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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 ## The number of diagonals of two different regular... tagged by: BTGmoderatorLU ##### This topic has 1 expert reply and 0 member replies ### Top Member ## The number of diagonals of two different regular... The number of diagonals of two different regular polygons each consists of two identical digits. The square root of the sum of the sides of both polygons equals the number of sides of a A. nonagon B. hendecagon C. heptagon D. pentagon E. triskaidecagon The OA is D. Experts, can you help me with this PS question please? I don't understand it. ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Dear LUANDATO. I understand you because this is a hard question. But I will try to give you a good explanation. First, the number of diagonals of a polygon is $$D=\frac{\left(n-3\right)\cdot n}{2}$$ where n is the number of sides. Now, we have that the number of diagonals of each polygon is {11, 22, 33, 44, 55, 66, 77, 88, 99}. So, we can set the equations $$\frac{\left(n-3\right)\cdot n}{2}=11,\ 22,\ 33,\ .\ .\ .\ ,\ 99.$$ The only solutions we are interested in are those where n is a positive integer. The unique numbers of diagonals that satisfy this are 44 and 77. Let's prove it: $$\frac{\left(n-3\right)\cdot n}{2}=44\ <=>\ n^2-3n=88\ <=>\ n^2-3n-88=0,$$ The solutions of the quadratic equation above are n=11 and n=-8. We have to select n=11. $$\frac{\left(n-3\right)\cdot n}{2}=77\ <=>\ n^2-3n=154\ <=>\ n^2-3n-154=0,$$ The solutions of the quadratic equation above are n=14 and n=-11. We have to select n=14. So, we have two regular polygons, one has 11 sides and the other has 14 sides. Finally, the square root of the sum of the sides of both polygons is $$\sqrt{11+14}=\sqrt{25}=5.$$ And this is the number of sides of a Petangon. So, the answer is option D. I hope this can help you. I'm available if you'd like any 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. • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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