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D.S overlapping sets

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D.S overlapping sets

by divyalr » Tue Oct 13, 2009 6:02 pm
At a college party, 70% of the women are wearing red t-shirts. If 60% of the people at the party are wearing red t-shirts, what is the ratio of women to men at the party?

1) Forty percent of the men at the party are wearing red t-shirts.

2) There are 120 people at the party.

I think the answer is C. Please let me know.
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by grockit_jake » Wed Oct 14, 2009 1:24 pm
The key here is that they are asking for the ratio of women to men. So the absolute number of each is not necessarily needed.

With Statement 1, we know:

7/10W + 4/10M = 6/10(M+W)

7W + 4M = 6M + 6W
W = 2M
W/M = 2

Again, this only tells us that the ratio of W:M is 2:1, and doesn't tell us how many of each, but the question only asks for the ratio. Statement 1 is sufficent

With Statement 2, we know:

7/10W + x/100M = 3/5(120)= 72

70W+xM = 72
M + W = 120

Since there are 3 variables and 2 equations, we can't figure it out. Namely, you can think about the variation of W's, and how the M figure could vary accordingly and still satisfy the M + W = 120 requirement. Statement 2 is insufficient.
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by kanagasu » Fri Sep 24, 2010 7:11 am
I thought the answer was A. When we need to know only the ratio, I don't think we need to find the individual values as well.. Correct me if am wrong.

Regards,
SURESH
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by kmittal82 » Fri Sep 24, 2010 7:39 am
Should be (A)

Let there be M men, and W women

total people wearing red tshirt = 0.6(M+W)
We also know number of women wearing red tshirt = 0.7W

Stmt 1)

Total number of people wearing red tshirt = men with red tshirt + women with red-tshirt

=> 0.6(M+W) = 0.4M + 0.7W

Solve to get W/M = 1/2

Sufficient to answer the question.
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