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Each of the 59 members in a high school class is required

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Each of the 59 members in a high school class is required [#permalink] New post 25 Nov 2011, 13:59
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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
[Reveal] Spoiler: OA

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Re: overlapping set [#permalink] New post 25 Nov 2011, 14:35
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59 - poetry - history - writing + 2*(two clubs) + three clubs = 0
59 - 22 - 27 - 28 + 12 + three clubs = 0
three clubs = 6

C
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Re: overlapping set [#permalink] New post 26 Nov 2011, 10:25
QUESTION

why did u multiply 2*(two clubs)?
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Re: overlapping set [#permalink] New post 03 Feb 2012, 05:31
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manalq8 wrote:
QUESTION

why did u multiply 2*(two clubs)?


Attachment:
Union_3sets.gif
Union_3sets.gif [ 11.63 KiB | Viewed 6988 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}\(-2*PnHnW + Neither\) --> \(59=22+27+28-6-2*x+0\) --> \(x=6\).

Answer: C.

For more check ADVANCED OVERLAPPING SETS PROBLEMS
Similar problem at: ps-question-94457.html#p728852

Hope it helps.
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Re: Each of the 59 members in a high school class is required [#permalink] New post 26 May 2012, 16:50
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:

overlapping-sets-84100.html
ps-venn-diagrams-77473.html

The 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 - [(Total-A) + (Total-B) + (Total-C)]

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-[(59-22)+(59-32)+(59-28)]=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!
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Re: Each of the 59 members in a high school class is required [#permalink] New post 08 Jun 2015, 02:10
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}\(-2*PnHnW + Neither\) --> \(59=22+27+28-6-2*x+0\) --> \(x=6\).

Answer: C.

For more check ADVANCED OVERLAPPING SETS PROBLEMS
Similar problem at: ps-question-94457.html#p728852

Hope 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?
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Re: Each of the 59 members in a high school class is required [#permalink] New post 08 Jun 2015, 02:13
Expert's post
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}\(-2*PnHnW + Neither\) --> \(59=22+27+28-6-2*x+0\) --> \(x=6\).

Answer: C.

For more check ADVANCED OVERLAPPING SETS PROBLEMS
Similar problem at: ps-question-94457.html#p728852

Hope 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 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: Each of the 59 members in a high school class is required   [#permalink] 08 Jun 2015, 02:13
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