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M01-15

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Bunuel
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M01-15 [#permalink] New post   16 Sep 2014, 00:15
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Question Stats:

68% (01:59) correct 32% (01:58) wrong based on 750 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 swim team members 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%
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D
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Bunuel
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Re M01-15 [#permalink] New post   16 Sep 2014, 00:15
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Official Solution:

At Daifu University, 40% of all students are members of both a chess club and a swim team. If 20% of swim team members 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 a 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 the number of members in the swim team, then 0.2S is the number of students who are members of the swim team only:

\(40 + 0.2S = S\), which implies \(S = 50\).

Alternatively, since "20% of members of the swim team are not members of the chess club," the remaining 80% of swim team members are part of the chess club. Therefore, the number of students in both clubs is \(0.8 * S = 40\), which also results in \(S = 50\).


Answer: D
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Re: M01-15 [#permalink] New post   10 Feb 2015, 09:25
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brinckma wrote:
I think the answer should be E. The question does not say that ALL swim team members are included in the 40%, but rather that 40% of all students are members of both. If we assume that there are 100 total students, there could be 40 members of the swim team, or 100 members of the swim team. All we know is that 40% of these students are members of both.

I set up a table:

Chess
Yes No Total
Swim Yes .40x .20x .60x
No n/a n/a .40x
Total 1.0x


Sorry if the above table is garbled, but I hope it presents properly. If you add all the members of the swim team (40% who are both Swim and Chess and 20% who are not on the Chess team) then you get 60%.


No, the answer is D, not E. Here is the correct table:
Attachment:
Untitled.png
Untitled.png [ 4.93 KiB | Viewed 99633 times ]
40 + 0.2S = S --> S = 50.

Hope it helps.
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Re: M01-15 [#permalink] New post   10 Feb 2015, 09:16
I think the answer should be E. The question does not say that ALL swim team members are included in the 40%, but rather that 40% of all students are members of both. If we assume that there are 100 total students, there could be 40 members of the swim team, or 100 members of the swim team. All we know is that 40% of these students are members of both.

I set up a table:

Chess
Yes No Total
Swim Yes .40x .20x .60x
No n/a n/a .40x
Total 1.0x


Sorry if the above table is garbled, but I hope it presents properly. If you add all the members of the swim team (40% who are both Swim and Chess and 20% who are not on the Chess team) then you get 60%.
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Re: M01-15 [#permalink] New post   06 Jul 2022, 11:21
Bunuel wrote:
Official Solution:

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 team:

\(40+0.2S=S\), so \(S=50\).

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: \(0.8*S=40\), so \(S=50\).


Answer: D



Hi Bunuel

I have a doubt about your explanation. Requesting you to please help.

out of 100 total students, there can be the case that a student is neither a part of chess club nor a part of swim team. How you have managed this case in your explanation? Please explain.

Thank You.
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Re: M01-15 [#permalink] New post   07 Jul 2022, 01:53
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760Abhi wrote:
Bunuel wrote:
Official Solution:

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 team:

\(40+0.2S=S\), so \(S=50\).

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: \(0.8*S=40\), so \(S=50\).


Answer: D



Hi Bunuel

I have a doubt about your explanation. Requesting you to please help.

out of 100 total students, there can be the case that a student is neither a part of chess club nor a part of swim team. How you have managed this case in your explanation? Please explain.

Thank You.


There certainly can be students who are neither in a chess club nor in a swim team but to solve the question we don't need to know how many. In this post there is a matrix that might help.
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760Abhi
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Re: M01-15 [#permalink] New post   22 Jul 2022, 13:54
Bunuel wrote:
760Abhi wrote:
Bunuel wrote:
Official Solution:

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 team:

\(40+0.2S=S\), so \(S=50\).

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: \(0.8*S=40\), so \(S=50\).


Answer: D



Hi Bunuel

I have a doubt about your explanation. Requesting you to please help.

out of 100 total students, there can be the case that a student is neither a part of chess club nor a part of swim team. How you have managed this case in your explanation? Please explain.

Thank You.


There certainly can be students who are neither in a chess club nor in a swim team but to solve the question we don't need to know how many. In this post there is a matrix that might help.


Thank you so much, Bunuel. Got it.
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Re M01-15 [#permalink] New post   09 Aug 2023, 06:11
I think this is a high-quality question and I agree with explanation.
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Bunuel
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Re: M01-15 [#permalink] New post   08 Sep 2023, 09:55
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re: M01-15 [#permalink]
08 Sep 2023, 09:55
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