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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 A set of number has an average of 50. If the largest element This topic has 4 expert replies and 1 member reply Top Member A set of number has an average of 50. If the largest element Timer 00:00 Your Answer A B C D E Global Stats Difficult A set of numbers has an average of 50. If the largest element is 4 greater than 3 times the smallest element, which of the following values cannot be in the set? (A) 85 (B) 90 (C) 123 (D) 150 (E) 155 OA E Source: Veritas Prep GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 1776 messages Followed by: 14 members Upvotes: 43 Top Reply BTGmoderatorDC wrote: A set of numbers has an average of 50. If the largest element is 4 greater than 3 times the smallest element, which of the following values cannot be in the set? (A) 85 (B) 90 (C) 123 (D) 150 (E) 155 We can let the smallest element = n and the largest = 3n + 4. Since the average is 50, then the smallest element, n, must be less than 50. Since n < 50, the largest element, 3n + 4, must be less than 3(50) + 4 = 154. We see that all the numbers in the choices are less than 154 except 155. Thus, 155 canâ€™t be in the set. Answer: E _________________ Scott Woodbury-Stewart Founder and CEO GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 964 messages Followed by: 27 members Upvotes: 59 Top Reply BTGmoderatorDC wrote: A set of numbers has an average of 50. If the largest element is 4 greater than 3 times the smallest element, which of the following values cannot be in the set? (A) 85 (B) 90 (C) 123 (D) 150 (E) 155 Source: Veritas Prep $?\,\,\,:\,\,\,{\text{not}}\,\,{\text{a}}\,\,{\text{member}}$ LetÂ´s call the smallest number x, so that the largest number is 3x+4 and we know each element of the set must belong to the [x, 3x+4] interval. From the fact that 50 is the average of all the elements of this set, and not all of them are equal (*), we have: $x < 50 < 3x + 4$ (*) If x = 3x+4 and we have all numbers equal to -2, their average would not be 50. Hence: $x < 50\,\,\,\, \Rightarrow \,\,\,\,{\text{largest}} = 3x + 4 < 3 \cdot 50 + 4 = 154\,\,\,\,\mathop \Rightarrow \limits^{{\text{alternatives}}\,!} \,\,\,? = 155$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or https://GMATH.com.br (Portuguese version) Course release PROMO : finish our test drive till 30/Dec with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount! GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12412 messages Followed by: 1244 members Upvotes: 5254 GMAT Score: 770 BTGmoderatorDC wrote: A set of numbers has an average of 50. If the largest element is 4 greater than 3 times the smallest element, which of the following values cannot be in the set? (A) 85 (B) 90 (C) 123 (D) 150 (E) 155 OA E Source: Veritas Prep The largest element is 4 greater than 3 times the smallest element Let x = the smallest number in the set. So, 3x + 4 = the largest number in the set. So, the set looks something like this {x, ?, ?, . . . . ?, 3x+4} The key to this question is that the AVERAGE = 50 Since all of the answer choices are greater than 50, there's a good likelihood that the correct answer will be the biggest number. So, let's start by checking answer choice E (E) 155 There are two possibilities here: i) 155 is the biggest number in the set ii) 155 is NOT the biggest number in the set If 155 IS the biggest number in the set, we can use the given information to determine the smallest number in the set That is, 3x +4 = 155 So, 3x = 152 So, x = 152/3 = 50 2/3 Hmmmm, the "smallest value" is GREATER than 50 (the average value on the set) This is impossible; if all of the values in the set are greater than 50, the average cannot equal 50. So, 155 CANNOT be the LARGEST number in the set (case i). This also means that 155 CANNOT be in the set at all (case ii), because if 155 is NOT the biggest number, then the biggest number is EVEN BIGGER, which would also make it impossible for the average to be 50. Answer: E 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! Top Member Legendary Member Joined 29 Oct 2017 Posted: 677 messages Followed by: 4 members Let L the largest and S the smallest of the numbers L = 3S + 4, given If 155 is a number between L and S, then L > 155. when S = 51, L = 157 when S = 50, L = 154 If the smallest number is equal to the average of all numbers, then all the numbers will be equal to 50. That means L cannot be greater than or equal to 154. L has to be less than 154. Therefore, 155 cannot be in the set. E is the correct option. GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 14922 messages Followed by: 1855 members Upvotes: 13060 GMAT Score: 790 BTGmoderatorDC wrote: A set of numbers has an average of 50. If the largest element is 4 greater than 3 times the smallest element, which of the following values cannot be in the set? (A) 85 (B) 90 (C) 123 (D) 150 (E) 155 Let S = the smallest number of L = the largest number. Since the largest number is 4 more than 3 times the smallest number, we get: L = 3S + 4 L-4 = 3S (L-4)/3 = S. Since the average is 50 -- and the numbers are not all the same -- S must be LESS THAN 50, while L must be greater than 50. Substituting S = (L-4)/3 into S < 50, we get; (L-4)/3 < 50 L-4 < 150 L < 154. Since the largest number must be less than 154, option E -- 155 -- cannot be in the set. The correct answer is E. _________________ 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! 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