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At Daifu university, 40% of all students are members of both [#permalink]

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15 Oct 2012, 15:28

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At Daifu university, 40% of all students are members of both a chess club and a swim team. If 20% of members of the swim team are not members of the chess club, what percentage of all Daifu students are members of the swim team?

At Daifu university, 40% of all students are members of both a chess club and a swim team. If 20% of members of the swim team are not members of the chess club, what percentage of all Daifu students are members of the swim team?

A) 20% B) 30% C) 40% D) 50% E) 60%

Please explain with your answers

At Daifu university, 40% of all students are members of both a chess club and a swim team. If 20% of members of the swim team are not members of the chess club, what percentage of all Daifu students are members of the swim team?

A. 20% B. 30% C. 40% D. 50% E. 60%

Assume there are total of 100 students. 40 students are members of both clubs. We are told that: "20% of members of the swim team are not members of the chess club", thus if S is a # of members of the swim team then 0.2S is # of members of ONLY the swim teem:

40+0.2S=S --> S=50.

Answer: D.

Or another way: since "20% of members of the swim team are not members of the chess club" then the rest 80% of members of the swim team (S) ARE members of the chess club, so members of both clubs: 0.8*S=40 --> S=50.

Re: At Daifu university, 40% of all students are members of both [#permalink]

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15 Oct 2012, 16:30

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Thanks for the quick reply Bunuel. Now I get it.

I am just laying out step by step:

Let's say Total Swim team = \(S\)

Information given in the statement Members of both teams (Both) = \(40%\) 20% of members of the swim team are not members of the chess club \((S - Both) = 20% S\)

Re: At Daifu university, 40% of all students are members of both [#permalink]

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16 Oct 2012, 21:29

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1.Out of total student 40% are member of chess and swim club. 2. 20% of swim club member are not chess club member= 80% of swim club member are also chess club member. From 1and 2, 80% of swim club = 40% of total student. So, 100% of swim club= 40/80*100= 50%.

Re: At Daifu university, 40% of all students are members of both [#permalink]

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19 Jun 2014, 10:13

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Re: At Daifu university, 40% of all students are members of both [#permalink]

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