Xbond wrote:Hi there,

I would like to understand why E is not the right answer.

xyz>0, is x>0 ?

(1) xy >0

(2) xz >0


OA is C

Hi Xbond,

Since you want to know why the answer is not E, let's proceed immediately to combining the statements.

Statement one tells you that both x and y are both positive or else both negative. Statement two tells you that x and z are both positive or else both negative. But, because the statements can never contradict each other, when you combine, you can't have x's sign being different in the two statements.

So from statement one, let's say x and y are both positive. In combination with statement two, this would mean that both x and z are positive as well (in order to satisfy both statements at the same time without x's sign changing).
That would make all three positive. So this is one way of satisfying the statements in combination.

The other case is that in statement one, let's say both x and y are negative. This would mean that, in combination with statement two, both x and z are negative as well (in order to satisfy both statement one and two at the same time). But that would mean that all three are negative (-)(-)(-), and that would betray the information given in the question stem.

So the only way to satisfy both of the statements as well as the information in the question stem all at the same time is if x is positive, and the answer to the question is "definitely yes".

Both statements sufficient in combination. We should choose C.

many thks