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# Is xy>0?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7462
GMAT 1: 760 Q51 V42
GPA: 3.82

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10 Sep 2018, 01:58
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Difficulty:

25% (medium)

Question Stats:

79% (00:46) correct 21% (01:02) wrong based on 46 sessions

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[Math Revolution GMAT math practice question]

Is $$xy>0?$$

$$1) x^3y>0$$
$$2) x^2y>0$$

_________________
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 $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Director Joined: 18 Jul 2018 Posts: 938 Location: India Concentration: Finance, Marketing WE: Engineering (Energy and Utilities) Re: Is xy>0? [#permalink] ### Show Tags 10 Sep 2018, 02:25 From statement 1: $$x^3$$y>0. If x is positive then xy>0. If x is negative then y also has to be negative to satisfy $$x^3$$y>0. In either the case xy will always be greater than 0. 1 is sufficient. From statement 2: $$x^2$$y>0. If x is positive then y is also positive. xy>0. If x is negative and y is positive then $$x^2$$y>0 is satisfied but xy will be less than 0. 2 is insufficient. A is the answer. _________________ Press +1 Kudo If my post helps! Math Expert Joined: 02 Aug 2009 Posts: 7752 Re: Is xy>0? [#permalink] ### Show Tags 10 Sep 2018, 02:29 Is $$xy>0?$$ Both X and y should be of same sign... $$1) x^3y>0$$ Even power will always result in positive value.. $$x^3y=x^2*xy>0$$, so xy>0 Sufficient $$2) x^2y>0$$ Just tells us that y>0 If x >0, yes but if x<0, no Insufficient A _________________ VP Joined: 31 Oct 2013 Posts: 1372 Concentration: Accounting, Finance GPA: 3.68 WE: Analyst (Accounting) Is xy>0? [#permalink] ### Show Tags 10 Sep 2018, 02:38 MathRevolution wrote: [Math Revolution GMAT math practice question] Is $$xy>0?$$ $$1) x^3y>0$$ $$2) x^2y>0$$ we are asked whether xy>0. Two possibilities can make our dream true. Both x and y are positive or both negative. Statement 1: $$x^3y>0$$. If x is negative , y has to be negative. xy>0 in this case. If both x and y are positive still xy has to be positive. SUFFICIENT. Statement 2: $$x^2$$ is always positive but x is not the same as $$x^2$$. x could be positive or negative. Thus , this one is NOT Sufficient as we don't know the exact sign of x. The best answer is A. CEO Joined: 12 Sep 2015 Posts: 3782 Location: Canada Re: Is xy>0? [#permalink] ### Show Tags 10 Sep 2018, 07:45 Top Contributor MathRevolution wrote: [Math Revolution GMAT math practice question] Is $$xy>0?$$ $$1) x^3y>0$$ $$2) x^2y>0$$ Target question: Is xy > 0? Statement 1: x³y > 0 Since x² is POSITIVE, we can safely divide both sides of the inequality by x² When we do this, we get xy > 0 So, the answer to the target question is YES, xy IS greater than 0 Since we can answer the target question with certainty, statement 1 is SUFFICIENT Statement 2: x²y > 0 Once again, we can safely divide both sides of the inequality by x² However, this time we get y > 0 So, we now know that y is POSITIVE, but we don't know whether x is positive or negative. As such statement 2 is NOT SUFFICIENT If you're not convinced, we can always test some values There are several values of x and y that satisfy statement 2. Here are two: Case a: x = 1 and y = 1. In this case, xy = (1)(1) = 1. So, the answer to the target question is YES, xy IS greater than 0 Case b: x = -1 and y = 1. In this case, xy = (-1)(1) = -1. So, the answer to the target question is NO, xy is NOT greater than 0 Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT Answer: A RELATED VIDEO FROM OUR COURSE _________________ Test confidently with gmatprepnow.com Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7462 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Is xy>0? [#permalink] ### Show Tags 12 Sep 2018, 02:38 => 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. We then recheck the question. Since even powers are always non-negative, we can ignore the even exponents. Condition 1) $$x^3y > 0$$ is equivalent to $$xy > 0$$, which is the question itself. Therefore, condition 1) is sufficient. Condition 2) $$x^2y>0$$ is equivalent to $$y > 0$$. It is not sufficient Therefore, A is the answer. Answer: A _________________ 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$149 for 3 month Online Course"
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Re: Is xy>0?   [#permalink] 12 Sep 2018, 02:38
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