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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 ## This year, x people won an Olympic medal for water tagged by: AAPL ##### This topic has 3 expert replies and 0 member replies ### Top Member ## This year, x people won an Olympic medal for water ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Veritas Prep This year, x people won an Olympic medal for water competitions. One-third of the winners earned a medal for swimming and one-fourth of those who earned a medal for swimming also earned a medal for diving. How many people won an Olympic medal for water competitions but did not both receive a medal for swimming and a medal for diving? A. 11x/12 B. 7x/12 C. 5x/12 D. 6x/7 E. x/7 OA A ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1125 messages Followed by: 29 members Upvotes: 59 AAPL wrote: Veritas Prep This year, x people won an Olympic medal for water competitions. One-third of the winners earned a medal for swimming and one-fourth of those who earned a medal for swimming also earned a medal for diving. How many people won an Olympic medal for water competitions but did not both receive a medal for swimming and a medal for diving? A. 11x/12 B. 7x/12 C. 5x/12 D. 6x/7 E. x/7 $$x\,\,\left( {{\rm{water}}} \right)\,\,\left\{ \matrix{ \,{x \over 3}\,\,\left( {{\rm{swim}}} \right)\,\,\, \to \,\,\,\left\{ \matrix{ \,{1 \over 4}\left( {{x \over 3}} \right)\,\,\left( {{\rm{swim}}\,\,{\rm{\& }}\,\,{\rm{dive}}} \right) \hfill \cr \,{3 \over 4}\left( {{x \over 3}} \right)\,\,\left( {{\rm{swim}}\,\,{\rm{\& }}\,\,{\rm{not}}\,\,{\rm{dive}}} \right) \hfill \cr} \right. \hfill \cr \,{{2x} \over 3}\,\,\left( {{\rm{not}}\,\,{\rm{swim}}} \right) \hfill \cr} \right.$$ $$? = \left( {{\rm{water}}} \right) - \left( {{\rm{swim}}\,\,{\rm{\& }}\,\,{\rm{dive}}} \right) = x - {1 \over 4}\left( {{x \over 3}} \right) = {{11} \over {12}}x$$ 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 May 2010 Posted: 15025 messages Followed by: 1859 members Upvotes: 13060 GMAT Score: 790 AAPL wrote: Veritas Prep This year, x people won an Olympic medal for water competitions. One-third of the winners earned a medal for swimming and one-fourth of those who earned a medal for swimming also earned a medal for diving. How many people won an Olympic medal for water competitions but did not both receive a medal for swimming and a medal for diving? A. 11x/12 B. 7x/12 C. 5x/12 D. 6x/7 E. x/7 Let x = the product of the two denominators in the prompt = 3*4 = 12. Since 1/3 won a medal for swimming, the number who won a medal for swimming = (1/3)(12) = 4. Since 1/4 of the medal winners for swimming also won a medal for diving, the number who won both a medal for swimming and a medal for diving = (1/4)(4) = 1. How many people won an Olympic medal for water competitions but did not both receive a medal for swimming and a medal for diving? Since only 1 winner received both a medal for swimming and a medal for diving, the remaining 11 did not. The correct answer must yield a value of 11 when x=12. Only A works: (11/12)x = (11/12)(12) = 11. The correct answer is A. _________________ 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 Elite Legendary Member Joined 23 Jun 2013 Posted: 10020 messages Followed by: 494 members Upvotes: 2867 GMAT Score: 800 Hi All, This question can be solved by TESTing VALUES (and taking a few notes). We're told that X people won a medal for water competitions. Of those X people, 1/3 won a medal for swimming; of those who won a medal for SWIMMING, 1/4 also won a medal for diving. The common denominator between 1/3 and 1/4 is 12, so let's TEST X = 12.... X = 12 medal winners (1/3)(12) = 4 won a medal for swimming (1/4)(4) = 1 of the swimming winners ALSO won a medal for diving We're asked how many of the X people did NOT win a medal for BOTH swimming and diving. Since there were 12 people, and only 1 won BOTH medals, the other 11 won JUST ONE medal - thus, the answer to the question is 11 (when X = 12). The answers are written in such a way that you don't have to do much math to find the correct answer. 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