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If 2/3rds of the members of the Golf Club are also members of the Tenn

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If 2/3rds of the members of the Golf Club are also members of the Tenn [#permalink]

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New post 06 Oct 2017, 04:55
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If 2/3rds of the members of the Golf Club are also members of the Tennis Club, and 1/2 of the members of the Tennis Club are also members of the Golf Club, what percentage of all people who belong to one or both Clubs belong only to the Golf Club?

A. 5%
B. 10%
C. 15%
D. 20%
E. 75%

This is a question given as an example by IanStewart several years ago.
[Reveal] Spoiler: OA

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If 2/3rds of the members of the Golf Club are also members of the Tenn [#permalink]

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New post 06 Oct 2017, 07:26
Bunuel wrote:
If 2/3rds of the members of the Golf Club are also members of the Tennis Club, and 1/2 of the members of the Tennis Club are also members of the Golf Club, what percentage of all people who belong to one or both Clubs belong only to the Golf Club?

A. 5%
B. 10%
C. 15%
D. 20%
E. 75%

This is a question given as an example by IanStewart several years ago.


Let the no of people in Golf club be \(x\) and that in Tennis club be \(y\)

People who belong to both the club \(= \frac{2x}{3}\)

So people who belong only to golf club \(= x-\frac{2x}{3}=\frac{x}{3}\)

Also half of the Tennis club member belong to both the clubs \(= \frac{y}{2}\)

Hence people who belong only to Tennis club \(= y-\frac{y}{2}=\frac{y}{2}\)

So we have \(\frac{2x}{3}=\frac{y}{2}\)

And total no of people who belong to only one or both the clubs \(= \frac{x}{3}+\frac{y}{2}+\frac{2x}{3}=\frac{x}{3}+\frac{2x}{3}+\frac{2x}{3}=\frac{5x}{3}\)

% who belong only to Golf club \(=\frac{x}{3}/\frac{5x}{3}*100=20\)%

Option D

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If 2/3rds of the members of the Golf Club are also members of the Tenn [#permalink]

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New post 06 Oct 2017, 08:34
Assume a simple number for the members of the Golf club, let it be 300.
Since \(\frac{2}{3}\)rd's of the members of the Golf Club are also members of the Tennis Club(they are members of both)
Therefore, the total number of people in both the clubs are 200 members

Hence, Only golf club people is 100(300-200)
200 is also half the members of the tennis club.

Therefore, The tennis club has 400 members, of which those belonging only to the tennis club is 200

Percentage is \(\frac{100}{200 + 200 + 100} = \frac{100}{500} = 20\)%(Option D)
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If 2/3rds of the members of the Golf Club are also members of the Tenn   [#permalink] 06 Oct 2017, 08:34
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