M25-34

Official Solution:


Is \(x^7y^2z^3 > 0\) ?

In order for \(x^7y^2z^3 > 0\) to be true, the following conditions must be met:

AND

(1) \(yz < 0\).

This statement implies that \(y \neq 0\), so the first condition is satisfied. However, we don't have information about the signs of \(x\) and \(z\). Not sufficient.

(2) \(xz > 0\).

This statement implies that \(x\) and \(z\) are either both positive or both negative. So, the second condition is met. However, we don't have information about \(y\); if \(y=0\), then the expression is not positive, but equal to 0. Not sufficient.

(1)+(2) Both conditions, \(y\) not being 0 and \(x\) and \(z\) having the same sign, are satisfied. Therefore, \(x^7y^2z^3 > 0\). Sufficient.


Answer: C