Official Guide Explanation:
Data Sufficiency #D41

Background

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Solution and Metadata

Question: D41
Page: 25
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Fractions >
Category 2: Algebra > Inequalities > other

Explanation: If ((x + y)/(z)) > 0, the numerator and denominator must have the same sign. We're trying to determine whether x is positive, which will depend on what we can find out about the other variables.

Statement (1) is insufficient. If x < y, it could be that both are negative, that both are positive, or that x is negative and y is positive. We don't know anything more without any knowledge of z.

Statement (2) is also insufficient. If z is negative and the overall expression is positive, x + y must also be negative. That isn't enough to find x, since either one (or both) of the two variables could be negative, but we don't know which one.

Taken together, the statements are sufficient. If z is negative, we know at least one of the variables x and y must be negative as well. Since (1) tells us that x is the smaller of those two, if only one of them is negative, x must be the one that is negative. Choice (C) is correct.

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