Problem Solving

Hi Vincen,

We're told that X people won an Olympic medal for water competitions, 1/3 of the winners earned a medal for swimming and 1/4 of THOSE who earned a medal for swimming ALSO earned a medal for diving. We're asked for the total number of people who won an Olympic medal for water competitions but did NOT receive BOTH a medal for swimming and a medal for diving. This question can be solved by TESTing VALUES.

IF... there are 12 medal winners, then...
1/3 of 12 = 4 won a medal for swimming and
1/4 of 4 = 1 ALSO won a medal for diving

This gives us:
3 who won JUST a swimming medal
1 who won BOTH a swimming medal and a diving medal
8 others who won a medal (presumably from just diving)

Thus, out of those 12 total winners, 11 did not win both swimming and diving medals. Thus, we're looking for an answer that equals 11 when we plug X = 12 into it. There's only one answer that matches..

Final Answer: A

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

Vincen wrote: ↑

Sun Sep 10, 2017 12:06 pm

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 is A.

How can I separate the two types of winners of medals? Can some expert explain it to me please.

We see that ⅓(¼x) = (1/12)x = x/12 people won a medal in both swimming and diving.

Thus x - x/12 = 12x/12 - x/12 = 11x/12 people did not win a medal in both swimming and diving.

Answer: A