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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? tagged by: Vincen ##### This topic has 2 expert replies and 0 member replies ## 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 The OA is the option B. How can I show that all three statements are true? I am interested in knowing how can I solve this PS question. Experts, I wait for your help. ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 1607 messages Followed by: 27 members Upvotes: 470 Vincen wrote: 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 The OA is the option B. How can I show that all three statements are true? I am interested in knowing how can I solve this PS question. Experts, I wait for your help. Let us first take statement (III). If (III) is correct, then (I) and (II) are true as they are the sub-sets of (III). Statement (III): The average (arithmetic mean) of five consecutive integers is equal to the average of the largest and smallest of them. Say the five consecutive integers are -1, 0, 1, 2, & 3. The average (arithmetic mean) of five consecutive integers = 1 and the average of the largest and smallest = (-1 + 3)/2 = 1. (III) is true. Thus, all the statements are true. You may take few examples to get this better. For example, {-2, -1, 0, 1, & 2}; All positive: {3, 4, 5, 6, 7, & 8}; All negative: {-10, -9, -8, -7, & -6}. The correct answer: B Hope this helps! -Jay _________________ Manhattan Review GMAT Prep Locations: New York | Jakarta | Nanjing | Berlin | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 1607 messages Followed by: 27 members Upvotes: 470 Vincen wrote: 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 The OA is the option B. How can I show that all three statements are true? I am interested in knowing how can I solve this PS question. Experts, I wait for your help. Let's take an Algebraic route to understand this. Say the five consecutive integers are x, (x + 1), (x + 2), (x + 3), & (x + 4), where they can be negative, 0, and positive. The average (arithmetic mean) of five consecutive integers = [x + (x + 1) + (x + 2) + (x + 3) + (x + 4)]/5 = (5x + 10)/5 = x + 2 The average of the largest and smallest integers = [x + (x + 4)]/2 = (2x + 4)/2 = x + 2 We see that the results are equal. This is a generic case and is applicable to all the three statements. Thus, all the three statements are true. The correct answer: B Hope this helps! -Jay _________________ Manhattan Review GMAT Prep Locations: New York | Jakarta | Nanjing | Berlin | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE 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 • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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