GRE Sample Test 5 Quantitative Reasoning 1

If x + y = 0, and neither x nor y = 0, then it must be the case that x and y are different numbers with the same absolute value. For example, x = −2 and y = 2. Based on this example, choices A and B are possible. For choice C to be possible, x and y would have to have the same sign. But they cannot have the same sign since they must cancel each other out. Choice C cannot be true and is thus a possible answer. Choice D cannot be true because any non-zero number raised to an even exponent will yield a positive result. Positive + positive > 0. Choice E is always true, since odd exponents preserve the sign of the base. Because x and y have different signs, ${\mathit{x}}^3$ and ${\mathit{y}}^3$ will also have different signs.