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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 ## Set S contains nine distinct points in the coordinate plane. tagged by: BTGmoderatorLU ##### This topic has 3 expert replies and 0 member replies ### Top Member ## Set S contains nine distinct points in the coordinate plane. ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Source: Veritas Prep Set S contains nine distinct points in the coordinate plane. If exactly five of the points lie on the x-axis, and if no other set of three points in S is collinear, how many triangles can be formed by taking points in S as vertices? A. 56 B. 70 C. 74 D. 79 E. 84 The OA is C. ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15348 messages Followed by: 1864 members Upvotes: 13060 GMAT Score: 790 BTGmoderatorLU wrote: Source: Veritas Prep Set S contains nine distinct points in the coordinate plane. If exactly five of the points lie on the x-axis, and if no other set of three points in S is collinear, how many triangles can be formed by taking points in S as vertices? A. 56 B. 70 C. 74 D. 79 E. 84 To form a triangle, we must select 3 points such that at most 2 are collinear. Case 1: Select 3 points not on the x-axis From the 4 points not on the x-axis, the number of ways to choose 3 = 4C3 = (4*3*2)/(3*2*1) = 4. Case 2: Select 1 point on the x-axis and two points not on the x-axis From the 5 points on the x-axis, the number of ways to choose 1 = 5C1 = 5. From the 4 points not on the x-axis, the number of ways to choose 2 = 4C2 = (4*3)/(2*1) = 6. To combine these options, we multiply: 5*6 = 30. Case 3: Select 2 points on the x-axis and 1 point not on the x-axis From the 5 points on the x-axis, the number of ways to choose 2 = 5C2 = (5*4)/(2*1) = 10. From the 4 points not on the x-axis, the number of ways to choose 1 = 4C1 = 4. To combine these options, we multiply: 10*4 = 40. Total ways = Case 1 + Case 2 + Case 3 = 4 + 30 + 40 = 74. The correct answer is C. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 BTGmoderatorLU wrote: Source: Veritas Prep Set S contains nine distinct points in the coordinate plane. If exactly five of the points lie on the x-axis, and if no other set of three points in S is collinear, how many triangles can be formed by taking points in S as vertices? A. 56 B. 70 C. 74 D. 79 E. 84 $? = C\left( {9,3} \right) - C\left( {5,3} \right) = \frac{{9 \cdot 8 \cdot 7}}{{3 \cdot 2}} - \frac{{5 \cdot 4}}{2} = 12 \cdot 7 - 10 = 74$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ 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 25 Apr 2015 Posted: 2791 messages Followed by: 18 members Upvotes: 43 BTGmoderatorLU wrote: Source: Veritas Prep Set S contains nine distinct points in the coordinate plane. If exactly five of the points lie on the x-axis, and if no other set of three points in S is collinear, how many triangles can be formed by taking points in S as vertices? A. 56 B. 70 C. 74 D. 79 E. 84 We have 5 (collinear) points that are on the x-axis and 4 points that are not on the x-axis. Since no set of three points in S is collinear except those on the x-axis, we can have the following 3 cases forming a triangle: 1) two points on the x-axis and one point not on the x-axis, 2) one point on the x-axis and two points not on the x-axis, and 3) three points not on the x-axis. Case 1: Two points on the x-axis and one point not on the x-axis There are 5C2 x 4C1 = 10 x 4 = 40 such triangles in this case. Case 2: one point on the x-axis and two points not on the x-axis There are 5C1 x 4C2 = 5 x 6 = 30 such triangles in this case. Case 3: Three points not on the x-axis There are 4C3 = 4 such triangles in this case. Therefore, there are 40 + 30 + 4 = 74 triangles that can be formed. Answer: C _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews • FREE GMAT Exam Know how you'd score today for$0

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