1961 AHSME Problem 21

Medians AD and CE of \triangle ABC intersect in M. The midpoint of AE is N. Let the area of \triangle MNE be k times the area of \triangle ABC. Then k equals:

\textbf{(A)}\ \frac{1}{6}\qquad \textbf{(B)}\ \frac{1}{8}\qquad \textbf{(C)}\ \frac{1}{9}\qquad \textbf{(D)}\ \frac{1}{12}\qquad \textbf{(E)}\ \frac{1}{16}

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