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3/8 of all students at Social High are in all three of the

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3/8 of all students at Social High are in all three of the [#permalink] New post 21 Aug 2010, 05:07
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3/8 of all students at Social High are in all three of the following clubs: Albanian, Bardic, and Checkmate. 1/2 of all students are in Albanian, 5/8 are in Bardic, and 3/4 are in Checkmate. If every student is in at least one club, what fraction of the student body is in exactly 2 clubs?

(A) 1/8
(B) 1/4
(C) 3/8
(D) 1/2
(E) 5/8
[Reveal] Spoiler: OA
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Re: The Quest for 700: Weekly GMAT Challenge [#permalink] New post 21 Aug 2010, 05:33
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zisis wrote:
3/8 of all students at Social High are in all three of the following clubs: Albanian, Bardic, and Checkmate. 1/2 of all students are in Albanian, 5/8 are in Bardic, and 3/4 are in Checkmate. If every student is in at least one club, what fraction of the student body is in exactly 2 clubs?

(A) 1/8
(B) 1/4
(C) 3/8
(D) 1/2
(E) 5/8


Let's # of students at Social High be 8 (I picked 8 as in this case 3/8 of total and 5/8 of total will be an integer).

3/8 of all students at Social High are in all three clubs --> 3/8*8=3 people are in exactly 3 clubs;

1/2 of all students are in Albanian club --> 1/2*8=4 people are in Albanian club;
5/8 of all students are in Bardic club --> 5/8*8=5 people are in Bardic club;
3/4 of all students are in Checkmate club --> 3/4*8=6 people are in Checkmate club;

Also as every student is in at least one club then # of students in neither of clubs is 0;

Total=A+B+C-{# of students in exactly 2 clubs}-2*{# of students in exactly 3 clubs}+{# of students in neither of clubs};

8=4+5+6-{# of students in exactly 2 clubs}-2*3+0 --> {# of students in exactly 2 clubs}=1, so fraction is 1/8.

Answer: A.

For more about the formula used check my post at: formulae-for-3-overlapping-sets-69014.html?hilit=exactly%20groups or overlapping-sets-problems-87628.html?hilit=exactly%20members

Hope it helps.
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Re: The Quest for 700: Weekly GMAT Challenge [#permalink] New post 20 Sep 2010, 21:30
If you plot this data on a venn diagram, the problem would be much clearer .
General formula for 3 intersecting sets of data:
n(A u B u C) = n(A) + n(B) + n(C) - n(A int B) - n(B int C) - n(A int C) + n(A int B int C).
Assuming all students were part of atleast 1.
My solution is giving me an absurd result and it was definitely not 1/8. Please explain, I might have missed the point.
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Re: The Quest for 700: Weekly GMAT Challenge [#permalink] New post 20 Sep 2010, 21:43
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vicksikand wrote:
If you plot this data on a venn diagram, the problem would be much clearer .
General formula for 3 intersecting sets of data:
n(A u B u C) = n(A) + n(B) + n(C) - n(A int B) - n(B int C) - n(A int C) + n(A int B int C).
Assuming all students were part of atleast 1.
My solution is giving me an absurd result and it was definitely not 1/8. Please explain, I might have missed the point.


It's not clear how you applied the formula you wrote and what answer did you get, so it's hard to tell where you went wrong.

But the problem might be in formula you apply. Actually there are 2 formulas for 3 overlapping sets and the second one is better for this particular problem. Check the solution above and also this link about the mentioned 2 formulas: formulae-for-3-overlapping-sets-69014.html?hilit=exactly%20groups

Hope it helps.
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Re: The Quest for 700: Weekly GMAT Challenge [#permalink] New post 20 Sep 2010, 21:57
1. For 3 sets A, B, and C: P(A u B u C) : P(A) + P(B) + P(C) – P(A n B) – P(A n C) – P(B n C) + P(A n B n C)
Thats the one I have used all along and has worked fine for me. I would think that this formula would apply to this problem.
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Re: The Quest for 700: Weekly GMAT Challenge [#permalink] New post 20 Sep 2010, 22:02
Expert's post
vicksikand wrote:
1. For 3 sets A, B, and C: P(A u B u C) : P(A) + P(B) + P(C) – P(A n B) – P(A n C) – P(B n C) + P(A n B n C)
Thats the one I have used all along and has worked fine for me. I would think that this formula would apply to this problem.


It depends how you apply the formula. Again it's not the only formula for 3-overlapping sets, there is a second one and it fits this problem better. You can check the link I gave if you are interested to know the difference and to study how to apply either of them.
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Re: The Quest for 700: Weekly GMAT Challenge [#permalink] New post 20 Sep 2010, 22:08
5. To determine the No of persons in two or more sets (at least 2 sets) : P(A n B) + P(A n C) + P(B n C) – 2P(A n B n C)

3/8 of all students at Social High are in all three of the following clubs: Albanian, Bardic, and Checkmate. 1/2 of all students are in Albanian, 5/8 are in Bardic, and 3/4 are in Checkmate. If every student is in at least one club, what fraction of the student body is in exactly 2 clubs?

It doesnt say 1/2 of students are in Albanian only - In my opinion 1/2 includes the number that are common with Bardic and Checkmate. Formula 2 is for finding no. of persons in one set. I kind of see how the author arrived at that formula, but I wouldnt apply it to our case.

We have to find (P(A n B) + P(A n C) + P(B n C))/2
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Re: The Quest for 700: Weekly GMAT Challenge [#permalink] New post 20 Sep 2010, 22:23
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vicksikand wrote:
5. To determine the No of persons in two or more sets (at least 2 sets) : P(A n B) + P(A n C) + P(B n C) – 2P(A n B n C)

3/8 of all students at Social High are in all three of the following clubs: Albanian, Bardic, and Checkmate. 1/2 of all students are in Albanian, 5/8 are in Bardic, and 3/4 are in Checkmate. If every student is in at least one club, what fraction of the student body is in exactly 2 clubs?

It doesnt say 1/2 of students are in Albanian only - In my opinion 1/2 includes the number that are common with Bardic and Checkmate. Formula 2 is for finding no. of persons in one set. I kind of see how the author arrived at that formula, but I wouldnt apply it to our case.

We have to find (P(A n B) + P(A n C) + P(B n C))/2


You are right it doesn't say that 1/2 of students are in Albanian only and nowhere in the solution above it's mentioned. Also this is not the formula I meant.

Refer to my post at: formulae-for-3-overlapping-sets-69014.html?hilit=exactly%20groups

And refer to the solution above to see how the second formula is applied to this problem.
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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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

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Re: The Quest for 700: Weekly GMAT Challenge [#permalink] New post 20 Sep 2010, 23:07
I agree. Good explanation on the proof.
(a n b n c) was bothering me and you did a good job explaining why we need to subtract it twice and let that 1 remain so that it is counted at least once.

I remember having seen 1 question based on this in the MGMAT test series.

Thanks!
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Re: 3/8 of all students at Social High are in all three of the [#permalink] New post 11 Jun 2013, 07:23
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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Overlapping Sets:
advanced-overlapping-sets-problems-144260.html
how-to-draw-a-venn-diagram-for-problems-98036.html

All DS Overlapping Sets Problems to practice: search.php?search_id=tag&tag_id=45
All PS Overlapping Sets Problems to practice: search.php?search_id=tag&tag_id=65

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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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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Re: 3/8 of all students at Social High are in all three of the   [#permalink] 11 Jun 2013, 07:23
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