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# 20% of employees are women with fair hair. 40% of

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Manager
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20% of employees are women with fair hair. 40% of [#permalink]

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15 Mar 2011, 15:45
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20% of employees are women with fair hair. 40% of fair-haired employees are women. What percent of employees have fair hair?

A. 25
B. 30
C. 50
D. 55
E. 60
[Reveal] Spoiler: OA

Last edited by Bunuel on 03 May 2012, 11:28, edited 1 time in total.
Edited the question and added the OA
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Re: GC) 20% of employees are women with fair hair. 40% of fair-h [#permalink]

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15 Mar 2011, 17:23
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I came up with (C) 50

Think of 100 people total:
From the first fact, 20 of these are women with fair hair.
From the second fact, these 20 women make up 40% of the total fair haired population.
We can then make a ratio of 60:40 fair haired men to fair haired women.
This means that (60/40)*20 equals the number of fair haired men, which is 30 men with fair hair.
Add this 30 to the 20 women and get 50 fair haired men and women out of 100 total men and women.

50%
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Re: GC) 20% of employees are women with fair hair. 40% of fair-h [#permalink]

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15 Mar 2011, 18:32
banksy wrote:
GC) 20% of employees are women with fair hair. 40% of fair-haired employees are women. What percent of employees have fair hair?
(A) 25
(B) 30
(C) 50
(D) 55
(E) 60

20% of employees are women with fair hair.
40% of fair-haired employees are women.

So,
20% * Employees = 40% * Fair Haired Employees (because both are equal to the number of fair haired women employees)
(1/2) * Employees = Fair Haired Employees

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Re: GC) 20% of employees are women with fair hair. 40% of fair-h [#permalink]

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15 Mar 2011, 20:22
Let x -> Total # of employees and y -> Employees with fair hair

So y/x = ?

0.2x = women with fair hair

0.4y = women

Both of these are equal, so 0.2x = 0.4y => y/x = 1/2, so the answer is 50.
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Re: GC) 20% of employees are women with fair hair. 40% of fair-h [#permalink]

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03 May 2012, 11:26
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I think this is a better and faster approach.
lets say the total number of employees is 100
20% of employees are women with fair hair
so 20 women have fair hair out of 100

the problem says that 40% of the fair-haired employees are women and asks what percent of the employees (t) have fair hair

so ===> 0.4t=20
t=50
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Re: GC) 20% of employees are women with fair hair. 40% of fair-h [#permalink]

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03 May 2012, 11:40
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Expert's post
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santivilla wrote:
I think this is a better and faster approach.
lets say the total number of employees is 100
20% of employees are women with fair hair
so 20 women have fair hair out of 100

the problem says that 40% of the fair-haired employees are women and asks what percent of the employees (t) have fair hair

so ===> 0.4t=20
t=50

Welcome to GMAT Club.

There is a little problem with your reasoning: you assumed that the total # of employees is 100, so t in your solution should denote Fair Haired Employees.

If 20% of employees are women with fair hair. 40% of fair-haired employees are women. What percent of employees have fair hair?
A. 25
B. 30
C. 50
D. 55
E. 60

Say the total # of employees is 100 --> then {Fair Haired Women}=0.2*100=20;

Since 40% of fair-haired employees are women then 0.4*{Fair Haired Employees}=20 --> {Fair Haired Employees}=50, which is 50% of 100.

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Re: 20% of employees are women with fair hair. 40% of [#permalink]

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03 May 2012, 18:13
i answered this, good, but i took 3 mins...
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Re: 20% of employees are women with fair hair. 40% of [#permalink]

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10 Dec 2014, 11:56
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20% of employees are women with fair hair. 40% of [#permalink]

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11 Dec 2014, 01:22
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Say total employees = 100

Women with fair hair = 20

Say total fair hair employees = x

Given that 40% of total fair hair employees are women

So, $$\frac{40x}{100} = 20$$

$$x = 20*\frac{100}{40} = 50$$

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20% of employees are women with fair hair. 40% of [#permalink]

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28 Nov 2016, 07:27
Bunuel wrote:
santivilla wrote:
I think this is a better and faster approach.
lets say the total number of employees is 100
20% of employees are women with fair hair
so 20 women have fair hair out of 100

the problem says that 40% of the fair-haired employees are women and asks what percent of the employees (t) have fair hair

so ===> 0.4t=20
t=50

Welcome to GMAT Club.

There is a little problem with your reasoning: you assumed that the total # of employees is 100, so t in your solution should denote Fair Haired Employees.

If 20% of employees are women with fair hair. 40% of fair-haired employees are women. What percent of employees have fair hair?
A. 25
B. 30
C. 50
D. 55
E. 60

Say the total # of employees is 100 --> then {Fair Haired Women}=0.2*100=20;

Since 40% of fair-haired employees are women then 0.4*{Fair Haired Employees}=20 --> {Fair Haired Employees}=50, which is 50% of 100.

Hi Bunuel,

Isn't it wrong to say that

0.4*{Fair Haired Employees}=20

20 is the number that represents 'woman with fair hair' !!!

I think the question is wrong. 60 is equally a correct answer.
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Re: 20% of employees are women with fair hair. 40% of [#permalink]

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28 Nov 2016, 07:32
undefinedrahulraj wrote:
Bunuel wrote:
santivilla wrote:
I think this is a better and faster approach.
lets say the total number of employees is 100
20% of employees are women with fair hair
so 20 women have fair hair out of 100

the problem says that 40% of the fair-haired employees are women and asks what percent of the employees (t) have fair hair

so ===> 0.4t=20
t=50

Welcome to GMAT Club.

There is a little problem with your reasoning: you assumed that the total # of employees is 100, so t in your solution should denote Fair Haired Employees.

If 20% of employees are women with fair hair. 40% of fair-haired employees are women. What percent of employees have fair hair?
A. 25
B. 30
C. 50
D. 55
E. 60

Say the total # of employees is 100 --> then {Fair Haired Women}=0.2*100=20;

Since 40% of fair-haired employees are women then 0.4*{Fair Haired Employees}=20 --> {Fair Haired Employees}=50, which is 50% of 100.

Hi Bunuel,

Isn't it wrong to say that

0.4*{Fair Haired Employees}=20

20 is the number that represents 'woman with fair hair' !!!

I think the question is wrong. 60 is equally a correct answer.

How did you get 60? Anyway, the question is correct and the answer is 50% as shown in several solutions above.
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Re: 20% of employees are women with fair hair. 40% of [#permalink]

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21 Dec 2016, 17:09
Assume Total employees = 100
20 Employees = Fair hair women
40% of fair = women
40% of fair = 20
Fair hair = 50
C
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Re: 20% of employees are women with fair hair. 40% of   [#permalink] 21 Dec 2016, 17:09
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