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

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Manager
Joined: 06 May 2012
Posts: 75

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

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15 Oct 2012, 16:28
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Difficulty:

35% (medium)

Question Stats:

72% (01:31) correct 28% (01:08) wrong based on 147 sessions

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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%

[Reveal] Spoiler: OA

Kudos [?]: 52 [2], given: 16

Math Expert
Joined: 02 Sep 2009
Posts: 42264

Kudos [?]: 132789 [1], given: 12373

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

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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%

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.

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.

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Kudos [?]: 132789 [1], given: 12373

Manager
Joined: 06 May 2012
Posts: 75

Kudos [?]: 52 [1], given: 16

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

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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, $$S = 50%$$

Kudos [?]: 52 [1], given: 16

Intern
Joined: 12 Aug 2012
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Kudos [?]: 1 [1], given: 95

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

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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%.

Kudos [?]: 1 [1], given: 95

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

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19 Jun 2014, 11:13
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Re: At Daifu university, 40% of all students are members of both [#permalink]

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03 Oct 2016, 17:33
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: At Daifu university, 40% of all students are members of both   [#permalink] 03 Oct 2016, 17:33
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