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12 Oct 2004, 20:37
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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:
55%
(hard)
Question Stats:
67% (02:20) correct
33%
(02:34)
wrong
based on 630
sessions
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Not Attempted Yet
Each of three charities in Novel Grove Estates has 8 persons serving on its board of directors. If exactly 4 persons serve on 3 boards each and each pair of charities has 5 persons in common on their boards of directors, then how many distinct persons serve on one or more boards of directors?
A. 8
B. 13
C. 16
D. 24
E. 27
A. 8
B. 13
C. 16
D. 24
E. 27
Each group has 8 = 8+8+8 = 24 max
4 people are in 2 groups, subtract 4 people twice as they are counted twice
Each pair of groups has 5 in common, so in addition to the 4 people subtract 1 from each group
Ans: 8+8+8-(2(4)) - 3 = 13
4 people are in 2 groups, subtract 4 people twice as they are counted twice
Each pair of groups has 5 in common, so in addition to the 4 people subtract 1 from each group
Ans: 8+8+8-(2(4)) - 3 = 13
31 Jan 2011, 21:26
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m990540
You can use the formula for 3 sets:
n(AUBUC) = n(A) + n(B) + n (C) - n(A and B) - n(B and C) - n(C and A) + n(A and B and C)
n(AUBUC) = 8 + 8 + 8 - 5 - 5 -5 + 4 = 13
Though, why would you not try using the Venn diagram for 3 overlapping sets. This question is relatively straight forward so the formula is no problem, but with the Venn diagram, it doesn't matter how much you twist the question, the answer is still apparent....
I am attaching it in case you would like to give it a look...
Attachment:
Ques2.jpg [ 10.5 KiB | Viewed 18509 times ]
14 May 2011, 23:43
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Let Communities be C1, C2 and C3. It given that exactly 4 members serve on 3 boards each. Hence 4 member in all three communities.
Also each pair of charity has 5 persons in common. hence 1 member between C1 and C2 Only.
Total = 2+2+2+1+1+1+4=13.
OA B.
Also each pair of charity has 5 persons in common. hence 1 member between C1 and C2 Only.
Total = 2+2+2+1+1+1+4=13.
OA B.
Attachments
venn diagram.JPG [ 22.61 KiB | Viewed 20057 times ]
