# Difference between revisions of "2019 AMC 10B Problems/Problem 2"

The following problem is from both the 2019 AMC 10B #2 and 2019 AMC 12B #2, so both problems redirect to this page.

## Problem

Consider the statement, "If $n$ is not prime, then $n-2$ is prime." Which of the following values of $n$ is a counterexample to this statement?

$\textbf{(A) } 11 \qquad \textbf{(B) } 15 \qquad \textbf{(C) } 19 \qquad \textbf{(D) } 21 \qquad \textbf{(E) } 27$

## Solution

Since a counterexample must be when n is not prime, n must be composite, so we eliminate A and C. Now we subtract 2 from the remaining answer choices, and we see that the only time $n-2$ is $\textbf{not}$ prime is when $n = 27$, which is $\fbox {E}$.

iron

minor edit (the inclusion of not) by AlcBoy1729