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
The OA is B.
Please, can someone assist me with this PS question? I'm not sure but I think that I can use the Venn Diagram to solve it. Thanks in advance!
Each of three charities in Novel Grove Estates has 8 persons
This topic has expert replies
-
- Moderator
- Posts: 2205
- Joined: Sun Oct 15, 2017 1:50 pm
- Followed by:6 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi All,
We're told that each of three charities in Novel Grove Estates has 8 persons serving on its board of directors and EXACTLY 4 persons serve on 3 boards each and each pair of charities has 5 persons in common on their boards of directors. We're asked for the number of distinct persons that serve on one or more boards of directors. You will likely find it easiest to use a few drawings and some 'brute force' work to help you to answer this question.
To start, let's focus on the 4 people who are on ALL 3 boards. We'll call those people A, B, C and D...
Charity 1: ABCD _ _ _ _
Charity 2: ABCD _ _ _ _
Charity 3: ABCD _ _ _ _
Next, we need each PAIR of charities to have 5 people in common (the first 4 plus one more); that 5th person CAN'T be on ALL 3 charities though, so we'll need a few additional people to make that happen:
Charity 1: ABCD E F _ _
Charity 2: ABCD E G _ _
Charity 3: ABCD F G _ _
The last two people on each charity have to be 'unique' (meaning that they each appear on ONLY that one charity....
Charity 1: ABCD E F M N
Charity 2: ABCD E G P Q
Charity 3: ABCD F G R S
Total people: ABCDE FGMNP QRS = 13 people
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
We're told that each of three charities in Novel Grove Estates has 8 persons serving on its board of directors and EXACTLY 4 persons serve on 3 boards each and each pair of charities has 5 persons in common on their boards of directors. We're asked for the number of distinct persons that serve on one or more boards of directors. You will likely find it easiest to use a few drawings and some 'brute force' work to help you to answer this question.
To start, let's focus on the 4 people who are on ALL 3 boards. We'll call those people A, B, C and D...
Charity 1: ABCD _ _ _ _
Charity 2: ABCD _ _ _ _
Charity 3: ABCD _ _ _ _
Next, we need each PAIR of charities to have 5 people in common (the first 4 plus one more); that 5th person CAN'T be on ALL 3 charities though, so we'll need a few additional people to make that happen:
Charity 1: ABCD E F _ _
Charity 2: ABCD E G _ _
Charity 3: ABCD F G _ _
The last two people on each charity have to be 'unique' (meaning that they each appear on ONLY that one charity....
Charity 1: ABCD E F M N
Charity 2: ABCD E G P Q
Charity 3: ABCD F G R S
Total people: ABCDE FGMNP QRS = 13 people
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
-
- Junior | Next Rank: 30 Posts
- Posts: 24
- Joined: Thu Jul 05, 2018 2:28 am
There are three types of directors: In One charity, In two Charity and In 3 charity
There are 4 directors in the 3 charities
And 3 directors in 2 charities(Because it says that 5 are common between each pair out of these 4 are in all three but 1 is unique to that pair and there are 3 pairs possible)
So, director in 1 charity are 3*(8-4-2)=6
So, total= 6+3+4= 13
There are 4 directors in the 3 charities
And 3 directors in 2 charities(Because it says that 5 are common between each pair out of these 4 are in all three but 1 is unique to that pair and there are 3 pairs possible)
So, director in 1 charity are 3*(8-4-2)=6
So, total= 6+3+4= 13
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
This problem involves 3 overlapping sets: Charity A, Charity B, and Charity C.BTGmoderatorLU 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
To organize the data, use a Venn Diagram:
Start in the CENTER and work outwards.
Exactly 4 persons serve on 3 boards each.
Inserting 4 people into the center of the diagram, we get:
Each pair of charities has 5 persons in common.
Thus -- in addition to the 4 people that all 3 charities have in common -- each pair must have 1 additional person in common:
Since each charity must have a total of 8 people, we get:
How many distinct persons serve on one or more boards of directors?
Adding together the values in the Venn Diagram, we get:
2+1+2+1+4+1+2 = 13.
The correct answer is B.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7223
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
BTGmoderatorLU 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
We can use the formula:
n(At least one set) = n(A) + n(B) + n(C) - n(A and B) - n(B and C) - n(C and A) + n(A and B and C)
Thus, we have:
n(At least one set) = 8 + 8 + 8 - 5 - 5 - 5 + 4 = 24 - 15 + 4 = 13
Answer: B
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews