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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 ## Set S contains consecutive natural numbers from 1 to 100, in tagged by: AAPL ##### This topic has 3 expert replies and 0 member replies ### Top Member ## Set S contains consecutive natural numbers from 1 to 100, in ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult e-GMAT Set S contains consecutive natural numbers from 1 to 100, in increasing order. S_1 and S_2 denote the sum of first n even numbers and last n odd numbers of set S, respectively. What is the value of n, if S_1:S_2 = 16:85? A. 5 B. 10 C. 15 D. 20 E. 25 OA C. ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15348 messages Followed by: 1864 members Upvotes: 13060 GMAT Score: 790 AAPL wrote: e-GMAT Set S contains consecutive natural numbers from 1 to 100, in increasing order. S_1 and S_2 denote the sum of first n even numbers and last n odd numbers of set S, respectively. What is the value of n, if S_1:S_2 = 16:85? A. 5 B. 10 C. 15 D. 20 E. 25 For any evenly spaced set: sum = (count)(median) Sum of the first n even numbers = n * median of the first n even numbers Sum of the last n odd numbers = n * median of the last n odd numbers Since the ratio of the two sums = 16/85, we get: (n * median of the first n even numbers) / (n * median of the last n odd numbers) = 16/85 (median of the first n even numbers)/(median of the last n odd numbers) = 16/85 Implication: The median of the first n even numbers = 16, with the result that the first n even numbers are as follows: 2, 4, 6, 8, 10, 12, 14, 16... Since there are 7 numbers below the median of 16, there must be 7 numbers above the median of 16. Thus, n = (7 numbers below the median) + (median of 16) + (7 numbers above the median) = 15 numbers. The correct answer is C. _________________ 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! Sign up now. ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 AAPL wrote: e-GMAT Set S contains consecutive natural numbers from 1 to 100, in increasing order. S_1 and S_2 denote the sum of first n even numbers and last n odd numbers of set S, respectively. What is the value of n, if S_1:S_2 = 16:85? A. 5 B. 10 C. 15 D. 20 E. 25 $${{{S_{\,{\rm{even}}}}} \over {{S_{\,{\rm{odd}}}}}} = {{16} \over {85}}\,\,\,\,\,;\,\,\,\,\,\,? = n$$ ItÂ´s easy to find a PATTERN! $$n = 2\,\,\,\, \to \,\,\,{{2 + 4} \over {97 + 99}} = {{2 \cdot 3} \over {2 \cdot 98}} = {3 \over {98}}\,\,\,\,\,\,\,\left\{ \matrix{ \,{\rm{numerator}} = n + 1 \hfill \cr \,{\rm{denominator}} = 100 - n \hfill \cr} \right.$$ $$n = 3\,\,\,\, \to \,\,\,{{2 + 4 + 6} \over {95 + 97 + 99}} = {{3 \cdot 4} \over {3 \cdot 97}} = {4 \over {97}}\,\,\,\,\left\{ \matrix{ \,{\rm{numerator}} = n + 1 \hfill \cr \,{\rm{denominator}} = 100 - n \hfill \cr} \right.$$ $$n = 4\,\,\,\, \to \,\,\,{{2 + 4 + 6 + 8} \over {93 + 95 + 97 + 99}} = {{4 \cdot 5} \over {4 \cdot 96}} = {5 \over {96}}\,\,\,\left\{ \matrix{ \,{\rm{numerator}} = n + 1 \hfill \cr \,{\rm{denominator}} = 100 - n \hfill \cr} \right.$$ $$n = 5\,\,\,\, \to \,\,\,{{2 + 4 + 6 + 8 + 10} \over {91 + 93 + 95 + 97 + 99}} = {{5 \cdot 6} \over {5 \cdot 95}} = {6 \over {95}}\,\,\,\,\left\{ \matrix{ \,{\rm{numerator}} = n + 1 \hfill \cr \,{\rm{denominator}} = 100 - n \hfill \cr} \right.$$ $${\rm{Hence}}\,\, \ldots \,\,\,\,\,\,\left\{ \matrix{ \,{\rm{numerator}} = n + 1 = 16 \hfill \cr \,{\rm{denominator}} = 100 - n = 85 \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,\,? = 15$$ 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 25 Apr 2015 Posted: 2791 messages Followed by: 18 members Upvotes: 43 AAPL wrote: e-GMAT Set S contains consecutive natural numbers from 1 to 100, in increasing order. S_1 and S_2 denote the sum of first n even numbers and last n odd numbers of set S, respectively. What is the value of n, if S_1:S_2 = 16:85? A. 5 B. 10 C. 15 D. 20 E. 25 The sum of the first n even numbers is: S_1 = 2 + 4 + â€¦ + 2n = (2 + 2n)/2 x n = 2(n + 1)/2 x n = n(n + 1) The sum of the last n odd numbers is: S_2 = 99 + 97 + â€¦ + (99 - 2(n - 1)) = [99 + 99 - 2(n - 1)]/2 x n = (99 - (n - 1)) x n = n(100 - n) So we have: S_1:S_2 = 16:85 [n(n + 1)]/[n(100 - n)] = 16:85 (n + 1)/(100 - n) = 16:85 85(n + 1) = 16(100 - n) 85n + 85 = 1600 - 16n 101n = 1515 n = 15 Answer: C _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. 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