"If a whole number $n$ is not prime, then the whole number $n-2$ is not prime." A value of $n$ which shows this statement to be false is
$\textbf{(A)}\ 9 \qquad \textbf{(B)}\ 12 \qquad \textbf{(C)}\ 13 \qquad \textbf{(D)}\ 16 \qquad \textbf{(E)}\ 23$
To show this statement to be false, we need a non-prime value of $n$ such that $n-2$ is prime.  Since $13$ and $23$ are prime, they won't prove anything relating to the truth of the statement.
Now we just check the statement for $n=9,12,16$.  If $n=12$ or $n=16$, then $n-2$ is $10$ or $14$, which aren't prime.  However, $n=9$ makes $n-2=7$, which is prime, so $n=9$ proves the statement false.
Therefore, the answer is $\boxed{\textbf{A}}$, 9.