Notice that x^2 must be nonnegative. Therefore, if x and z and are nonzero numbers, z^3, will be positive if y is positive, and z^3 will be negative if y is negative. The upshot is that y is the key.NandishSS wrote:If (x^2)y=z^3, is z^3>0?
(1) x(y^2)>0
(2) yz > 0
OA:E
Source:GMATPrep EP2
1) Because y^2 must be nonnegative, this tells us that x is positive. However, we don't know if y is positive or negative - if y is positive, z^3 will be positive, giving us a YES. if y is negative, z^3 will be negative, giving us a NO. so this statement alone is not sufficient.
2) All this tells us is that z and y are both positive or both negative. But, unless both sides of the equation are equal to zero, we already knew that! Statement 2 alone is insufficient (and basically useless.)
Together: y could be positive or negative, and so z^3 could be positive or negative, meaning we can still get a YES or a NO. Together the statements are not sufficient. The answer is E
