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

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Question Stats:

88% (02:06) correct
12% (01:18) wrong based on 24 sessions

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?

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.

Re: Of 20 Adults, 5 belong to X, 7 belong to Y, and 9 belong to [#permalink]
07 Jun 2014, 00:10

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Re: Of 20 Adults, 5 belong to X, 7 belong to Y, and 9 belong to [#permalink]
28 Jun 2015, 03:06

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