Bunuel wrote:
If x ≠ 0, is xy > 0?
(1) x > 0
(2) 1/x < y
Kudos for a correct solution.
MANHATTAN GMAT OFFICIAL SOLUTION:(1) INSUFFICIENT: This tells us nothing about the sign of y.
In evaluating Statement (2), you might be tempted to assume that x must be positive. After all, we just read information in Statement (1) that tells us that x is positive. Besides, it is natural to assume that a given variable will have a positive value, because positive numbers are much more intuitive than negative numbers.
Instead, if we follow Principle #4, we will
actively try to violate Statement (1), helping us expose the trick in this question.
(2) INSUFFICIENT: If we contradict Statement (1) to consider the possibility that x is negative, we would realize that it is necessary to flip the sign of the inequality when we cross multiply. That is, if x < 0, then 1/x < y means that 1 > xy, and the answer to the question is MAYBE.
(1) & (2) SUFFICIENT: If x is positive, then statement (2) says that 1 < xy (we do not flip the sign when cross multiplying). Thus, xy > 0.
The correct answer is C.Hi Bunuel ? Could you please explain how could we infer 1 < xy from statement 2 ??