1997 Cayley Problem 11

In the chart, the products of the numbers represented by the letters in each of the rows and columns are given. For example, xy = 6 and xz = 12. If x, y, z, and w are integers, what is the value of xw?

\begin{array}{|c|c||c|} \hline x & y & 6 \\ \hline z & w & 50 \\ \hline\hline 12 & 25 & \\ \hline \end{array}

\textbf{(A)}\ 150\quad \textbf{(B)}\ 300\quad \textbf{(C)}\ 31\quad \textbf{(D)}\ 75\quad \textbf{(E)}\ 30

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.