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CAT 1997 Question-1

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)


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