Is xy + xy < xy ? : GMAT Data Sufficiency (DS)
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Is xy + xy < xy ?

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Is xy + xy < xy ? [#permalink]

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Is xy + xy < xy ?

(1) x^2/y < 0

(2) x^9*(y^3)^3 < (x^2)^4*y^8
[Reveal] Spoiler: OA

Last edited by Bunuel on 18 Jun 2014, 00:04, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to DS forum.
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Re: Is xy + xy < xy ? [#permalink]

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New post 18 Jun 2014, 00:17
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nitin1negi wrote:
Is xy + xy < xy ?

(1) x^2/y < 0

(2) x^9*(y^3)^3 < (x^2)^4*y^8


Is xy+xy<xy?

Is \(xy+xy<xy\)? --> cancel xy in both sides: is \(xy<0\)? So, the question basically asks whether x and y have the opposite signs.

(1) x^2/y<0. This statement implies that y is negative and x can be anything but zero. Not sufficient.

(2) x^9*(y^3)^3 < (x^2)^4*y^8 --> \((xy)^9<(xy)^8\). Since \((xy)^8>0\) (from the inequality we can deduce that neither of the unknowns is zero, thus even power of xy will ensure that it's positive), then we can safely reduce by it: \(xy<1\) (\(xy\neq{0}\)). So, we cannot say whether \(xy<0\). Not sufficient.

(1)+(2) \(y<0\) and \(xy<1\). If \(x=-\frac{1}{2}\) and \(y=-1\), then the answer is NO but if \(x=1\) and \(y=-1\), then the answer is YES. Not sufficient.

Answer: E.

Hope it's clear.

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Re: Is xy + xy < xy ?   [#permalink] 18 Jun 2014, 00:17
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