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# If x + y > 0, is xy^2 + x^2y > 0?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 9277
GMAT 1: 760 Q51 V42
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If x + y > 0, is xy^2 + x^2y > 0?  [#permalink]

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12 Mar 2018, 00:01
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25% (medium)

Question Stats:

71% (01:20) correct 29% (02:01) wrong based on 139 sessions

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[GMAT math practice question]

If $$x + y > 0$$, is $$xy^2 + x^2y > 0?$$

$$1) x > y$$
$$2) xy > 1$$

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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: 21 Aug 2013 Posts: 1355 Location: India Re: If x + y > 0, is xy^2 + x^2y > 0? [#permalink] ### Show Tags 12 Mar 2018, 01:12 MathRevolution wrote: [GMAT math practice question] If $$x + y > 0$$, is $$xy^2 + x^2y > 0?$$ $$1) x > y$$ $$2) xy > 1$$ xy^2 + x^2y can also be written as: xy*(x+y). So the question asks whether xy*(x+y) is > 0 or not? We are given that x+y is > 0 so all we need to know is whether xy is > 0 or not. Statement 1: x > y But both could be positive, both could be negative or x positive and y negative. So we cannot say what the sign of xy will be. Not suffcient. Statement 2: xy > 1 If xy >1, then definitely xy> 0. Sufficient. Hence B answer GMAT Club Legend Joined: 11 Sep 2015 Posts: 4999 Location: Canada GMAT 1: 770 Q49 V46 Re: If x + y > 0, is xy^2 + x^2y > 0? [#permalink] ### Show Tags 12 Mar 2018, 06:30 2 Top Contributor MathRevolution wrote: [GMAT math practice question] If $$x + y > 0$$, is $$xy^2 + x^2y > 0?$$ $$1) x > y$$ $$2) xy > 1$$ Given: x + y > 0 Target question: Is xy² + x²y > 0 This is a good candidate for rephrasing the target question. Aside: Below is a video with tips on rephrasing the target question Take the inequality: xy² + x²y > 0 Factor to get: xy(y + x)> 0 Since it is GIVEN than x + y > 0, we can write: xy(SOME POSITIVE NUMBER)> 0 For this inequality to be true, it must be the case that xy > 0 So, we can REPHRASE our target question.... REPHRASED target question: Is xy > 0? Statement 1: x > y There are several values of x and y that satisfy statement 1. Here are two: Case a: x = 2 and y = 1. In this case, xy = 2. So, the answer to the REPHRASED target question is YES, xy IS greater than zero Case b: x = 2 and y = -1. In this case, xy = -2. So, the answer to the REPHRASED target question is NO, xy is NOT greater than zero Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: xy > 1 If xy>1, then it MUST be the case that xy > 0 So, the answer to the REPHRASED target question is YES, xy IS greater than zero Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT Answer: B RELATED VIDEO _________________ If you enjoy my solutions, you'll love my GMAT prep course. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 9277 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If x + y > 0, is xy^2 + x^2y > 0? [#permalink] ### Show Tags 13 Mar 2018, 23:22 => 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. Question: $$xy^2 + x^2y > 0$$ $$=> xy(x+y) > 0$$ $$=> xy > 0$$, since $$x + y > 0$$ So, the question asks if $$xy > 0.$$ Since $$xy > 1 > 0$$ can be derived from condition 2), it is sufficient. Condition 1) gives us no information about the sign of $$xy$$. Therefore, B is the answer. Answer: B _________________ 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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If x + y > 0, is xy^2 + x^2y > 0?  [#permalink]

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24 Dec 2019, 05:45
amanvermagmat wrote:
MathRevolution wrote:
[GMAT math practice question]

If $$x + y > 0$$, is $$xy^2 + x^2y > 0?$$

$$1) x > y$$
$$2) xy > 1$$

xy^2 + x^2y can also be written as: xy*(x+y).
So the question asks whether xy*(x+y) is > 0 or not?
We are given that x+y is > 0 so all we need to know is whether xy is > 0 or not.

Statement 1:
x > y
But both could be positive, both could be negative or x positive and y negative. So we cannot say what the sign of xy will be. Not suffcient.

Statement 2:

xy > 1
If xy >1, then definitely xy> 0. Sufficient.

Hi amanvermagmat,

I do not feel that both negative (highlighted above) would be valid. Both negative will violate the inequality $$x+y>0$$ provided in the question stem. Let me know your thoughts!

Warm Regards,
Pritishd
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If x + y > 0, is xy^2 + x^2y > 0?   [#permalink] 24 Dec 2019, 05:45