frac{x}{11}$

5

Remainder Calculation:

If $\frac{a^n}{a-1}$, then remainder will always be 1,whether n is even or odd.

6

Remainder Calculation:

If $\frac{a^{\left(even\ number\right)}}{a+1}$, then remainder will be 1.

7

Remainder Calculation:

If $\frac{a^{\left(odd \ number\right)}}{a+1}$, then remainder will be a.

8

If n is a single digit number, then in $n^3,n$ will be at unit place.

It is valid for the number $0, 1, 4, 5, 6 \ or \ 9$.

9

If n is a single digit number then in $n^p$, where p is any number (+ve), n will be at unit place.

It is valid for 5 and 6.