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

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Math Expert
Joined: 02 Sep 2009
Posts: 47920
At a college party, 70% of the women are wearing red t-shirts. If 60%  [#permalink]

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18 Jul 2018, 23:42
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Difficulty:

55% (hard)

Question Stats:

59% (01:38) correct 41% (01:56) wrong based on 34 sessions

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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.

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Manager
Joined: 17 Jan 2017
Posts: 136
Location: India
GPA: 4
WE: Information Technology (Computer Software)
Re: At a college party, 70% of the women are wearing red t-shirts. If 60%  [#permalink]

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19 Jul 2018, 00:53
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.

_________________

Correct me If I'm wrong !! looking for valuable inputs

KUDOS please, if you like the post or if it helps !!

Manager
Joined: 05 Feb 2016
Posts: 144
Location: India
Concentration: General Management, Marketing
WE: Information Technology (Computer Software)
Re: At a college party, 70% of the women are wearing red t-shirts. If 60%  [#permalink]

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19 Jul 2018, 01:09
2
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.

Hi Akash720

Lets consider total people as 100X
so 60X wearing tshirt.
in which 70% is women so 42X is female
Therefore 18X is male.
From A it is given 40% male so 40% of M =18X
So total M=45X ,Then total Female will be 55X
so ratio will be 45/55.

We can get sol from A. Total number is not required.
Manager
Joined: 17 Jan 2017
Posts: 136
Location: India
GPA: 4
WE: Information Technology (Computer Software)
At a college party, 70% of the women are wearing red t-shirts. If 60%  [#permalink]

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19 Jul 2018, 01:20
kunalcvrce wrote:
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.

Hi Akash720

Lets consider total people as 100X
so 60X wearing tshirt.
in which 70% is women so 42X is female
Therefore 18X is male.
From A it is given 40% male so 40% of M =18X
So total M=45X ,Then total Female will be 55X
so ratio will be 45/55.

We can get sol from A. Total number is not required.

Hi Kunal

Given data is 70% of women are wearing Red t shirts. So I assume this means there are x women and 70% of x are wearing Red t-shirts. So we really don't have the value of x women.
I hope my concern is clear. Correct me if I'm wrong

Posted from my mobile device
_________________

Correct me If I'm wrong !! looking for valuable inputs

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Manager
Joined: 05 Feb 2016
Posts: 144
Location: India
Concentration: General Management, Marketing
WE: Information Technology (Computer Software)
Re: At a college party, 70% of the women are wearing red t-shirts. If 60%  [#permalink]

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19 Jul 2018, 01:51
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.

Hi Akash720
You are right i misread the question.
Intern
Joined: 18 Apr 2018
Posts: 3
Re: At a college party, 70% of the women are wearing red t-shirts. If 60%  [#permalink]

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19 Jul 2018, 02:41
1
Hi,

I will go with A.
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.

Let Men be "x" and Women be "y". It says that 70% of women are wearing red t-shirts i.e. 7y/10. 60% of the people are wearing red t-shirts i.e. 3(x+y)/5.
1.2x/5 men are wearing red t-shirt. Hence, 2x/5 + 7y/10 = 3(x+y)/5. you get y/x= 2. Sufficient.

2. Insufficient. It just tells (x+y)=120. Doesn't tell anything about either percentage or number of men wearing red t-shirt.

Correct me if i am wrong in my approach.
Manager
Joined: 11 Aug 2016
Posts: 66
At a college party, 70% of the women are wearing red t-shirts. If 60%  [#permalink]

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19 Jul 2018, 05:02
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.

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, $$Mr=\frac{40M}{100}$$
(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 need either M or W to solve this equation. We have neither.
Hence, InSufficient.

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