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# Each of three charities in Novel Grove Estates has 8 persons

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Intern
Joined: 19 Dec 2010
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Each of three charities in Novel Grove Estates has 8 persons [#permalink]

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30 Jan 2011, 19:26
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Difficulty:

55% (hard)

Question Stats:

66% (03:15) correct 34% (02:02) wrong based on 103 sessions

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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
[Reveal] Spoiler: OA

Attachments

Overlapping Problem.jpg [ 12.62 KiB | Viewed 2777 times ]

Problem.pdf [24.45 KiB]

Last edited by Bunuel on 13 Aug 2014, 07:56, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Intern
Joined: 19 Dec 2010
Posts: 28
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Kudos [?]: 12 [0], given: 4

Re: Each of three charities in Novel Grove Estates has 8 persons [#permalink]

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30 Jan 2011, 19:51
Sorry, the answer is 13. I know that this question can be found in the forum, but I'd like to know if there's a way (such as using the standard overlapping set equation) to attack the problem other than by drawing out each of the three groups!

Thanks so much!
Veritas Prep GMAT Instructor
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Re: Each of three charities in Novel Grove Estates has 8 persons [#permalink]

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31 Jan 2011, 21:26
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m990540 wrote:
Sorry, the answer is 13. I know that this question can be found in the forum, but I'd like to know if there's a way (such as using the standard overlapping set equation) to attack the problem other than by drawing out each of the three groups!

Thanks so much!

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 2722 times ]

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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Math Expert Joined: 02 Sep 2009 Posts: 32549 Followers: 5629 Kudos [?]: 68302 [0], given: 9797 Re: Each of three charities in Novel Grove Estates has 8 persons [#permalink] ### Show Tags 01 Feb 2011, 03:08 Expert's post m990540 wrote: Hello, Here's an overlapping set question that I came across and obviously got wrong. Thanks in advance to anyone who can help me sort this one out! Check this link for different formulas on 3 overlapping sets (theory and examples): formulae-for-3-overlapping-sets-69014.html#p729340 _________________ Intern Joined: 19 Dec 2010 Posts: 28 Followers: 0 Kudos [?]: 12 [0], given: 4 Re: Each of three charities in Novel Grove Estates has 8 persons [#permalink] ### Show Tags 01 Feb 2011, 06:50 Wow, thanks for the great explanations and link! GMAT Club Legend Joined: 09 Sep 2013 Posts: 9240 Followers: 454 Kudos [?]: 114 [0], given: 0 Re: Each of three charities in Novel Grove Estates has 8 persons [#permalink] ### Show Tags 05 Aug 2014, 20:20 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1858 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Followers: 34 Kudos [?]: 1472 [1] , given: 193 Re: Each of three charities in Novel Grove Estates has 8 persons [#permalink] ### Show Tags 05 Aug 2014, 21:51 1 This post received KUDOS Distinct persons means addition of all colours (As per diagram below) = 2+1+4+1+2+1+2 = 13 Answer = 13 Attachments Ques2.jpg [ 16.69 KiB | Viewed 1383 times ] _________________ Kindly press "+1 Kudos" to appreciate GMAT Club Legend Joined: 09 Sep 2013 Posts: 9240 Followers: 454 Kudos [?]: 114 [0], given: 0 Re: Each of three charities in Novel Grove Estates has 8 persons [#permalink] ### Show Tags 12 Aug 2015, 04:30 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Manager Joined: 10 Jun 2015 Posts: 128 Followers: 1 Kudos [?]: 19 [0], given: 0 Re: Each of three charities in Novel Grove Estates has 8 persons [#permalink] ### Show Tags 14 Aug 2015, 01:52 m990540 wrote: 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 intersec B intersec C = 4 A intersec B but not C = 1 B intersec C but not A = 1 C intersec A but not B = 1 A only is 2; B only is 2; C only is 2 Therefore, total 13 members serve on one or more boards of directors. Re: Each of three charities in Novel Grove Estates has 8 persons [#permalink] 14 Aug 2015, 01:52 Similar topics Replies Last post Similar Topics: 2 A charity collected$1,199 from donors during the last month. If each 4 29 Feb 2016, 10:34
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