AHSME 1951 Problem 35

If $a^{x}= c^{q}= b$ and $c^{y}= a^{z}= d$, then $\textbf{(A)}\ xy = qz \textbf{(B)}\ \frac{x}{y}=\frac{q}{z} \textbf{(C)}\ x+y = q+z \textbf{(D)}\ x-y = q-z$ $\textbf{(E)}\ x^{y}= q^{z}$