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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 ## Are all of the terms in Set A equal? ##### This topic has 2 expert replies and 0 member replies ### Top Member ## Are all of the terms in Set A equal? ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Are all of the terms in Set A equal? (1) The sum of all 14 terms in Set A is 98. (2) The sum of any 3 terms in Set A is 21. OA C Source: Veritas Prep ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12563 messages Followed by: 1245 members Upvotes: 5254 GMAT Score: 770 Top Reply BTGmoderatorDC wrote: Are all of the terms in Set A equal? (1) The sum of all 14 terms in Set A is 98. (2) The sum of any 3 terms in Set A is 21. Target question: Are all of the terms in Set A equal? Statement 1: The sum of all 14 terms in Set A is 98 There are several possible scenarios that satisfy this statement. Here are two. Case a: Set A = {7,7,7,7,7,7,7,7,7,7,7,7,7,7} in which case all of the numbers ARE equal Case b: Set A = {0,0,0,0,0,0,0,0,0,0,0,0,0,98}, in which case all of the numbers are NOT equal Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: The sum of any 3 terms in Set A is 21 Under most conditions this statement WOULD be sufficient. However, if set A has only 3 terms in total, then the statement is NOT sufficient. To see what I mean, consider these two possible scenarios that satisfy statement 2: Case a: Set A = {7,7,7} in which case all of the numbers ARE equal Case b: Set A = {0, 0, 21}, in which case all of the numbers are NOT equal Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT Statements 1 and 2 combined The combined statements ARE sufficient. Here's why: Let's let a,b,c and d be four of the 14 numbers in set A. From statement 2, we know that a + b + c = 21 Notice that if I replace ANY of these three values (a,b or c) with d, the sum must still be 21 (according to statement 2) This tells us that a, b and c must all equal d. I can use a similar approach to show that all of the other numbers must also equal d. This means that all of the numbers in set A must be equal. Since we can answer the target question with certainty, the COMBINED statements are SUFFICIENT Answer: C Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15029 messages Followed by: 1859 members Upvotes: 13060 GMAT Score: 790 Top Reply I posted a solution to a very similar problem here: https://www.beatthegmat.com/from-og-12-t73239.html _________________ 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. • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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