Data Sufficiency

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.

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.

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

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.