mgmt_gmat wrote:A club with a total membership of 30 has formed 3 committees, M, S, and R, which have
8, 12, and 5 members, respectively. If no member of committee M is on either of the
other 2 committees, what is the greatest possible number of members in the club who are
on none of the committees?
A. 5
B. 7
C. 8
D. 10
E. 12
If no member of committee M is on either of the other 2 committees, then two cases arise:
1. The other 2 committees, S and R have member(s) in common.
2. The other 2 committees, S and R do not have a member in common.
For maximizing the number of members in the club who are on none of the committees, we will have to take the case 1 at its best in minimizing the net number of members in the other 2 committees, S and R.
When M is already away with 8 members, we are left with 22 members to discuss. If R is contained in S, n (S ∪ R) = n (S) = 12.
Hence, at most [spoiler]
10 (
subtracted 17 in place of 12 from 22, initially, hence edited)[/spoiler] members in the club could be on none of the committees.
[spoiler]
D[/spoiler]
Last edited by
sanju09 on Fri Feb 12, 2010 6:07 am, edited 1 time in total.
The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
