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# x and y are non-negative integers. If xy+2x+3y=0, then y=?

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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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x and y are non-negative integers. If xy+2x+3y=0, then y=?  [#permalink]

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26 Oct 2018, 00:55
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15% (low)

Question Stats:

81% (01:26) correct 19% (02:24) wrong based on 92 sessions

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[Math Revolution GMAT math practice question]

$$x$$ and $$y$$ are non-negative integers. If $$xy+2x+3y=0$$, then $$y=?$$

$$A. 0$$
$$B. 1$$
$$C. 2$$
$$D. 3$$
$$E. 4$$

_________________
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" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" CEO Status: GMATINSIGHT Tutor Joined: 08 Jul 2010 Posts: 2977 Location: India GMAT: INSIGHT Schools: Darden '21 WE: Education (Education) Re: x and y are non-negative integers. If xy+2x+3y=0, then y=? [#permalink] ### Show Tags 26 Oct 2018, 01:02 MathRevolution wrote: [Math Revolution GMAT math practice question] $$x$$ and $$y$$ are non-negative integers. If $$xy+2x+3y=0$$, then $$y=?$$ $$A. 0$$ $$B. 1$$ $$C. 2$$ $$D. 3$$ $$E. 4$$ $$xy+2x+3y=0$$ i.e. $$xy+2x+3y+6-6 =0$$ i.e. $$x(y+2)+3(y+2)-6 =0$$ i.e. $$(y+2)*(x+3) =6$$ But 2*3 = 6 i.e. y = 0 and x = 0 is the only possible case we get because x and y are NON-NEGATIVE integers Answer: Option A _________________ Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION Senior Manager Joined: 07 Jul 2012 Posts: 367 Location: India Concentration: Finance, Accounting GPA: 3.5 Re: x and y are non-negative integers. If xy+2x+3y=0, then y=? [#permalink] ### Show Tags 26 Oct 2018, 03:02 xy+2x+3y=0 is possible only when both x and y are equal to 0. So Answer must be A. _________________ Kindly hit kudos if my post helps! Senior Manager Joined: 13 Jan 2018 Posts: 342 Location: India Concentration: Operations, General Management GMAT 1: 580 Q47 V23 GMAT 2: 640 Q49 V27 GPA: 4 WE: Consulting (Consulting) Re: x and y are non-negative integers. If xy+2x+3y=0, then y=? [#permalink] ### Show Tags 26 Oct 2018, 03:27 By carefully observing the equation, we can say that for all values of $$y\geq1$$ the RHS part fo the equation will be a negative value. So the only value that satisfies the equation is $$Zero$$. OPTION : A _________________ ____________________________ Regards, Chaitanya +1 Kudos if you like my explanation!!! VP Joined: 31 Oct 2013 Posts: 1469 Concentration: Accounting, Finance GPA: 3.68 WE: Analyst (Accounting) x and y are non-negative integers. If xy+2x+3y=0, then y=? [#permalink] ### Show Tags 26 Oct 2018, 05:13 MathRevolution wrote: [Math Revolution GMAT math practice question] $$x$$ and $$y$$ are non-negative integers. If $$xy+2x+3y=0$$, then $$y=?$$ $$A. 0$$ $$B. 1$$ $$C. 2$$ $$D. 3$$ $$E. 4$$ whenever the the phrase " non-negative" is used , pay special attention to Zero. It's test makers silent trick. xy + 2x + 3y = 0 How? If x = 0 xy = 0 2x = 0 but still we have 3y. 2 variables in this question. say y = 0 xy = 0 3y = 0 but what's about 2x. So, both x and y are 0 as ultimate result is 0. Number plugging is helpful here. Back solving is also useful. But remember that ultimate result is 0 and u have 2 variables. The best answer is A. Senior Manager Joined: 04 Aug 2010 Posts: 474 Schools: Dartmouth College Re: x and y are non-negative integers. If xy+2x+3y=0, then y=? [#permalink] ### Show Tags 26 Oct 2018, 05:48 MathRevolution wrote: [Math Revolution GMAT math practice question] $$x$$ and $$y$$ are non-negative integers. If $$xy+2x+3y=0$$, then $$y=?$$ $$A. 0$$ $$B. 1$$ $$C. 2$$ $$D. 3$$ $$E. 4$$ NONNEGATIVE implies that we should test ZERO. Let x=0. Substituting x=0 into xy + 2x + 3y = 0, we get: 0*y + 2*0 + 3y = 0 3y = 0 y = 0 _________________ GMAT and GRE Tutor Over 1800 followers GMATGuruNY@gmail.com New York, NY If you find one of my posts helpful, please take a moment to click on the "Kudos" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. GMAT Club Legend Joined: 18 Aug 2017 Posts: 5009 Location: India Concentration: Sustainability, Marketing GPA: 4 WE: Marketing (Energy and Utilities) Re: x and y are non-negative integers. If xy+2x+3y=0, then y=? [#permalink] ### Show Tags 26 Oct 2018, 23:57 xx and yy are non-negative integers. If xy+2x+3y=0xy+2x+3y=0, then y=?y=? A.0A.0 B.1B.1 C.2C.2 D.3D.3 E.4 Plug in for values of y only at y=0 we get is a even +ve integer value which is x=0 Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8011 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: x and y are non-negative integers. If xy+2x+3y=0, then y=? [#permalink] ### Show Tags 28 Oct 2018, 19:19 => $$xy+2x+3y=0$$ $$=> xy+2x+3y+6=6$$ $$=> (x+3)(y+2)=6$$ Since $$x$$ and $$y$$ are integers, $$x+3$$ and $$y+2$$ are integers. The possible pairs $$(x+3,y+2)$$ are as follows: $$( x+3, y+2 ) = (1,6), (2,3), (3,2), (6,1), (-1,-6), (-2,-3), (-3,-2)$$ and $$(-6,-1).$$ The corresponding pairs $$(x,y)$$ are: $$(x,y) = (-2,4), (-1,2), (0,0), (3,-1), (-4,-8), (-5,-5), (-6,-4)$$ and $$(-9,-3).$$ The unique pair with non-negative $$x$$ and $$y$$ is $$(x,y)=(0,0).$$ Thus, $$y = 0.$$ Therefore, the answer is A. 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$79 for 1 month Online Course"
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Re: x and y are non-negative integers. If xy+2x+3y=0, then y=?  [#permalink]

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08 Nov 2018, 19:38
y(x+3) + 2x=0
y=-2x/(x+3)

only way y can be non-negative is if y=0
Re: x and y are non-negative integers. If xy+2x+3y=0, then y=?   [#permalink] 08 Nov 2018, 19:38
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