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jcerdae
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This year, x people won an Olympic medal for water competitions. One 18 Dec 2020, 03:02
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dave13
Bunuel
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

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hey pushpitkc is my understanding correct ? :-) have a great weekend :-)

Let SWIMMERS be S
Let DIVERS be D
let total # of winners be x

One-third of the winners earned a medal for swimming \(\frac{1}{3}x\) (S) ( remaining part \(\frac{2}{3}x\); we shall use it later)

One-fourth of those who earned a medal for swimming also earned a medal for diving \(\frac{1}{3}x\) * \(\frac{1}{4}\)= \(\frac{1}{12}x\) (S+D)

Now we know that both D and S = \(\frac{1}{12}x\)

To find only DIVERS subtract both from remaining part i.e \(\frac{2}{3}x\) \(-\) \(\frac{1}{12}x\)= \(\frac{7}{12}x\) (D)

(NOTE: we subtract only once because there are two group overlaps, in other words no need to make similar subtraction like this 1/3x -1/12x to find SWIMMERS )


To find only swimmers and only divers \(\frac{1}{3}x\)+ \(\frac{7}{12}x\) = \(\frac{11}{12}x\)
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Hi!
Is there a way to solve this with the Matrix Method?
thank you!
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Aditim12
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This year, x people won an Olympic medal for water competitions. One 17 Jan 2022, 04:47
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SOLVING IT BY OVERLAPPING SETS METHOD
x = number of winners
thus, there are no losers in this set => NO SWIMMING MEDAL & NO DIVING MEDAL = 0
I hadn't understood the question either so in simple terms, we have to find number of people who won a diving medal but did not win a swimming medal and vice versa.

first, we write what is given.
we have to find the highlighted boxes i.e. D&NS S&ND

making this answer took a lot of my effort; let me know if it helped you. :thumbsup:
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This year, x people won an Olympic medal for water competitions. One 09 Oct 2024, 01:58
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Quote:
How many people won an Olympic medal for water competitions but did not both receive a medal for swimming and a medal for diving?
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This part tells us that number of individuals who did not win a medal either in Swimming or Diving is 0 and we need to find the summation of the yellow highlighted part in below image.

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randomname4
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This year, x people won an Olympic medal for water competitions. One 06 Jun 2026, 07:29
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The key is to carefully identify the group that the question wants us to exclude.
There are x total people who won an Olympic medal for water competitions.
One-third of the winners earned a medal for swimming.
So the number of swimming medalists is:
x/3
One-fourth of the swimming medalists also earned a medal for diving.
So the number of people who earned medals for both swimming and diving is:
1/4 × x/3 = x/12
The question asks how many people won an Olympic medal for water competitions but did not both receive a medal for swimming and diving.
So we subtract the “both swimming and diving” group from the total:
x - x/12 = 12x/12 - x/12 = 11x/12
Therefore, the correct answer is A. 11x/12.
Takeaway: The phrase “did not both” means we should exclude only the people who received medals in both swimming and diving, not everyone who received either a swimming medal or a diving medal.

Bunuel
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
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DrTushita
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This year, x people won an Olympic medal for water competitions. One 06 Jun 2026, 23:12
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This question is perfect example of how confusing questions can be.. it is simply asking people with 1 medal but in the most confusing way
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