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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

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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 3659 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!
Re: Each of the 59 members in a high school class is required   [#permalink] 26 May 2012, 16:50
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