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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 Top Reply 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 _________________ 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 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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