1964 AHSME Problem 22

Given parallelogram ABCD with E the midpoint of diagonal BD. Point E is connected to a point F in DA so that DF=\frac{1}{3}DA. What is the ratio of the area of \triangle DFE to the area of quadrilateral ABEF?

\textbf{(A)}\ 1:2 \qquad \textbf{(B)}\ 1:3 \qquad \textbf{(C)}\ 1:5 \qquad \textbf{(D)}\ 1:6 \qquad \textbf{(E)}\ 1:7

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