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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 If three different integers are selected at random from the tagged by: VJesus12 This topic has 1 expert reply and 0 member replies Top Member If three different integers are selected at random from the Timer 00:00 Your Answer A B C D E Global Stats Difficult If three different integers are selected at random from the integers 1 through 8, what is the probability that the three selected integers can be the side lengths of a triangle? A. 11/28 B. 27/56 C. 1/2 D. 4/7 E. 5/8 OA=A Source: Manhattan GMAT GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2811 messages Followed by: 18 members Upvotes: 43 VJesus12 wrote: If three different integers are selected at random from the integers 1 through 8, what is the probability that the three selected integers can be the side lengths of a triangle? A. 11/28 B. 27/56 C. 1/2 D. 4/7 E. 5/8 OA=A Source: Manhattan GMAT In order for the three numbers selected to be the side lengths of a triangle, we need the sum of the two smallest numbers to be greater than the largest number. Thus, we have: 2 + 3 > 4, 2 + 4 > 5, 2 + 5 > 6, 2 + 6 > 7, 2 + 7 > 8 --- (5 instances if the smallest number is 2) 3 + 4 > 5, 3 + 4 > 6, 3 + 5 > 6, 3 + 5 > 7, 3 + 6 > 7, 3 + 6 > 8, 3 + 7 > 8 --- (7 instances if the smallest is 3) 4 + 5 > 6, 4 + 5 > 7, 4 + 5 > 8, 4 + 6 > 7, 4 + 6 > 8, 4 + 7 > 8 --- (6 instances if the smallest is 4) 5 + 6 > 7, 5 + 6 > 8, 5 + 7 > 8 --- (3 instances if the smallest is 5) 6 + 7 > 8 --- (1 instance if the smallest is 6) Therefore, there are a total of 5 + 7 + 6 + 3 + 1 = 22 sets of three distinct numbers that can be selected from the integers 1 through 8 that can be the side lengths of a triangle. Since the total number of ways of selecting 3 numbers from 8 is 8C3 = (8 x 7 x 6)/(3 x 2) = 56, the probability that the 3 numbers can be the side lengths of a triangle is 22/56 = 11/28. Answer: A • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE 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 • Award-winning private GMAT tutoring Register now and save up to$200

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