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Updated on: 31 Aug 2017, 11:07
Originally posted by pardeepattri on 18 May 2010, 16:52.
Last edited by abhimahna on 31 Aug 2017, 11:07, edited 1 time in total.
Last edited by abhimahna on 31 Aug 2017, 11:07, edited 1 time in total.
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
75% (01:28) correct
25%
(01:49)
wrong
based on 829
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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
A) 4
B) 6
C) 8
D) 10
E) 12
24 May 2010, 04:00
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pardeepattri
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 [ 11.63 KiB | Viewed 30753 times ]
For more check ADVANCED OVERLAPPING SETS PROBLEMS
16 Jul 2018, 03:56
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Here is the Venn Diagram Method, which is more applicable than using the formula with no understanding.
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ITEMSABC.PNG [ 69.56 KiB | Viewed 19291 times ]
