AHSME 1983 Problem 1

If $x \neq 0, \frac x{2} = y^2$ and $\frac{x}{4} = 4y$, then $x$ equals $\textbf{(A)}\ 8 \textbf{(B)}\ 16 \textbf{(C)}\ 32 \textbf{(D)}\ 64 \textbf{(E)}\ 128$