1965 AHSME Problem 26

For the numbers a, b, c, d, e define m to be the arithmetic mean of all five numbers; k to be the arithmetic mean of a and b; l to be the arithmetic mean of c, d, and e; and p to be the arithmetic mean of k and l. Then, no matter how a, b, c, d, and e are chosen, we shall always have:

\begin{array}{l} \textbf{(A)}\ m = p \qquad \textbf{(B) }\ m \ge p \qquad \textbf{(C) }\ m > p \qquad \\ \textbf{(D) }\ m < p\qquad \textbf{(E) }\ \text{none of these} \end{array}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.