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

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.

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

NandishSS wrote:If (x^2)y=z^3, is z^3>0?

(1) x(y^2)>0

(2) yz > 0

We are given that (x^2)y = z^3, and we need to determine whether z^3 > 0. Recall that the values of z^3 and z have the same sign; thus, we need to determine whether z > 0.

Statement One Alone:

x(y^2) > 0

Since y^2 is always nonnegative, x(y^2) > 0 means x > 0. However, since we cannot determine the sign of y, we cannot determine whether z^3 = (x^2)y is greater than 0.

For example, if y > 0, then z^3 > 0; however, if y < 0, then z^3 < 0. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

yz > 0

Since yz > 0, we know that either both y and z are positive or both y and z are negative. However, since we cannot determine the sign of y, we cannot determine whether z^3 = (x^2)y is greater than 0.

For example, if y > 0, then z > 0, and hence z^3 > 0; however, if y < 0, then z < 0, and hence z^3 < 0. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

Using the two statements together, we still cannot determine the sign of y and thus cannot determine whether z^3 > 0.

Answer: E