The positive integers $m$ and $n$ leave remainders of 2 and 3, respectively, when divided by 6. $m > n$.

What is the remainder when $m – n$ is divided by 6?

2

3

5

6

Solution:Option(C) is correct

We are given that the numbers $m$ and $n$, when divided by 6, leave remainders of 2 and 3, respectively.

Hence, we can represent the numbers $m$ and $n$ as $6p + 2$ and $6q + 3$, respectively, where $p$ and $q$ are suitable integers.

Now, $\begin{align*} m - n &= (6p + 2) - (6q + 3)\\ &= 6p - 6q - 1 \\ &= 6(p - q) - 1 \end{align*}$

A remainder must be positive, so let’s add 6 to this expression and compensate by subtracting 6: $\begin{align*} 6(p - q) - 1 &= 6(p - q) - 6 + 6 - 1\\ & =6(p - q) - 6 + 5\\ & = 6(p - q - 1) + 5 \end{align*}$

Thus, the remainder is 5

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