xy > 0 can be in two conditions: both x and y are positive or both x and y are negative. Thus, x and y must have the same signs.Vincen wrote:Is \(xy > 0?\)
(1) \(x^2 > 0\)
(2) \(xy^2 > 0\)
[spoiler]OA=E[/spoiler]
Source: Manhattan GMAT
Let's take each statement one by one.
(1) \(x^2 > 0\)
x can have any sign plus/minus; moreover, we do not about y. Insufficient.
(2) \(xy^2 > 0\)
Irrespective of the sign of y, y^2 is positive. Thus, for xy^2 to be greater than 0, x must be positive. However, we do not know the sign of y. Insufficient.
(1) and (2) together
Even after combining the two statements, we cannot know the sign of y. Insufficient.
The correct answer: E
Hope this helps!
-Jay
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