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
This problem involves 3 overlapping sets: Charity A, Charity B, and Charity C.
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
