Venn Diagram

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heshamelaziry: Legendary Member; Posts: 869; Joined: Wed Aug 26, 2009 3:49 pmFollowed by: 3 members; Location: California; Thanked: 13 times

by heshamelaziry » Mon Nov 16, 2009 8:09 pm

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?

I can't figure out what parts of the diagram this represents "If 6 students sign up for exactly two clubs" ? Also, the Oe can never be done in 4 minutes, not to mention 2 minutes. Any creativity ?

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Source: Beat The GMAT — Problem Solving | Mon Nov 16, 2009 8:09 pm

palvarez: Master | Next Rank: 500 Posts; Posts: 199; Joined: Sat Oct 24, 2009 4:43 pm; Thanked: 22 times; GMAT Score:710

by palvarez » Mon Nov 16, 2009 8:16 pm

|P&H| + |H&W| + | P&W| - 3|P&H&W| = 6

59 = |P|+|H|+|W| - |P&H| - |H&W|-|P&W| + |P&H&W|
59 = 22+27+28 -6 - 2|P&H&W|
|P&H&W| = 6

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Mon Nov 16, 2009 8:32 pm

heshamelaziry wrote: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?

I can't figure out what parts of the diagram this represents "If 6 students sign up for exactly two clubs" ? Also, the Oe can never be done in 4 minutes, not to mention 2 minutes. Any creativity ?

If you know the right formula, it's a 30 second question.

True # of items = (total # in group 1) + (total # in group 2) + (total # in group 3) - (# in only groups 1/2) - (# in only groups 1/3) - (# in only groups 2/3) - 2(# in all 3 groups) + (# in no groups)

More generally:

True # of items = G1 + G2 + G3 - (# in exactly 2 groups) - 2(# in 3 groups)

(On 3 group questions, the # in no groups is almost always 0).

Applying the formula to this question:

59 = 22 + 27 + 28 - 6 - 2(# in all 3 groups)

59 = 71 - 2(# in all 3 groups)

2(# in all 3 groups) = 12
# in all 3 groups = 6

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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heshamelaziry: Legendary Member; Posts: 869; Joined: Wed Aug 26, 2009 3:49 pmFollowed by: 3 members; Location: California; Thanked: 13 times

by heshamelaziry » Mon Nov 16, 2009 9:26 pm

There is no pattern with overlapping sets problem. I have seen different formulas for different problems. although i understand the relationships between the different parts, i can't relate which method to use .

However, I solved it by simultaneous equations.

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Abdulla: Master | Next Rank: 500 Posts; Posts: 328; Joined: Thu Aug 07, 2008 5:25 pm; Location: Philadelphia; Thanked: 4 times; GMAT Score:550

by Abdulla » Mon Nov 16, 2009 11:48 pm

heshamelaziry wrote: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?

I can't figure out what parts of the diagram this represents "If 6 students sign up for exactly two clubs" ? Also, the Oe can never be done in 4 minutes, not to mention 2 minutes. Any creativity ?

Another way...

If you draw the venn diagram chart start by filling from inside outside.

Three clubs = x-6 ( which is what we need minus exactly two clubs)
Total exactly two clubs = 6
Poetry = 22
History = 27
Writing = 28

28 + 27 + 22 - x-6 - 6 = 59
77 -12 -x = 59
65- x =59
x = 6

Abdulla

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heshamelaziry: Legendary Member; Posts: 869; Joined: Wed Aug 26, 2009 3:49 pmFollowed by: 3 members; Location: California; Thanked: 13 times

by heshamelaziry » Mon Nov 16, 2009 11:53 pm

Abdulla wrote:
heshamelaziry wrote: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?

I can't figure out what parts of the diagram this represents "If 6 students sign up for exactly two clubs" ? Also, the Oe can never be done in 4 minutes, not to mention 2 minutes. Any creativity ?
Another way...

If you draw the venn diagram chart start by filling from inside outside.

Three clubs = x-6 ( which is what we need minus exactly two clubs)
Total exactly two clubs = 6
Poetry = 22
History = 27
Writing = 28

28 + 27 + 22 - x-6 - 6 = 59
77 -12 -x = 59
65- x =59
x = 6

I added three equations, one for each club. Then, from the result, I subtracted a+b+c+d+M+k+x = 59, i got a+b+c+2x = 18, then I substituted 6 for a+b+c -----> x = 6

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asha328: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Sat Dec 25, 2010 11:28 pmFollowed by: 4 members; Thanked: 11 times

by asha328 » Tue Jan 04, 2011 6:20 am

Abdulla wrote:
heshamelaziry wrote: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?

I can't figure out what parts of the diagram this represents "If 6 students sign up for exactly two clubs" ? Also, the Oe can never be done in 4 minutes, not to mention 2 minutes. Any creativity ?
Another way...

If you draw the venn diagram chart start by filling from inside outside.

Three clubs = x-6 ( which is what we need minus exactly two clubs)
Total exactly two clubs = 6
Poetry = 22
History = 27
Writing = 28

28 + 27 + 22 - x-6 - 6 = 59
77 -12 -x = 59
65- x =59
x = 6

Will take my GMAT in two weeks and still struggling with overlapping sets. Thank you for giving a simple and straightforward solution.

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strider123: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Wed Jul 13, 2011 9:32 pm

by strider123 » Tue Aug 30, 2011 8:46 pm

A+B+C-AB-BC-AC+ABC???

Is this the correct formula also???

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edvhou812: Master | Next Rank: 500 Posts; Posts: 143; Joined: Sat Nov 06, 2010 9:06 pmFollowed by: 1 member; Thanked: 10 times

by edvhou812 » Wed Aug 31, 2011 12:27 am

I normally use Venn Diagrams for these, but I decided to be brave with this one.

Since there are six in two groups, I dealt with that as 6*2 against the count of 22+27+28 which left me with 77-12=65. I then subtracted 59 from 65; 65-59=6.

As I said though, I was brave. Hopefully my correct answer wasn't a stroke of dumb luck.

I don't know what to say, really. Three minutes to the biggest battle of our professional lives. You find out life's this game of inches, so is football. Because in either game - life or football - the margin for error is so small. I mean, one half a step too late or too early and you don't quite make it. One half second too slow, too fast and you don't quite catch it. I'll tell you this, in any fight it's the guy whose willing to die whose gonna win that inch. That's football guys, that's all it is. Now, what are you gonna do?

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