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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GPA: 3.82
If xy>0, which of the following must be positive? [#permalink]

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14 Apr 2017, 06:39
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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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Manager
Joined: 18 Jan 2017
Posts: 85
Location: India
Concentration: Finance, Economics
GMAT 1: 700 Q50 V34
Re: If xy>0, which of the following must be positive? [#permalink]

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14 Apr 2017, 07:05
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
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4862
GPA: 3.82
Re: If xy>0, which of the following must be positive? [#permalink]

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16 Apr 2017, 17:30
==> 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, 17:30
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