dabral wrote:With these types of inequalities, always rephrase the question by pulling out the even powers:
(x^3)(y^2)(z^3)>0 is equivalent to (x^2)(y^2)(z^2)(xz)>0, here the product (x^2)(y^2)(z^2) is always positive irrespective of whether x, y, and z are positive or negative, therefore the original question is equivalent to
Is xz>0?
1) xy>0
Insufficient: If x and y are both positive then we satisfy the statement, however if z is positive then the answer to the question is Yes, but if z is negative then the answer is No.
2) Sufficient, the statement xz>0 is identical to the question being posed.
Answer should be A.
Dabral
I think you meant to say the answer is B (since you said Statement 2 was sufficient alone), but that's not quite right. With Statement 2 alone, there is still the possibility that y=0, in which case the answer to the question would be 'no'. That is, with Statement 2 alone, all we can be sure of is that x^3 * y^2 * z^3
> 0. When we combine the two statements, we know from Statement 1 that y cannot be 0, and the two Statements together are sufficient. So the answer should be C.
The 'trap' in this question (noticing that there is one exceptional value of y, y=0, which makes Statement 2 insufficient alone) is not the 'style' of trap I see in real GMAT questions, however. In every similar real GMAT question I've seen, the question always tells you in advance the letters represent nonzero numbers, and the question is testing if you understand the more mathematically important fact that odd powers can be negative, but even powers cannot.
