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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 4x^2 + 9y^2 = 100 and (2x + 3y)^2 = 150, then what is... tagged by: BTGmoderatorLU ##### This topic has 1 expert reply and 0 member replies ### Top Member ## If 4x^2 + 9y^2 = 100 and (2x + 3y)^2 = 150, then what is... If $$4x^2+9y^2=100$$ and $$(2x+3y)^2=150$$ then what is the value of 6xy? $$(A)\ 5(2+\sqrt{6})$$ $$(B)\ 10\sqrt{6}$$ $$(C)\ 25$$ $$(D)\ 50$$ $$(E)\ 100$$ The OA is C. I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced. ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Quote: If $$4x^2+9y^2=100$$ and $$(2x+3y)^2=150$$ then what is the value of 6xy? $$(A)\ 5(2+\sqrt{6})$$ $$(B)\ 10\sqrt{6}$$ $$(C)\ 25$$ $$(D)\ 50$$ $$(E)\ 100$$ The OA is C. I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced. Hi LUANDATO, Let's take a look at your question. We will be solving this question using the following polynomial identity. $$\left(a+b\right)^2=a^2+b^2+2ab$$ We are given with: $$\left(2x+3y\right)^2=150$$ Evaluate the LHS using the polynomial identity (a+b)^2 = a^2 + b^2 + 2ab, we get: $$\left(2x\right)^2+\left(3y\right)^2+2\left(2x\right)\left(3y\right)=150$$ $$4x^2+9y^2+2\left(6xy\right)=150...(i)$$ Also it is given in the question that: $$4x^2+9y^2=100$$ Plugging in the value in eq(i), we get: $$100+2\left(6xy\right)=150$$ $$2\left(6xy\right)=150-100$$ $$2\left(6xy\right)=50$$ $$\left(6xy\right)=\frac{50}{2}$$ $$6xy=25$$ Therefore value of 6xy is 25. Option C is correct. Hope it helps. I am available if you'd like any follow up. _________________ 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. • Free Practice Test & Review How would you score if you took the GMAT 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 Trial & Practice Exam 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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