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The positive integers $m, n$ leave remainders of 2 and 3 respectively when divided by ‘6’ $m > n$ what is the remainder when $m - n$ is divided by 6?

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answer is C.

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Detailed Solution

Given $m = 6 p + 2$

$n = 6 q + 3$

$\Rightarrow m - n = 6 p + 2 - 6 q - 3$

$= 6 p - 6 q - 1$

$= 6 (p - q) - 1$

Add and subtract ‘6’

$= 6 (p - q) - 1 + 6 - 6$

$\Rightarrow 6 (p - q - 1) + 5$

$∴$ reminder is ‘5’

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