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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 If set S consists of the numbers 1, 5, -2, 8, and n, is 0 &l This topic has 2 expert replies and 0 member replies Top Member If set S consists of the numbers 1, 5, -2, 8, and n, is 0 &l Timer 00:00 Your Answer A B C D E Global Stats Difficult If set S consists of the numbers 1, 5, -2, 8, and n, is 0 < n < 7 ? (1) The median of the numbers in S is less than 5. (2) The median of the numbers in S is greater than 1. OA C Source: GMAT Prep GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1125 messages Followed by: 29 members Upvotes: 59 BTGmoderatorDC wrote: If set S consists of the numbers 1, 5, -2, 8, and n, is 0 < n < 7 ? (1) The median of the numbers in S is less than 5. (2) The median of the numbers in S is greater than 1. Source: GMAT Prep $$S = \left\{ { - 2,1,5,8} \right\} \cup \left\{ n \right\}$$ $$?\,\,\,:\,\,\,0 < n < 7$$ $$\left( 1 \right)\,\,\,{\rm{Med}}\left( S \right) < 5\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,n = 0\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\,\,\,\,\,\,\,\,\left[ {Med\left( S \right) = {\rm{Med}}\left( {\left\{ { - 2,0,1,5,8} \right\}} \right) = 1} \right]\,\, \hfill \cr \,{\rm{Take}}\,\,n = 1\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\,\,\,\,\,\,\,\,\left[ {Med\left( S \right) = {\rm{Med}}\left( {\left\{ { - 2,1,1,5,8} \right\}} \right) = 1} \right]\,\,\, \hfill \cr} \right.\,$$ $$\left( 2 \right)\,\,\,{\rm{Med}}\left( S \right) > 1\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,n = 7\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\,\,\,\,\,\,\,\,\left[ {Med\left( S \right) = {\rm{Med}}\left( {\left\{ { - 2,1,5,7,8} \right\}} \right) = 5} \right]\,\, \hfill \cr \,{\rm{Take}}\,\,n = 6\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\,\,\,\,\,\,\,\,\left[ {Med\left( S \right) = {\rm{Med}}\left( {\left\{ { - 2,1,5,6,8} \right\}} \right) = 5} \right]\,\,\, \hfill \cr} \right.$$ $$\left( {1 + 2} \right)\,\,\,\,1 < {\rm{Med}}\left( S \right) < 5\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle$$ $$\left( * \right)\,\,\left\{ \matrix{ \,n \le 0\,\,\, \Rightarrow \,\,\,\,Med\left( S \right) = 1\,\,,\,\,\,\,{\rm{impossible}} \hfill \cr \,n \ge 7\,\,\, \Rightarrow \,\,\,\,Med\left( S \right) = 5\,\,,\,\,\,\,{\rm{impossible}} \hfill \cr} \right.\,\,\,\,\,\,$$ 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 GMAT Instructor Joined 22 Aug 2016 Posted: 1702 messages Followed by: 28 members Upvotes: 470 BTGmoderatorDC wrote: If set S consists of the numbers 1, 5, -2, 8, and n, is 0 < n < 7 ? (1) The median of the numbers in S is less than 5. (2) The median of the numbers in S is greater than 1. OA C Source: GMAT Prep Given: Set S: {-2, 1, 5, 8, n} Question; Is 0 < n < 7 ? Let's take each statement one by one. (1) The median of the numbers in S is less than 5. Case 1: Considering n â‰¤ 0. Say n = -3 => Set S: : {-3, -2, 1, 5, 8}. Median = 1 < 5. The answer is No. Case 2: Considering 0 < n < 7. Say n = 1 => Set S: : {-2, 1, 1, 5, 8}. Median = 1 < 5. The answer is Yes. No unique answer. Insufficient. (2) The median of the numbers in S is greater than 1. Case 1: Considering 0 < n < 7. Say n = 3 => Set S: : {-2, 1, 3, 5, 8}. Median = 3 > 1. The answer is Yes. Case 2: Considering n > 7. Say n = 10 => Set S: : {-2, 1, 5, 8, 10}. Median = 5 > 1. The answer is No. No unique answer. Insufficient. (1) and (2) together Considering the two statements, we have 1< Median < 5. Since 1< Median < 5, in the set, excluding n, {-2, 1, 5, 8}, we must have the middle-most term, n, such that 1 < n < 5; thus, the inequality 0 < n < 7 is true. Sufficient. The correct answer: C Hope this helps! -Jay _________________ Manhattan Review Locations: Manhattan Review Himayatnagar | GMAT Prep Hyderabad | GRE Prep Bangalore | Chennai GRE Coaching | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for 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 • 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 GMAT Exam Know how you'd score today for$0

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