BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

Board of Directors

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 46
Joined: Sat Feb 27, 2010 2:58 am
Location: GMAT
by GMATSUCKER » Mon Mar 01, 2010 12:09 pm
Q: 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
GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT
What's life without GMAT !!!!!!!!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 3225
Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members
Location: Toronto
Thanked: 1710 times
GMAT Score:800

by Stuart@KaplanGMAT » Mon Mar 01, 2010 1:45 pm
GMATSUCKER wrote:Q: 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 easiest way to solve this is via brute force. Let's work it out:

3 charities, 8 slots each. Therefore, we have 24 slots to fill.

4 people sit on all 3 boards - let's start to fill slots:

Ch 1: ABCD
Ch 2: ABCD
Ch 3: ABCD

Each pair has exactly 5 persons in common. Well, 4 of those are ABCD, so each pair of charities has to have one more person in common. To make that work, we need exactly 1 person on each pair of charities. So, we now have:

Ch 1: ABCDEF
Ch 2: ABCDEG
Ch 3: ABCDFG

(ABCDE are on 1/2, ABCDF are on 1/3, ABCDG are on 2/3, fulfilling the requirement). So far we've used up A through G.

We have 2 slots left to fill on each board. Since we're not allowed any more overlap, we need 6 individuals for those 6 slots:

Ch 1: ABCDEFHI
Ch 2: ABCDEGJK
Ch 3: ABCDFGLM

We've used up A through M: that's 13 letters. Choose (b)!
Image

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 111
Joined: Tue Dec 30, 2008 1:25 pm
Location: USA
Thanked: 28 times
GMAT Score:770

by goalevan » Mon Mar 01, 2010 6:46 pm
I find it easier conceptually to quickly sketch a Venn diagram, and start with the problem with the middle region.

The boards have four people in common:

In the center region shared by all four clubs, mark a 4.

Each pair has five people in common:

In the regions shared by two clubs, mark a 1. (5-4=1)

Each club has eight people in total:

In the regions exclusive to one club, mark a 2. (8-4-1-1=2)


Counting all regions on the diagram, you will get 4 + 1 + 1 + 1 + 2 + 2 + 2 = 13
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 46
Joined: Sat Feb 27, 2010 2:58 am
Location: GMAT

by GMATSUCKER » Tue Mar 02, 2010 11:18 am
Ans.B . Source :Kaplan Advanced. Now the answer suggested in that book is quite lengthy and time consuming. So is there any other fast and shortcut approach to this problem.
GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT
What's life without GMAT !!!!!!!!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 3225
Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members
Location: Toronto
Thanked: 1710 times
GMAT Score:800

by Stuart@KaplanGMAT » Tue Mar 02, 2010 12:03 pm
GMATSUCKER wrote:Ans.B . Source :Kaplan Advanced. Now the answer suggested in that book is quite lengthy and time consuming. So is there any other fast and shortcut approach to this problem.
You mean other than the two posted here?

Each of the approaches in this thread are doable in well under 2 minutes - they key is to think of them quickly. The implementation is pretty fast, it's coming up with the approach that often takes too long.

So, as you study, keep looking for multiple approaches - that way you're more likely to find the quickest one when you need it: on test day.
Image

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 15
Joined: Wed Feb 03, 2010 12:09 am
GMAT Score:540

by stufigol » Tue Mar 02, 2010 10:25 pm
what s the 1 u dewleted in 8-4-1-1
i mean the last one
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 3225
Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members
Location: Toronto
Thanked: 1710 times
GMAT Score:800

by Stuart@KaplanGMAT » Wed Mar 03, 2010 2:35 pm
stufigol wrote:what s the 1 u dewleted in 8-4-1-1
i mean the last one
Looking at group 1, for example:

8 people total
4 people in all 3 groups
1 person doubles up with group 2
1 person doubles up with group 3

So, each "1" represents one of the doubles for that group.

Looking at the "group 1" circle in our venn diagram, it has 8 total members and 4 components:

Group 1 only = ?
Group 1/2 = 1
Group 1/3 = 1
Group 1/2/3 = 4

8 - 4 - 1 - 1 = 2, which means that the "group 1 only" part of the venn diagram has 2 people in it.
Image

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1