Akash720 wrote:

Bunuel wrote:

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'm poor with Percentages. Please let me know if the below answer is wrong.

Given:

Women with Red T-Shirts, W = 70%

Total people with Red T shirts, P = 60%

Total People at Party = P

Total Women at Party = W

Total Men at Party = M

Find - W/M

Statement 1:

Men with Red T-Shirts, M = 40%

Insufficient as we don't know the total number of people, Total percentage of Women/Men.

Statement 2:

Total People at Party = 120

We can find the number of people wearing Red T shirts at the party i.e., 60% of 120 = 72.

But we don't know the number/percentage of Women/Men at the party

Hence insufficient

Statement 1 & 2:

Insufficient. We still don't get the percentage of Women/Men at the party to find the ratio.

Answer: E

No of women at party: W

No of men at party: M

No of women wearing Red t shirt: Wr

No of men wearing Red t shirt: Mr

Total No of people at party:W+M

Now,

Given:

70% of the women are wearing red t-shirts : \(Wr=\frac{70W}{100}\) .....................................(1)

60% of the people at the party are wearing red t-shirts : \((Wr+Mr)=\frac{60(W+M)}{100}\) ......(2)

To Calculate:

\(\frac{W}{M}\)

Statement1: Forty percent of the men at the party are wearing red t-shirts.

Therefore, \(Mr=\frac{40M}{100}\)

Adding (1) to Mr above:

(Wr+Mr) = \(\frac{70W}{100}+\frac{40M}{100}\)

=\(\frac{(7W+4M)}{10}\)

Equating the above equation with (2)

We get, \((7W+4M)=6(W+M)\)

This implies, W=2M

or, \(\frac{W}{M}=2\)

Sufficient.Statement1: There are 120 people at the party

Therefore, M+W=120

We nee

d either M or W to solve this equation. We have neither.

Hence, InSufficient.Hence, the Answer is A

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R.

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