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# If xy>0, is x^3y^4>0?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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22 Jan 2018, 01:03
1
2
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Difficulty:

45% (medium)

Question Stats:

52% (00:56) correct 48% (00:33) wrong based on 69 sessions

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[GMAT math practice question]

If $$xy>0$$, is $$x^3y^4>0?$$

$$1) x>0$$
$$2) y>0$$

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Retired Moderator Joined: 25 Feb 2013 Posts: 1178 Location: India GPA: 3.82 Re: If xy>0, is x^3y^4>0? [#permalink] ### Show Tags 22 Jan 2018, 10:00 MathRevolution wrote: [GMAT math practice question] If $$xy>0$$, is $$x^3y^4>0?$$ $$1) x>0$$ $$2) y>0$$ $$x^3y^4>0=>y(xy)^3>0$$ as $$xy>0=>(xy)^3>0$$. Hence we need to know Is $$y>0$$? Statement 1: $$x>0$$ and we know $$xy>0$$ so $$y>0$$. Sufficient Statement 2: directly provides $$y>0$$. Sufficient Option D Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8017 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If xy>0, is x^3y^4>0? [#permalink] ### Show Tags 24 Jan 2018, 01:24 => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question. Modifying the question: $$x^3y^4>0$$ $$⇔ x>0$$ since $$y^4>0$$ is always true. We can ignore even exponents in inequalities that have $$0$$ on one side. So, the question becomes, ‘is $$x>0$$?’. Condition 1) is certainly sufficient. Condition 2): $$x > 0$$ since $$y > 0$$ and $$xy > 0$$. Thus, condition 2) is also sufficient. Therefore, D is the answer. Note: Tip 1) of the VA method states that D is most likely to be the answer if condition 1) gives the same information as condition 2). Answer: D _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: If xy>0, is x^3y^4>0?  [#permalink]

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21 May 2019, 03:35
MathRevolution wrote:
[GMAT math practice question]

If $$xy>0$$, is $$x^3y^4>0?$$

$$1) x>0$$
$$2) y>0$$

Simplify the question first: it is asking is X>0? The rest of the product term is squared so must be +ve.

Statement 1.

Sufficient, X>0 given

Statement 2.

Since XY>0 and given Y>0 then x has to be >0. Also sufficient.
D Either 1 Or 2 independently sufficient.
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Re: If xy>0, is x^3y^4>0?   [#permalink] 21 May 2019, 03:35
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