1986 AHSME Problem 15

A student attempted to compute the average, A, of x, y and z by computing the average of x and y, and then computing the average of the result and z. Whenever x < y < z, the student's final result is

\begin{array}{l} \textbf{(A)}\ \text{correct}\quad \textbf{(B)}\ \text{always less than A}\quad \textbf{(C)}\ \text{always greater than A}\quad\\ \textbf{(D)}\ \text{sometimes less than A and sometimes equal to A}\quad\\ \textbf{(E)}\ \text{sometimes greater than A and sometimes equal to A} \quad \end{array}

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