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# Set theory

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Manager
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22 Feb 2012, 04:41
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?

20%
30%
40%
50%
60%

I have solved the question differently. Can anybody please correct me as where did I go wrong.

From the attached figure we get B = 40% and C = 20%
so the number of students who are member of swim team is 40%+40% = 80%
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22 Feb 2012, 04:57
subhajeet 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?

20%
30%
40%
50%
60%

I have solved the question differently. Can anybody please correct me as where did I go wrong.

From the attached figure we get B = 40% and C = 20%
so the number of students who are member of swim team is 40%+40% = 80%

The red part is not correct.

Assume there are total of 100 students. 40 students are members of both clubs (B in your diagram). 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 swim team then S/5 is the segment you denoted as C.

40+S/5=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 ARE members of the chess club, so members of both clubs: 0.8*S=40 --> S=50.

Hope it's clear.
_________________
Manager
Status: MBA Aspirant
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22 Feb 2012, 22:18
Bunuel wrote:
subhajeet 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?

20%
30%
40%
50%
60%

I have solved the question differently. Can anybody please correct me as where did I go wrong.

From the attached figure we get B = 40% and C = 20%
so the number of students who are member of swim team is 40%+40% = 80%

The red part is not correct.

Assume there are total of 100 students. 40 students are members of both clubs (B in your diagram). 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 swim team then S/5 is the segment you denoted as C.

40+S/5=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 ARE members of the chess club, so members of both clubs: 0.8*S=40 --> S=50.

Hope it's clear.

Bunnel: Thanks for the explanation. Here it is mentioned as 40% of the students are members of both clubs so it means 0.4S. so do we here take it as 40 students???

I am not able to understand why are u taking here the base as 40 students and not 40% of students.
Math Expert
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Kudos [?]: 92869 [0], given: 10528

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22 Feb 2012, 22:27
subhajeet wrote:
Bunnel: Thanks for the explanation. Here it is mentioned as 40% of the students are members of both clubs so it means 0.4S. so do we here take it as 40 students???

I am not able to understand why are u taking here the base as 40 students and not 40% of students.

Since we assumed in my previous post that total # of students is 100, then 40% of it would be 40 students --> 40+S/5=S --> S=50 --> 50 students out of 100 is 50%.

Hope it's clear.
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23 Feb 2012, 02:52
Bunuel wrote:
subhajeet wrote:
Bunnel: Thanks for the explanation. Here it is mentioned as 40% of the students are members of both clubs so it means 0.4S. so do we here take it as 40 students???

I am not able to understand why are u taking here the base as 40 students and not 40% of students.

Since we assumed in my previous post that total # of students is 100, then 40% of it would be 40 students --> 40+S/5=S --> S=50 --> 50 students out of 100 is 50%.

Hope it's clear.

Got it Bunnel, Thanks for your help.
Re: Set theory   [#permalink] 23 Feb 2012, 02:52
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# Set theory

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