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Of 20 Adults, 5 belong to X, 7 belong to Y, and 9 belong to [#permalink]
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18 May 2010, 16:52
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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? A) 4 B) 6 C) 8 D) 10 E) 12
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Last edited by abhimahna on 31 Aug 2017, 11:07, edited 1 time in total.
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Re: Of 20 Adults, 5 belong to X, 7 belong to Y, and 9 belong to [#permalink]
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23 May 2010, 12:36
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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.
Roy



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Re: Of 20 Adults, 5 belong to X, 7 belong to Y, and 9 belong to [#permalink]
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24 May 2010, 04:00
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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+932*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 [ 11.63 KiB  Viewed 10192 times ]
For more check ADVANCED OVERLAPPING SETS PROBLEMS
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Re: Of 20 Adults, 5 belong to X, 7 belong to Y, and 9 belong to [#permalink]
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24 May 2010, 07:00
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!
Roy



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Re: Of 20 Adults, 5 belong to X, 7 belong to Y, and 9 belong to [#permalink]
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26 Jul 2010, 05:12
thanks for sharing this question



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Re: Of 20 Adults, 5 belong to X, 7 belong to Y, and 9 belong to [#permalink]
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25 Jun 2011, 10:15
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: Of 20 Adults, 5 belong to X, 7 belong to Y, and 9 belong to [#permalink]
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25 Jun 2011, 18:20
total = X+Y+Z2(all three) (sum of two overlaps) + neither
20 = 5+ 7+9  2(2)3+neither =>neither = 6



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Re: Of 20 Adults, 5 belong to X, 7 belong to Y, and 9 belong to [#permalink]
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29 Sep 2017, 08:44
Ans is B 20None = 5+7+932x2 20N=14 N=6
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