Say p = 9n + 2 and q = 9m + 7. This means p - q = 9(n - m) - 5, where n and m are positive integers. The term 9(n - m) is divisible by 3, so the remainder is -5, but 5 is greater than 3, so we need to divide 5 by 3 to get the actual remainder.
This gives us the remainder of 2.
However, because of the negative sign before the 5, the remainder now becomes -2. The significance of -2 is that -2 + 3 = 1.
The correct answer choice is C.
Multiple theories suggest the origin of the expression “mind your Ps and Qs,” everything from how parents reminded children to use polite words to how bartenders monitored the consumption of alcohol in 17th century taverns.