This year, x people won an Olympic medal for water

Question

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

fskilnik@GMATH · Answer

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 $$x\,\,\left( {{m{water}}} ight)\,\,\left\{ \matrix{ \,{x \over 3}\,\,\left( {{m{swim}}} ight)\,\,\, 	o \,\,\,\left\{ \matrix{ \,{1 \over 4}\left( {{x \over 3}} ight)\,\,\left( {{m{swim}}\,\,{m{\& }}\,\,{m{dive}}} ight) \hfill \cr \,{3 \over 4}\left( {{x \over 3}} ight)\,\,\left( {{m{swim}}\,\,{m{\& }}\,\,{m{not}}\,\,{m{dive}}} ight) \hfill \cr} ight. \hfill \cr \,{{2x} \over 3}\,\,\left( {{m{not}}\,\,{m{swim}}} ight) \hfill \cr} ight.$$ $$? = \left( {{m{water}}} ight) - \left( {{m{swim}}\,\,{m{\& }}\,\,{m{dive}}} ight) = x - {1 \over 4}\left( {{x \over 3}} ight) = {{11} \over {12}}x$$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.

GMATGuruNY · Answer

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.

Rich.C@EMPOWERgmat.com · Answer

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.

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Scott@TargetTestPrep · Answer

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 We see that ⅓(¼x) = (1/12)x = x/12 people won a medal in both swimming and dividing. Thus x - x/12 = 12x/12 - x/12 = 11x/12 people did not win a medal in both swimming and dividing. Answer: A

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