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

Redeem

Put on Your Problem Solving Hat II

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 487
Joined: Fri Mar 27, 2009 5:49 am
Thanked: 36 times

Put on Your Problem Solving Hat II

by dtweah » Tue May 12, 2009 6:18 am
The City Council has nine members, who serve on different committees. Each committee has
three members and no two members serve together on more than one committee. Determine the
largest possible number of committees.

a. 9
b. 10
c. 12
d. 13
e. 24
Top
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 238
Joined: Tue Feb 10, 2009 8:44 am
Thanked: 9 times

by avenus » Wed May 13, 2009 4:05 pm
Total number of possible committees 9C3
Every group of two people comes up in 7 different 3-people groups so:

9C3/7 = 12

Answer is C
Top
Master | Next Rank: 500 Posts
Posts: 487
Joined: Fri Mar 27, 2009 5:49 am
Thanked: 36 times

by dtweah » Wed May 13, 2009 4:29 pm
avenus wrote:Total number of possible committees 9C3
Every group of two people comes up in 7 different 3-people groups so:

9C3/7 = 12

Answer is C
Avenues please expound on the above particularly "Every group of two people comes up in 7 different 3-people groups ". I am more interested in the logic than the answer. What led you to 7? Can you build up an argument in a clear way?
Top
Master | Next Rank: 500 Posts
Posts: 238
Joined: Tue Feb 10, 2009 8:44 am
Thanked: 9 times

by avenus » Thu May 14, 2009 5:08 am
dtweah wrote: Avenues please expound on the above particularly "Every group of two people comes up in 7 different 3-people groups ". I am more interested in the logic than the answer. What led you to 7? Can you build up an argument in a clear way?
Sure. 9 people; take 2 of them as the first members of the committee. you have 7 left to choose from for the last member ==> Every pair will appear in 7 of all the possible options. Since we don't want them to be together in more than one committee, we have a 1:7 ratio, so you divide by 7.

does that help?
Top
Post new topic Post Reply
• Page 1 of 1