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**Q.)If m and n are integers divisible by 5 , which of the following is not necessarily true?**

A) m-n is divisible by 5

B)${m}^{2}-{n}^{2}$ is divisible by 25

C)m+n is divisible by 10

D)None of these

Solution :

Let m = $5K_{ 1 }$ and n = $5K_{ 2 }$

A) m-n = $5K_{ 1 } – 5K_{ 2 }$ = 5($K_{ 1 }-K_{ 2 }$) So, this is divisible by 5.

B)${m}^{2}-{n}^{2} = (5{ K_{ 1 }) }^{ 2 }-(5{ K_{ 2 }) }^{ 2 }=25({ { K_{ 1 } }^{ 2 } }-{ K_{ 2 } }^{ 2 }) $ . So , this is divisible by 25

C) m+n = $5K_{ 1 } + 5K_{ 2 }$ = 5( $K_{ 1 } + K_{ 2 }$) , This is divisible by 5 but may not be divisible by 10 as ( $K_{ 1 } + K_{ 2 }$) can be 1,2,3,4,5……

So, OPTION(C) is not necessarily true.

Hence , OPTION(C)