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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 ## Which of the following is always true ##### This topic has 1 expert reply and 0 member replies ### Top Member ## Which of the following is always true Which of the following is always true? (I) The average (arithmetic mean) of five negative consecutive integers is equal to the average of the largest and smallest of them. (II) The average (arithmetic mean) of four positive consecutive integers is equal to the average of the largest and smallest of them. (III) The average (arithmetic mean) of five consecutive integers is equal to the average of the largest and smallest of them. A. I and III B. I, II and III C. II D. I and II E. None Can some experts explain how to find the best Option? OA B ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Top Reply Quote: Which of the following is always true? (I) The average (arithmetic mean) of five negative consecutive integers is equal to the average of the largest and smallest of them. (II) The average (arithmetic mean) of four positive consecutive integers is equal to the average of the largest and smallest of them. (III) The average (arithmetic mean) of five consecutive integers is equal to the average of the largest and smallest of them. A. I and III B. I, II and III C. II D. I and II E. None Hi lheiannie07, Let's take a look at your question. We will take some random values to check each statement. Let's start from statement (I). Let 5 negative consecutive integers be -1, -2, -3, -4, -5. Average of five numbers = (-1-2-3-4-5)/5 = -15/5 = -3 Average of largest and smallest number = (-1-5) / 2 = -6/2 =-3 It means Statement (I) is correct. We will now check statement (II). Let 4 positive consecutive integers be 1, 2, 3, 4. Average of four numbers = (1+2+3+4)/4 = 10/4 = 2.5 Average of largest and smallest number = (1+4) / 2 = 5/2 =2.5 Hence, statement (II) is also true. Now check statement (III). Let 5 consecutive integers be -1, 0, 1, 2, 3. Average of five numbers = (-1+0+1+2+3)/5 = 5/5 = 1 Average of largest and smallest number = (-1+3) / 2 = 2/2 =1 Hence, statement (III) is also true. Therefore, option B is correct, because statement I, II and III are true. Hope it helps. I am available if you'd like any follow up. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now. • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • 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 • 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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