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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]

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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
[Reveal] Spoiler: OA

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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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New post 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.


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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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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 9319 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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New post 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

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New post 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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New post 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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New post 25 Jun 2011, 18:20
total = X+Y+Z-2(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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Re: Of 20 Adults, 5 belong to X, 7 belong to Y, and 9 belong to [#permalink]

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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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New post 20 Jan 2016, 21:36
safaria25 wrote:
Bunuel wrote:
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


For more check ADVANCED OVERLAPPING SETS PROBLEMS


Hi Bunuel,

I'm not sure when to use the first or second formulas (GMAT CLUB Quant Book) for these Venn Diagram questions, can you please help?

Thanks!


The very post you quote has a link which explains it. Here it is again: ADVANCED OVERLAPPING SETS PROBLEMS
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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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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New post 29 Sep 2017, 08:44
Ans is B

20-None = 5+7+9-3-2x2
20-N=14
N=6
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Re: Of 20 Adults, 5 belong to X, 7 belong to Y, and 9 belong to   [#permalink] 29 Sep 2017, 08:44
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