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# If xy>0, which of the following must be positive?

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Math Revolution GMAT Instructor
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If xy>0, which of the following must be positive? [#permalink]

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14 Apr 2017, 07:39
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If xy>0, which of the following must be positive?

A. $$x$$
B. $$y$$
C. $$x^2y$$
D. $$y^2x$$
E. $$x^3y$$
[Reveal] Spoiler: OA

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Re: If xy>0, which of the following must be positive? [#permalink]

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14 Apr 2017, 08:05
xy>0, implies both x and y are of the same sign
Only option E satisfies, remaining are dependent on sign of x,y
x^3y is positive provided both x and y are of the same sign

Kudos [?]: 58 [0], given: 356

Math Revolution GMAT Instructor
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Re: If xy>0, which of the following must be positive? [#permalink]

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16 Apr 2017, 18:30
==> Squares are always positive, so the inequality sign doesn’t change even if you multiply or divide. Thus, from xy>0 and $$(x^2)xy>(x^2)0$$, you get $$x^3y>0$$.

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Re: If xy>0, which of the following must be positive?   [#permalink] 16 Apr 2017, 18:30
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