2011 Fermat Problem 14

Which of the following *must* be an even integer?

\textbf{(A)} The average of two even integers \textbf{(B)} The average of two prime numbers \textbf{(C)} The average of two perfect squares \textbf{(D)}\ The average of two multiples of 4\quad \textbf{(E)} The average of three consecutive integers

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Fermat contests here.