Problem 10 (1998 AJHSME)

Each of the letters $W$, $X$, $Y$, and $Z$ represents a different integer in the set $\{1, 2, 3, 4\}$, but not necessarily in that order. If $\frac{W}{X} - \frac{Y}{Z} = 1$, then the sum of $W$ and $Y$ is