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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 ## S is a set of points in the plane. How many distinct ##### This topic has 1 expert reply and 0 member replies ### Top Member ## S is a set of points in the plane. How many distinct ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult S is a set of points in the plane. How many distinct triangles can be drawn that have three of the points in S as vertices? (1) The number of distinct points in S is 5. (2) No three of the points in S are collinear. OA C Source: Official Guide ### GMAT/MBA Expert GMAT Instructor Joined 02 Jun 2008 Posted: 2418 messages Followed by: 349 members Upvotes: 1090 GMAT Score: 780 We clearly need to know how many points we have, since if we have, say, only 2 points, we can't draw any triangles, but if we have many points that aren't all in a line, we can draw at least one triangle. So Statement 1 is indispensable. But knowing we have exactly 5 points is not sufficient, since if all of the points lie on a single line, connecting three of them will make a line, not a triangle. Using both statements, we know we have 5 points, and picking any 3 of them will always let us draw a triangle, since no 3 points ever form a straight line. So the number of triangles we can make is equal to the number of sets of 3 we can pick from a set of 5. Since this is DS, you don't need to even know how to calculate that, but that number equals (5)(4)(3)/3! = 10, and the answer is C. _________________ If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com • FREE GMAT Exam Know how you'd score today for$0

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