GRE Sample Test 5 Quantitative Reasoning 2

Use the given constraints to determine whether each choice could equal zero.
A: If x = 0, then xy = 0. Eliminate A.
B: If x = 3, and y = −3, then x + y = 0. Eliminate B.
C: If x = 3, and y = 3, then x − y = 0, Eliminate C.
D: Factor: $\mathit{x}\mathit{y}-{\mathit{y}}^2$ = y(x − y). For y(x − y) to be zero, either y must be zero or x − y must be 0; y cannot be 0, but x − y = 0 if x = y. Eliminate D.
E: When a value is raised to an even exponent, the result must be greater than or equal to zero. Thus, ${\mathit{y}}^2$ > 0, and ${\mathit{x}}^2$ ≥ 0. The sum of ${\mathit{y}}^2$ and ${\mathit{x}}^2$ is thus greater than 0.