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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 15 different integers has median of 25 and a range ##### This topic has 3 expert replies and 0 member replies ### Top Member ## A set of 15 different integers has median of 25 and a range ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult A set of 15 different integers has median of 25 and a range of 25. What is greatest possible integer that could be in this set? A. 32 B. 37 C. 40 D. 43 E. 50 OA D Source: GMAT Prep ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1273 messages Followed by: 29 members Upvotes: 59 BTGmoderatorDC wrote: A set of 15 different integers has median of 25 and a range of 25. What is greatest possible integer that could be in this set? A. 32 B. 37 C. 40 D. 43 E. 50 Source: GMAT Prep WLOG (without loss of generality) we may assume that: $$a = {x_1} < {x_2} < \ldots < {x_7} < {x_8} = 25 < {x_9} < \ldots < {x_{14}} < {x_{15}} = a + 25\,\,\,\,\,{\text{ints}}$$ Considering this powerful structure, the problem is trivialized: $$?\,\, = \,\,\left( {a + 25} \right)\,\,\max \,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,a\,\,\max$$ $$a\,\,\max \,\,\,\,\, \Leftrightarrow \,\,\,\,\left( {{x_7},{x_6},{x_5},{x_4},{x_3},{x_2},{x_1} = a} \right) = \left( {24,23,22,21,20,19,18} \right)\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,a = 18\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,a + 25 = 43$$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10071 messages Followed by: 494 members Upvotes: 2867 GMAT Score: 800 Hi All, When it comes to maximizing or minimizing a value in a group of numbers, you have to think about what the other numbers would need to be to accomplish your goal. Here, we have a group of 15 DISTINCT (meaning DIFFERENT) integers with a median of 25 and a RANGE of 25. That range will dictate how large the largest value can be. With a median of 25, we know that 7 numbers are LESS than 25 and 7 numbers are GREATER than 25: _ _ _ _ _ _ _ 25 _ _ _ _ _ _ _ To maximize the largest value, we need to maximize the smallest value. Here's how we can do it: 18 19 20 21 22 23 24 25 _ _ _ _ _ _ _ With 18 as the smallest value, and a range of 25, the largest value would be 43. Final Answer: D GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2006 messages Followed by: 14 members Upvotes: 43 BTGmoderatorDC wrote: A set of 15 different integers has median of 25 and a range of 25. What is greatest possible integer that could be in this set? A. 32 B. 37 C. 40 D. 43 E. 50 OA D Source: GMAT Prep We are given that there are 15 different integers in a set with a median of 25 and a range of 25. We must determine the greatest possible integer that could be in the set. To determine this integer, we need to first determine the greatest possible value of the least integer from the set. Since there are 15 total integers in the set, there are 7 integers before the median and 7 integers after the median if we list them in order. We must also keep in mind that each integer is different. We want the smallest integer in the set to be as large as possible. Thus, the first 8 integers, including the median, are the following: 18, 19, 20, 21, 22, 23, 24, 25 Since the range of this set is 25, the greatest number in this set must be 25 more than the smallest integer in the set, and thus the largest number in the set is 18 + 25 = 43. Answer: D _________________ Scott Woodbury-Stewart Founder and CEO • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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