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?

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 as 6p +2 and 6q + 3, respectively, where p and q are suitable integers.
Now, m - n = (6p + 2) - (6q + 3) = 6p - 6q - 1 = 6(p-q) - 1.
A remainder must be positive, so let's add 6 to this expression and compensate by subtracting 6 :
6(p - q) - 1 =
6 (p - q) - 6 + 6 - 1 =
6 (p - q) - 6 = 5 =
6 (p - q - 1) + 5
Thus, the remainder is 5,
and the answer is 5