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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 ## Twelve points are spaced evenly around a circle, lettered tagged by: AAPL ##### This topic has 3 expert replies and 0 member replies ### Top Member ## Twelve points are spaced evenly around a circle, lettered ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Magoosh Twelve points are spaced evenly around a circle, lettered from A to L. Let N be the total number of isosceles triangles, including equilateral triangles, that can be constructed from three of these points. A different orientation of the same lengths counts as a different triangle, because a different combination of points form the vertices. What is the value of N? A. 48 B. 52 C. 60 D. 72 E. 120 OA B. ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 2015 messages Followed by: 31 members Upvotes: 470 AAPL wrote: Magoosh Twelve points are spaced evenly around a circle, lettered from A to L. Let N be the total number of isosceles triangles, including equilateral triangles, that can be constructed from three of these points. A different orientation of the same lengths counts as a different triangle, because a different combination of points form the vertices. What is the value of N? A. 48 B. 52 C. 60 D. 72 E. 120 OA B. Let's draw a circle with 12 equally spaced points, named A through L. Originating from the point A, make all the possible isosceles triangles: âˆ†ABL, âˆ†ACK, âˆ†ADJ, âˆ†AEI, and âˆ†AFH So, there are 5 isosceles triangles with vertex A. Since there are 12 points, we have 12*5 = 60 isosceles triangles Note that âˆ†AEI is an equilateral triangle, thus, is counted thrice: once taking A as the vertex; once taking E as the vertex; and once taking I as the vertex, thus, we must remove 2 equilateral triangles. Since 3 points make 2 extra equilateral triangles, 12 points will make (12/3)*2 = 8 equilateral triangles. Thus, the actual number of isosceles triangles, incl. equilateral triangles = 60 - 8 = 52 The correct answer: B Hope this helps! -Jay _________________ Manhattan Review Locations: Manhattan Review Jayanagar | GMAT Prep Jayanagar | GRE Prep Madhapur | Kukatpally GRE Coaching | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE 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 • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep 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 • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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