Venn Diagram

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elgrower: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Mon Feb 08, 2010 4:28 pm

by elgrower » Tue Mar 02, 2010 11:29 am

Can someone please help me solve this question:

Of 20 Adults, 5 belong to X, 7 belong to Y, and 9 belong to Z. If 2 belong to all three organizations and 3 belong to exactly 2 organizations, how many belong to none of these organizations?

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Source: Beat The GMAT — Problem Solving | Tue Mar 02, 2010 11:29 am

yeahdisk: Senior | Next Rank: 100 Posts; Posts: 45; Joined: Tue Mar 02, 2010 4:27 am; Thanked: 2 times

by yeahdisk » Tue Mar 02, 2010 12:14 pm

Draw a venn diagram - 3 overlapping circles.

"2 belong to all 3 organizations" - so put a 2 in the intersect of all 3 of your circles.

"3 belong to exactly 2 organisations" - so stick a 3 in any* of the intersects between 2 of your circles.

Then, work out the remainder you need to put in each of the single sets to make the total add up to 5 for X, 7 for Y, and 9 for Z.

The answer to the question is 6 - all of your numbers in your diagram should add up to 14, subtract this from 20

*I thought this would need to be better defined but I tries out a few variations and they all came to the same answer

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elgrower: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Mon Feb 08, 2010 4:28 pm

by elgrower » Tue Mar 02, 2010 12:57 pm

I get the first step, put 2 in the middle. I am confused from there. Put a "3" in "any of the circles", How do I determine "the remainder"?

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girish3131: Master | Next Rank: 500 Posts; Posts: 194; Joined: Thu Jan 14, 2010 5:18 am; Thanked: 2 times

by girish3131 » Fri Mar 12, 2010 3:27 am

20 = 5 +7+9 -3 +2 + A

A = 0

Acc to me ... there is nobody who dont belong to any organization.... ie everybody belongs to atleast one org...

wats OA...

TA

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elgrower: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Mon Feb 08, 2010 4:28 pm

by elgrower » Fri Mar 12, 2010 6:53 am

Thanks for that response. Although you are wrong, you showed me how to complete the problem.

5+7+9 = 21

21-3-2(2)=14

6 people is the answer.

You added 2 rather than multiply and then subtract.

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