Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 16 Feb 2010
Posts: 190

3/8 of all students at Social High are in all three of the [#permalink]
Show Tags
21 Aug 2010, 06:07
Question Stats:
69% (01:50) correct 31% (02:07) wrong based on 499 sessions
HideShow timer Statistics
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
Official Answer and Stats are available only to registered users. Register/ Login.



Math Expert
Joined: 02 Sep 2009
Posts: 46272

Re: The Quest for 700: Weekly GMAT Challenge [#permalink]
Show Tags
21 Aug 2010, 06:33
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: formulaefor3overlappingsets69014.html?hilit=exactly%20groups or overlappingsetsproblems87628.html?hilit=exactly%20membersHope it helps.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Joined: 29 Sep 2009
Posts: 383

Re: The Quest for 700: Weekly GMAT Challenge [#permalink]
Show Tags
20 Sep 2010, 22:30
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.



Math Expert
Joined: 02 Sep 2009
Posts: 46272

Re: The Quest for 700: Weekly GMAT Challenge [#permalink]
Show Tags
20 Sep 2010, 22:43
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: formulaefor3overlappingsets69014.html?hilit=exactly%20groupsHope it helps.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Joined: 29 Sep 2009
Posts: 383

Re: The Quest for 700: Weekly GMAT Challenge [#permalink]
Show Tags
20 Sep 2010, 22:57
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.



Math Expert
Joined: 02 Sep 2009
Posts: 46272

Re: The Quest for 700: Weekly GMAT Challenge [#permalink]
Show Tags
20 Sep 2010, 23:02



Senior Manager
Joined: 29 Sep 2009
Posts: 383

Re: The Quest for 700: Weekly GMAT Challenge [#permalink]
Show Tags
20 Sep 2010, 23:08
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



Math Expert
Joined: 02 Sep 2009
Posts: 46272

Re: The Quest for 700: Weekly GMAT Challenge [#permalink]
Show Tags
20 Sep 2010, 23:23
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: formulaefor3overlappingsets69014.html?hilit=exactly%20groupsAnd refer to the solution above to see how the second formula is applied to this problem.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Joined: 29 Sep 2009
Posts: 383

Re: The Quest for 700: Weekly GMAT Challenge [#permalink]
Show Tags
21 Sep 2010, 00:07
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!



Math Expert
Joined: 02 Sep 2009
Posts: 46272

Re: 3/8 of all students at Social High are in all three of the [#permalink]
Show Tags
11 Jun 2013, 08:23



Intern
Joined: 28 Feb 2014
Posts: 9
GPA: 3.27

Re: 3/8 of all students at Social High are in all three of the [#permalink]
Show Tags
30 Oct 2014, 09:58
Why did you multiply {# of students in exactly 3 clubs} by 2?



Math Expert
Joined: 02 Sep 2009
Posts: 46272

Re: 3/8 of all students at Social High are in all three of the [#permalink]
Show Tags
30 Oct 2014, 10:01



Director
Joined: 23 Jan 2013
Posts: 598

3/8 of all students at Social High are in all three of the [#permalink]
Show Tags
01 Nov 2014, 22:40
Basic formula is:
Total=A+B+C  exactly two  2*all three, so
Let pick 16 as total number of students
16=8+10+12  exactly two  2*6 16=30x12 x=2
2/16=1/8
with fractions:
8/8=1/2+5/8+3/4  x  3/4 8/8=15/8x3/4 x=1/8
A



NonHuman User
Joined: 09 Sep 2013
Posts: 7021

Re: 3/8 of all students at Social High are in all three of the [#permalink]
Show Tags
09 May 2018, 15:53
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). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: 3/8 of all students at Social High are in all three of the
[#permalink]
09 May 2018, 15:53






