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At Daifu university, 40% of all students are members of both

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At Daifu university, 40% of all students are members of both [#permalink] New post 15 Oct 2012, 16:28
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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?

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

Please explain with your answers
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Re: At Daifu university, 40% of all students are members of both [#permalink] New post 15 Oct 2012, 16:51
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gmatchase wrote:
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.

Answer: D.
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Re: At Daifu university, 40% of all students are members of both [#permalink] New post 15 Oct 2012, 17:30
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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

From above

S = Both + 20% S
S = 40% + 20% S

Finally, S = 50%
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Re: At Daifu university, 40% of all students are members of both [#permalink] New post 16 Oct 2012, 22:29
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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] 16 Oct 2012, 22:29
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