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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 ## In the given figure, if AS = 10 cm, SN = 5 cm and TN = 8 cm, ##### This topic has 1 expert reply and 0 member replies ### Top Member ## In the given figure, if AS = 10 cm, SN = 5 cm and TN = 8 cm, ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult In the given figure, if AS = 10 cm, SN = 5 cm and TN = 8 cm, which of the following could be the positive difference between the maximum and minimum value of AT, if all the sides shown in the figure are positive integers? A) 16 B) 18 C) 20 D) 21 E) 23 OA C Source: e-GMAT ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15362 messages Followed by: 1866 members Upvotes: 13060 GMAT Score: 790 Top Reply BTGmoderatorDC wrote: In the given figure, if AS = 10 cm, SN = 5 cm and TN = 8 cm, which of the following could be the positive difference between the maximum and minimum value of AT, if all the sides shown in the figure are positive integers? A) 16 B) 18 C) 20 D) 21 E) 23 Third-side rule: The third side a triangle must be LESS THAN THE SUM OF and GREATER THAN THE DIFFERENCE OF the other two sides. Here, all the sides must be INTEGER values. In triangle ANS, AS=10 and NS=5. Thus, third side AN must be an integer value less than 10+5 = 15 and greater than 10-5 = 5, yielding the following options for AN: 6, 7, 8, 9, 10, 11, 12, 13, 14 In triangle ANT, TN=8. If AN=8, then third side AT must be an integer value less than 8+8=16 and greater than 8-8=0, making it possible that AT=1. Since AT must be a positive value, the minimum possible value for AT=1. If AN=14, then third side AT must be an integer value less than 14+8=22 and greater than 14-8=6, making it possible that AT=21. Since any other value for AN will yield a lower upper limit than the blue equation above, it is not possible that AN>21. Implication: The greatest possible value for AN=21. Thus: Maximum - minimum = 21-1 = 20. 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. • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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