xy > 0 will be true if x and y have the same sign, so if both are positive, or if both are negative.
x^2 is always positive or zero, so Statement 1 tells us almost nothing (it only tells us x is not zero). In Statement 2, we can divide by y^2 on both sides, because we know y^2 is positive (so we don't need to worry about whether to reverse the inequality), so Statement 2 tells us x > 0. But we have no idea, even using both Statements, whether y is positive or negative, so the answer is E.
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