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Of 20 Adults, 5 belong to X, 7 belong to Y, and 9 belong to

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Of 20 Adults, 5 belong to X, 7 belong to Y, and 9 belong to [#permalink] New post 18 May 2010, 15:52
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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?

Sorry I don't have OA.
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Re: PS question [#permalink] New post 18 May 2010, 21:47
I guess the answer is 0.
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Re: PS question [#permalink] New post 23 May 2010, 11:36
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The answer should be 10. This is how I got to it,

Total - 20
Group X - 5
Group Y - 7
Group Z - 9

Common Between 2 Groups - 3 (Lets take this as X+Y)
Common Between 3 Groups - 2 (Lets take this as X+Y+Z)
Neither - N

Total - N = (X+Y+Z) - 2(common b/w 2 groups) - 2(common b/w 3 groups)
20 - N = 20 - (4 + 6)
20 - N = 10 & N = 10

Though you might want to check on the figures because 5,7 & 9 add upto 21 not 20. So if the total is 20 then 10 are part of neither.


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Re: PS question [#permalink] New post 24 May 2010, 03:00
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Expert's post
pardeepattri wrote:
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?

Sorry I don't have OA.


Above solution is not right.

The formula would be:

ALL = 20 = X+Y+Z - {Members of Exactly 2} - 2*{Members of All 3} + None --> 20=5+7+9-3-2*2+N --> N=6.

We subtract {Members of Exactly 2} once as when we add X+Y+Z, this intersection (exactly 2 - segments 1, 2 and 3 on the diagram below) is counted twice thus one should be subtracted.

We subtract {Members of All 3} twice as when we add X+Y+Z, this intersection (all 3 - segment 4 in the diagram below) is counted thrice, thus two should be subtracted.
Attachment:
Union_3sets.gif
Union_3sets.gif [ 11.63 KiB | Viewed 3788 times ]


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Re: PS question [#permalink] New post 24 May 2010, 06:00
Sorry pradeep I stand corrected.

my quant is bit rusty and venn diagrams is something i really want to improve at, thank Quant Forum Moderator

Kudos to you!

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Re: PS question [#permalink] New post 26 Jul 2010, 04:12
thanks for sharing this question
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Re: PS question [#permalink] New post 25 Jun 2011, 09:15
Total = (Neither) + x + y + z - (Exactly 2) - 2*(All 3)

20 = (N) + 21 - (3) - (4)

20 = 14 + N

Neither = 6

Good question this -- helps if one knows the formula.
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Re: PS question [#permalink] New post 25 Jun 2011, 17:20
total = X+Y+Z-2(all three) -(sum of two overlaps) + neither

20 = 5+ 7+9 - 2(2)-3+neither
=>neither = 6
Re: PS question   [#permalink] 25 Jun 2011, 17:20
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