If x ≠ 0 is xy 0 ? (1) x 0 (2) x/y 1

Question

If  x ≠ 0  is   xy > 0  ?

(1)    x > 0  
(2)    x/y > 1

Thelegend2631 · Answer

I thought answer should be B.
Since

Statement 2 will be
\((x-y) /y > 0\)

Taking \(x-y > 0 \)and \(y > 0\)

\(X > y\) and \(y > 0\) then both x and y will ne positive.
Taking x-y<0 and y< 0

\(x < y\)
\(y < 0\)

That means both x and y will be negative.

Manhattan prep says statement 2 is not sufficient but i don't see why it isn't sufficient.

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Rahul3193 · Answer

I think we need both statement to answer

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Thelegend2631 · Answer

Yeah the OA is mentioned as C. But want to know how statement 2 is insufficient. Want to know your my explanation above doesn't serve its purpose

Bunuel · Answer

Can you please post a screenshot of the questions from Manhattan guide? Thank you!

Thelegend2631 · Answer

If x ≠ 0, is xy > 0 ?
The question is actually asking whether x and y have the same sign.
(1) INSUFFICIENT: This indicates nothing about the sign of y.
In evaluating statement (2), you might be tempted to assume that x must
be positive.

2) INSUFFICIENT: Consider the possibility that x is negative. In this case, it
is necessary to flip the sign of the inequality when you cross-multiply. That
is, if x < 0, then means that 1 > xy, and the answer to the question
is MAYBE.
(1) & (2) SUFFICIENT: If x is positive, then statement (2) says that 1 < xy (do
not flip the sign when cross-multiplying). Thus, xy > 0.

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Bunuel · Answer

Yes, their solution does not make sense. Correct answer is B.

If x is not equal to 0 is xy > 0 ?

(1) x > 0. Clearly insufficient.

(2) x/y > 1 --> this means that x/y is positive --> x/y is positive means that x and y have the same sign --> x and y have the same sign means that xy is positive. Sufficient.

Answer: B.

Hope it helps.

chetan2u · Answer

Statement II, looking at the way the solution is written, seems to be suggesting the inequality to be \frac{1}{x}xy. Maybe the solution has been written erroneously thinking they are dealing with 1/x1>0 means x and y have same sign.

Bunuel · Answer

You might be right. Here is that GMAT question: https://gmatclub.com/forum/if-x-0-is-xy-200160.html

IanStewart · Answer

Another way to look at Statement 2: multiply by y^2 on both sides (which we can safely do, because y^2 is never negative). Then you get xy > y^2, and if xy is greater than a square, xy is definitely positive.

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If x ≠ 0 is xy > 0 ? (1) x > 0 (2) x/y > 1

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