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Set theory

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Set theory [#permalink]

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New post 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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Re: Set theory [#permalink]

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New post 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.

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

Answer: D.

Hope it's clear.
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Re: Set theory [#permalink]

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New post 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.

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

Answer: D.

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.
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Re: Set theory [#permalink]

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New post 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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Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Kudos [?]: 76 [0], given: 1

Re: Set theory [#permalink]

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New post 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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