Which of the following must be an even integer?

(A) The average of two even integers

(B) The average of two prime numbers

(C) The average of two perfect squares

(D) The average of two multiples of 4

(E) The average of three consecutive integers
The average of two multiples of 4 must be even, since we can write these multiples of 4 as $4 \mathrm{~m}$ and $4 n$ for some integers $m$ and $n$, which means that their average is $\frac{1}{2}(4 m+4 n)$ which equals $2 m+2 n$ or $2(m+n)$, which is a multiple of 2 , and so is even.

Each of the other four choices may be an odd integer in some cases. Here is an example for each:

(A) The average of 2 and 4 is 3 , which is not even

(B) The average of 3 and 7 is 5 , which is not even

(C) The average of 1 and 9 is 5 , which is not even

(E) The average of 2,3 and 4 is 3 , which is not even

Therefore, the correct answer is (D).

ANSWER: (D)