Author 
Message 
TAGS:

Hide Tags

Manager
Status: DDay is on February 10th. and I am not stressed
Affiliations: American Management association, American Association of financial accountants
Joined: 12 Apr 2011
Posts: 209
Location: Kuwait
Schools: Columbia university

Each of the 59 members in a high school class is required [#permalink]
Show Tags
25 Nov 2011, 14:59
3
This post received KUDOS
15
This post was BOOKMARKED
Question Stats:
81% (00:57) correct 19% (01:17) wrong based on 685 sessions
HideShow timer Statistics
Each of the 59 members in a high school class is required to sign up for a minimum of one and a maximum of three academic clubs. The three clubs to choose from are the poetry club, the history club, and the writing club. A total of 22 students sign up for the poetry club, 27 students for the history club, and 28 students for the writing club. If 6 students sign up for exactly two clubs, how many students sign up for all three clubs? A. 2 B. 5 C. 6 D. 8 E. 9
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Sky is the limit



Manager
Joined: 29 Oct 2011
Posts: 167
Concentration: General Management, Technology
GPA: 3.76

Re: overlapping set [#permalink]
Show Tags
25 Nov 2011, 15:35
4
This post received KUDOS
1
This post was BOOKMARKED
59  poetry  history  writing + 2*(two clubs) + three clubs = 0 59  22  27  28 + 12 + three clubs = 0 three clubs = 6
C



Manager
Status: DDay is on February 10th. and I am not stressed
Affiliations: American Management association, American Association of financial accountants
Joined: 12 Apr 2011
Posts: 209
Location: Kuwait
Schools: Columbia university

Re: overlapping set [#permalink]
Show Tags
26 Nov 2011, 11:25
QUESTION why did u multiply 2*(two clubs)?
_________________
Sky is the limit



Math Expert
Joined: 02 Sep 2009
Posts: 45497

Re: overlapping set [#permalink]
Show Tags
03 Feb 2012, 06:31
3
This post received KUDOS
Expert's post
8
This post was BOOKMARKED
manalq8 wrote: QUESTION
why did u multiply 2*(two clubs)? Attachment:
Union_3sets.gif [ 11.63 KiB  Viewed 21031 times ]
Each of the 59 members in a high school class is required to sign up for a minimum of one and a maximum of three academic clubs. The three clubs to choose from are the poetry club, the history club, and the writing club. A total of 22 students sign up for the poetry club, 27 students for the history club, and 28 students for the writing club. If 6 students sign up for exactly two clubs, how many students sign up for all three clubs?A. 2 B. 5 C. 6 D. 8 E. 9 Translating: "Each of the 59 members in a high school class is required to sign up for a minimum of one and a maximum of three academic clubs" Total=59; Neither=0 (as members are required to sign up for a minimum of one); "22 students sign up for the poetry club": P=22; "27 students for the history club": H=27; "28 students for the writing club": W=28; "6 students sign up for exactly two clubs": {Exactly 2 groups members}=6, so sum of sections 1, 2, and 3 is given to be 6, (among these 6 students there are no one who is the member of ALL 3 clubs) "How many students sign up for all three clubs": question is \(PnHnW=x\). Or section 4 =? Apply formula: \(Total=P+H+W \){Sum of Exactly 2 groups members}\(2*PnHnW + Neither\) > \(59=22+27+2862*x+0\) > \(x=6\). Answer: C. For more check ADVANCED OVERLAPPING SETS PROBLEMSSimilar problem at: psquestion94457.html#p728852Hope 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



Manager
Joined: 12 Feb 2012
Posts: 125

Re: Each of the 59 members in a high school class is required [#permalink]
Show Tags
26 May 2012, 17:50
Hey Bunuel, Dude your awesome! Just a quick question, as I like to attack problems from different methods. The forumula you used is perfect but I also learned another cool formula from another problem which you can see here: overlappingsets84100.htmlpsvenndiagrams77473.htmlThe formula involves finding the minimum value for the intersection of all the sets (A and B and C) in a three overlapping set problem. Here it is: According to a survey, at least 70% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three? The way it is attacked is by finding the # of people that arent in the set So the solution to the above problem I posted would be : A and B and C = Total  [(TotalA) + (TotalB) + (TotalC)] My question is if I were to use this method to find the solution I get weird numbers. Total=59 A=Poetry=22 B=History=27 C=Writing=39 A and B and C =59[(5922)+(5932)+(5928)]=49. Actual answer is 6. Why does this formula work on the problem I posted but not on this question? Your my hero dude. Thank you!



Retired Moderator
Joined: 29 Apr 2015
Posts: 871
Location: Switzerland
Concentration: Economics, Finance
WE: Asset Management (Investment Banking)

Re: Each of the 59 members in a high school class is required [#permalink]
Show Tags
08 Jun 2015, 03:10
Bunuel wrote: manalq8 wrote: QUESTION
why did u multiply 2*(two clubs)? Attachment: Union_3sets.gif Each of the 59 members in a high school class is required to sign up for a minimum of one and a maximum of three academic clubs. The three clubs to choose from are the poetry club, the history club, and the writing club. A total of 22 students sign up for the poetry club, 27 students for the history club, and 28 students for the writing club. If 6 students sign up for exactly two clubs, how many students sign up for all three clubs?A. 2 B. 5 C. 6 D. 8 E. 9 Translating: "Each of the 59 members in a high school class is required to sign up for a minimum of one and a maximum of three academic clubs" Total=59; Neither=0 (as members are required to sign up for a minimum of one); "22 students sign up for the poetry club": P=22; "27 students for the history club": H=27; "28 students for the writing club": W=28; "6 students sign up for exactly two clubs": {Exactly 2 groups members}=6, so sum of sections 1, 2, and 3 is given to be 6, (among these 6 students there are no one who is the member of ALL 3 clubs) "How many students sign up for all three clubs": question is \(PnHnW=x\). Or section 4 =? Apply formula: \(Total=P+H+W \){Sum of Exactly 2 groups members}\(2*PnHnW + Neither\) > \(59=22+27+2862*x+0\) > \(x=6\). Answer: C. For more check ADVANCED OVERLAPPING SETS PROBLEMSSimilar problem at: psquestion94457.html#p728852Hope it helps. Dear Bunuel How can you logically explain that you subtract 2*x+0 > why is this 2 and how does it change with different question?
_________________
Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!
PS Please send me PM if I do not respond to your question within 24 hours.



Math Expert
Joined: 02 Sep 2009
Posts: 45497

Re: Each of the 59 members in a high school class is required [#permalink]
Show Tags
08 Jun 2015, 03:13
reto wrote: Bunuel wrote: manalq8 wrote: QUESTION
why did u multiply 2*(two clubs)? Attachment: Union_3sets.gif Each of the 59 members in a high school class is required to sign up for a minimum of one and a maximum of three academic clubs. The three clubs to choose from are the poetry club, the history club, and the writing club. A total of 22 students sign up for the poetry club, 27 students for the history club, and 28 students for the writing club. If 6 students sign up for exactly two clubs, how many students sign up for all three clubs?A. 2 B. 5 C. 6 D. 8 E. 9 Translating: "Each of the 59 members in a high school class is required to sign up for a minimum of one and a maximum of three academic clubs" Total=59; Neither=0 (as members are required to sign up for a minimum of one); "22 students sign up for the poetry club": P=22; "27 students for the history club": H=27; "28 students for the writing club": W=28; "6 students sign up for exactly two clubs": {Exactly 2 groups members}=6, so sum of sections 1, 2, and 3 is given to be 6, (among these 6 students there are no one who is the member of ALL 3 clubs) "How many students sign up for all three clubs": question is \(PnHnW=x\). Or section 4 =? Apply formula: \(Total=P+H+W \){Sum of Exactly 2 groups members}\(2*PnHnW + Neither\) > \(59=22+27+2862*x+0\) > \(x=6\). Answer: C. For more check ADVANCED OVERLAPPING SETS PROBLEMSSimilar problem at: psquestion94457.html#p728852Hope it helps. Dear Bunuel How can you logically explain that you subtract 2*x+0 > why is this 2 and how does it change with different question? All this is explained in the post given there.
_________________
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



Intern
Joined: 27 Aug 2015
Posts: 1

Re: Each of the 59 members in a high school class is required [#permalink]
Show Tags
27 Aug 2015, 13:19
2
This post received KUDOS
1
This post was BOOKMARKED
The following may be helpful to those struggling with the logic of the formula Total=P+H+W {Sum of Exactly 2 groups members}2*PnHnW + Neither .
First, forget this formula for a moment and rather recall the first "easier" formula: Total = A + B + C  (all cases of 2 group overlap, which equals AnB + AnC + BnC) + (the single 3 group overlap, which is AnBnC, or g) + (neither)
Recall that when we subtract all cases of group overlap, AnB + AnC + BnC, then we also subtract the 3 group overlap, g, 3 times. Since we add g 3 times when we add A +B + C, we are back at 0 regarding g, hence why we add it back following this subtraction, as you can see up there in the first formula.
In the gmat question we have above, the "simpler" first formula rendition would therefore go: 59 = 22 + 27 + 28  (AnB + AnC + BnC) + g + 0
We know that the total number of members in exactly two groups (so NOT the ones in all three) is 6.
Now, can we make AnB + AnC + BnC just equal 6? No, since AnB, and the rest of them, also include those members of all three groups, and thus may be larger than 6. The work around is that we simply need to account for g in each case, by including it explicitly in the formula and then set the part that is NOT g equal to 6.
Hence, AnB = (some part of the total 6) + g, and the same for the others. Just to give 'the part of the total 6' on A and B's side a name, let's substitute 'anb'. Don't get confused here: anb is just AnB with g subtracted.
Hence AnB + AnC + BnC = (anb + g) + (anc + g) + (bnc + g)
But what does anb equal? We don't know, but what we DO know that anb + anc + bnc, all the sets that have ONLY members of two and no more or less, is equal to 6.
Hence anb + anc + bnc = 6
With this understood we just replace anb, anc, and bnc with 6.
Hence, (AnB + AnC + BnC) = (6 + g + g + g)
Back to the first formula rendition, we now have 59 = 22 + 27 + 28  (6 + g + g +g) + g + 0 Simplified (a little): 59 = 22 + 27 + 28  6  g  g  g + g + 0 Simplified (a little more): 59 = 22 + 27 + 28  6  2g + 0
But wait, this just is the second formula!
Second formula: Total = P+H+W {Sum of Exactly 2 groups members}2*PnHnW + Neither
Where we left off: 59 = 22 + 27 + 28  6  2g + 0
You can now hopefully see WHY 6, the sum of those in exactly 2 groups, is subtracted, as well as WHY 2g is subtracted.



Intern
Joined: 28 May 2015
Posts: 29
Location: India
GPA: 2.2

Re: Each of the 59 members in a high school class is required [#permalink]
Show Tags
12 Nov 2017, 06:30
Hi, the question states that A total of 22 students sign up for the poetry club which means 22 is the whole of poetry club including the intersections with other clubs....Can you please explain how do we know if poetry is exclusive of the intersections?



Math Expert
Joined: 02 Aug 2009
Posts: 5784

Re: Each of the 59 members in a high school class is required [#permalink]
Show Tags
12 Nov 2017, 06:37
irishiraj87 wrote: Hi, the question states that A total of 22 students sign up for the poetry club which means 22 is the whole of poetry club including the intersections with other clubs....Can you please explain how do we know if poetry is exclusive of the intersections? it is inclusive....P+N+W(sum of two clubs)..... Means that P and N and W are inclusive and you are subtracting repeated elements from the SUM
_________________
Absolute modulus :http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
GMAT online Tutor




Re: Each of the 59 members in a high school class is required
[#permalink]
12 Nov 2017, 06:37






