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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## If x^2 + xy - 32 = 0, and x and y are integers, then y . . . tagged by: VJesus12 ##### This topic has 1 expert reply and 1 member reply ## If x^2 + xy - 32 = 0, and x and y are integers, then y . . . If x^2 + xy - 32 = 0, and x and y are integers, then y could equal each of the following except? A) -31 B) -14 C) 2 D) 4 E) 14 The OA is C. How can I find the value of y? Should I use the quadratic equation? I am confused. ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Top Reply Hello Vjesus12. Let's take a look at your question. If $$x^2+xy-32=0$$ then we could rewrite this as follows: $$x^2+xy-32=0\ \leftrightarrow\ \left(x-a\right)\left(x-b\right)=0$$ where "a" and "b" satisfy $$a+b=y\ \ \ \ \ and\ \ \ \ \ \ a\cdot b=-32.$$ The possible values for "a" and "b" are: $$\left(a,b\right)=(1,-32);\ (2,-16);\ (4,-8);(-1,32);(-2,16);(-4,8).$$ So, the possible sums a+b are: $$-31,\ -14,\ \ -4,\ \ 31,\ \ 14,\ \ \ 4.$$ So, the correct answer is option C. I hope this explanation can help you. I'm available if you'd like a follow up. Regards. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now. Master | Next Rank: 500 Posts Joined 29 Nov 2017 Posted: 100 messages Upvotes: 14 VJesus12 wrote: If x^2 + xy - 32 = 0, and x and y are integers, then y could equal each of the following except? A) -31 B) -14 C) 2 D) 4 E) 14 The OA is C. How can I find the value of y? Should I use the quadratic equation? I am confused. y should be the sum of two factors of -32 factors could be 1. -16 and 2 their sum is -14 2. -8 and 4 ............ -4 3. -4 and 8 ............. +4 4. -16 and 2 ............. -14 5 -1 and 32............. +31 6 -32 and 1...............-31 thus there are no two factors of -32 whose sum is 2 hence C is the correct answer. • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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