This year, x people won an Olympic medal for water

[BTGmoderatorDC]

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

Source: Veritas Prep

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Hi All,

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. This question can be solved by TESTing VALUES (and taking a few notes).

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

[Scott@TargetTestPrep]

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

Source: Veritas Prep

We see that 1/3(x/4) = (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