P.S Overlapping sets

This topic has expert replies
Junior | Next Rank: 30 Posts
Posts: 12
Joined: Wed Jul 23, 2008 6:28 am

P.S Overlapping sets

by divyalr » Tue Oct 13, 2009 7:04 pm
If 20% of the people at a college party were men who were wearing red t-shirts, and 60% of the men at the party were not wearing red t-shirts, what percent of the people at the party were men?

(A) 80 %
(B) 60 %
(C) 50 %
(D) 40 %
(E) 33 1/3 %

I got answer C. Can anyone verify?

Let # of people at party = x
Let # of men at the party = m
.2x = .4m
m/x= 1/2
Question asked : %/100 * x = m
% = 100*m/x = 100*1/2 = 50 ( answer c)
Source: — Problem Solving |

User avatar
GMAT Instructor
Posts: 80
Joined: Wed Aug 12, 2009 8:49 pm
Location: San Francisco, CA
Thanked: 16 times

by grockit_jake » Wed Oct 14, 2009 12:57 pm
It may help to use absolute numbers instead of percentages. We'd use 100, since that's the best with %s.

100 total
20 red shirt + man
40% of men had red T-shirts.

2/5M = 20
M=50

Your way looks correct to me. You can do it algebraically like you did, or use absolutes and plug in where possible. Whatever makes more sense to you.
Jake Becker
Academic Director
Grockit Test Prep
https://www.grockit.com