AHSME 1951 Problem 21

Given: $x > 0, y > 0, x > y$ and $z\ne 0$. The inequality which is not always correct is: $\textbf{(A)}\ x + z > y + z \textbf{(B)}\ x - z > y - z \textbf{(C)}\ xz > yz$ $\textbf{(D)}\ \frac {x}{z^2} > \frac {y}{z^2} \textbf{(E)}\ xz^2 > yz^2$