General Math Question (Question from Horacio Q.)

[yaoandi]

Here is another data sufficiency problem I need help setting it up:

At a college party, 70% of the women are wearing red t-shirts. If 60% of the people at the party are wearing read 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


Thanks for your help

[julien.pitteloud]

Hallo, nice to meet you. I'm quite new on this forum.

For your problem, we can use conditional probability theorem :

p(red)=0.6=p(red|f)p(f)+p(red|m)p(m)

p(f/m)=probability of being f or m, p(red|m)=prob. having a red T-shirt knowing the gender, p(red|f)=0.7, p(red|m)=0.4

Hence, p(m)=1-p(f) and

0.6=.7p(f)+0.4(1-p(f))=0.4+0.3p(f)

=>p(f)=0.2/0.3=2/3=66.6%=number of f/total

See you.

[tim]

Feel free to use conditional probability if you want, but you'll likely find that this problem is much more approachable if you use a double-set matrix. Your rows should be labeled "female", "male", and "total", and your columns should be labeled "red", "not red", and "total". Start filling in information, and anytime you have two entries in a row or column go ahead and fill in the third. Try this out and then let us know if you need more help..

[yaoandi]

Hi Tim,

I'm still having difficulty setting up the information from the two statements given. I think the answer is E where both statements are not sufficient. Even if we know the total number of people, we still can't figure out.

[debmalya.dutta]

We need to find W/M

From statement 1:
Forty percent of the men at the party are wearing red t-shirts.
40%(M) + 70%(W) = 60%(M+W)
10%W=20%M
W/M=20/10=2

From statement 1:
M+W=120
70%W = women at party wearing read
60%(M+W) = people wearing read = 72
We are stuck here and cannot proceed
We cannot find M . Hence insufficient

Is this the right approach?

[adiagr]

We need to find W/M

From statement 1:
Forty percent of the men at the party are wearing red t-shirts.
40%(M) + 70%(W) = 60%(M+W)
10%W=20%M
W/M=20/10=2

From statement 1:
M+W=120
70%W = women at party wearing read
60%(M+W) = people wearing read = 72
We are stuck here and cannot proceed
We cannot find M . Hence insufficient

Is this the right approach?

Agreed. Answer will be A.

[dinesh19aug]

Feel free to use conditional probability if you want, but you'll likely find that this problem is much more approachable if you use a double-set matrix. Your rows should be labeled "female", "male", and "total", and your columns should be labeled "red", "not red", and "total". Start filling in information, and anytime you have two entries in a row or column go ahead and fill in the third. Try this out and then let us know if you need more help..

I will add to Tim's sattement above and suggest to stick to 2-set matrix. This is a venn diagram 2 set question.

-------------------------------------------------------
|Red Shirt | No Red Shirt | Total |
-------------------------------------------------------
Men | | | 100 - x |
-------------------------------------------------------
Women | 0.7x | | x |
-------------------------------------------------------
Total | 60 | | 100 |

Statement 1: 40% men are in red shirt . So I fill in first cell with 0.4x. See below So I can solve for x ==> 0.4x + 0.7X = 60,
So Men/Women = 110-x/x can be found. SUFFICIENT

-------------------------------------------------------
|Red Shirt | No Red Shirt | Total |
-------------------------------------------------------
Men | 0.4x | | 100 - x |
-------------------------------------------------------
Women | 0.7x | | x |
-------------------------------------------------------
Total | 60 | | 100 |


STATEMENT 2:There are 120 people at the party.
This does not add any new information. INSUFFICIENT

-------------------------------------------------------
|Red Shirt | No Red Shirt | Total |
-------------------------------------------------------
Men | | | 120 - x |
-------------------------------------------------------
Women | 0.7x | | x |
-------------------------------------------------------
Total | 60% of 120 = 72 | | 120 |




HENCE ANS = A

[andreasm.mba]

Dear dinesh19aug,
Thank you for your great explanation regarding the problem with the Red T-Shirts and Male to Female ratio.

I just have one questions regarding the set up of the first statement. 0.4x + 0.7x = 60

Wouldn't it be 0.4(100-x) + 0.7x = 60?
Don't we want to take the unknown total of men?

-------------------------------------------------------
|Red Shirt | No Red Shirt | Total |
-------------------------------------------------------
Men | 0.4x | | 100 - x | ?? --> 0.4(100-x) - in place of 0.4x??
-------------------------------------------------------
Women | 0.7x | | x |
-------------------------------------------------------
Total | 60 | | 100 |


I am not sure if I make a thinking mistake, but in case I do it would be great to have it corrected.

Thank you and I hope to hear from you.

[dinesh19aug]

Dear dinesh19aug,
Thank you for your great explanation regarding the problem with the Red T-Shirts and Male to Female ratio.

I just have one questions regarding the set up of the first statement. 0.4x + 0.7x = 60

Wouldn't it be 0.4(100-x) + 0.7x = 60?
Don't we want to take the unknown total of men?

-------------------------------------------------------
|Red Shirt | No Red Shirt | Total |
-------------------------------------------------------
Men | 0.4x | | 100 - x | ?? --> 0.4(100-x) - in place of 0.4x??
-------------------------------------------------------
Women | 0.7x | | x |
-------------------------------------------------------
Total | 60 | | 100 |


I am not sure if I make a thinking mistake, but in case I do it would be great to have it corrected.

Thank you and I hope to hear from you.

correct. typo mistake.

[andreasm.mba]

Thank you. I appreciate your response.

[StaceyKoprince]

FYI: I'm locking this thread.

This thread is for General Strategy questions only. Specific quant or verbal problems should be posted in the relevant folder for that problem source. Note that we now only accept ManhattanGMAT problems and GMATPrep problems; if you have a problem from a different source, then that problem unfortunately can't be posted on the MGMAT forums.