In a corporation, 50 percent of the male employees and 40 : GMAT Problem Solving (PS)
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# In a corporation, 50 percent of the male employees and 40

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In a corporation, 50 percent of the male employees and 40 [#permalink]

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26 Aug 2010, 06:40
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In a corporation, 50 percent of the male employees and 40 percent of the female employees are at least 35 years old. If 42 percent of all the employees are at least 35 years old, what fraction of the employees in the corporation are females?

A. 3/5
B. 2/3
C. 3/4
D. 4/5
E. 5/6
[Reveal] Spoiler: OA
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26 Aug 2010, 07:12
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udaymathapati wrote:
In a corporation, 50 percent of the male employees and 40 percent of the female
employees are at least 35 years old. If 42 percent of all the employees are at least 35
years old, what fraction of the employees in the corporation are females?
A. 3/5
B. 2/3
C. 3/4
D. 4/5
E. 5/6

Given weighted average employees who are at least 35 years old: $$\frac{0.5m+0.4f}{m+f}=0.42$$. Question: $$\frac{f}{m+f}=?$$

$$\frac{0.5m+0.4f}{m+f}=0.42$$ --> $$50m+40f=42m+42f$$ --> $$4m=f$$ --> $$\frac{f}{m}=4$$ --> $$\frac{f}{m+f}=\frac{4}{5}$$.

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26 Aug 2010, 08:46
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I have a different approach that may be useful for you:

Let's say that “x” is the % of male employees in the corporation. So, (1-x) is the % of female employees in the same company.
Therefore:
$$(50%)(x) + (40%)(1-x) = 42%$$

Expressed in fractions:
$$(1/2)(x) + (2/5)(1-x) = 21/50$$

We solve the equation and we have:
$$x = 1/5$$

$$(1-x) = 4/5$$

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15 Oct 2010, 02:34
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In corporation, 50% of the male employees and 40% of the female employees are at least 35 years old. If 42 employees of all the employees are at least 35 years old. What fraction of the employees in the corporation are females?
A) 3/5
B) 2/3
C) 3/4
D) 4/5
E) 5/6
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19 Oct 2010, 06:58
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Hi Buneul -

I understood your explanation until the last step. How do you get from f/m= 4 to the 4/5?

Thanks!
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19 Oct 2010, 13:33
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Atrain13gm wrote:
Hi Buneul -

I understood your explanation until the last step. How do you get from f/m= 4 to the 4/5?

Thanks!

$$4m=f$$ --> $$\frac{f}{m+f}=\frac{4m}{m+4m}=\frac{4m}{5m}=\frac{4}{5}$$.

Hope it's clear.
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05 Apr 2012, 12:01
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In a corporation, 50 percent of the male employees and 40 percent of the female employeesa re at least 35 years old. If 42 percent of all the employees are at least 35 years old, what fraction of the employees in the corporation are females?

a) 3/5

b) 2/3

c) 3/4

d) 4/5

e) 5/6
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Re: GWD #1 Math 11 [#permalink]

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05 Apr 2012, 12:05
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eybrj2 wrote:
In a corporation, 50 percent of the male employees and 40 percent of the female employeesa re at least 35 years old. If 42 percent of all the employees are at least 35 years old, what fraction of the employees in the corporation are females?

a) 3/5

b) 2/3

c) 3/4

d) 4/5

e) 5/6

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Re: GWD #1 Math 11 [#permalink]

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05 Apr 2012, 19:34
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eybrj2 wrote:
In a corporation, 50 percent of the male employees and 40 percent of the female employeesa re at least 35 years old. If 42 percent of all the employees are at least 35 years old, what fraction of the employees in the corporation are females?

a) 3/5

b) 2/3

c) 3/4

d) 4/5

e) 5/6

You can use the weighted averages formula for a 10 sec solution.

No of females/No of males = (50 - 42)/(42 - 40 ) = 4/1

No of females as a fraction of total employees = 4/(4+1) = 4/5

For details of this method, check: http://www.veritasprep.com/blog/2011/03 ... -averages/
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Re: In a corporation, 50 percent of the male employees and 40 [#permalink]

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02 Jun 2012, 18:06
your post on veritas blog is amazing Karishma
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Re: In a corporation, 50 percent of the male employees and 40 [#permalink]

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23 Sep 2013, 10:39
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Re: In a corporation, 50 percent of the male employees and 40 [#permalink]

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28 Sep 2014, 12:36
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Re: In a corporation, 50 percent of the male employees and 40 [#permalink]

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28 Sep 2014, 23:20
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Let Male employees = x

Let Female employees = y

Total Employees = x+y

We require to find $$\frac{y}{x+y}$$

Setting up the equation:

$$\frac{50x}{100} + \frac{40y}{100} = \frac{42}{100} (x+y)$$

$$\frac{y}{x} = 4$$

$$\frac{y}{x+y} = \frac{4}{1+4} = \frac{4}{5}$$

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Re: In a corporation, 50 percent of the male employees and 40 [#permalink]

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04 Oct 2015, 10:32
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Re: In a corporation, 50 percent of the male employees and 40 [#permalink]

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05 Oct 2015, 20:42
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x- total number of employees
f - all females
x-f - all males

we need f/x

50(x-f)+40f=42x
50x-50f+40f=42x
10f=8x
f/x=8/10=4/5

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Re: In a corporation, 50 percent of the male employees and 40 [#permalink]

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22 Aug 2016, 06:08
.5m+.40f=.42
m+f=1

solve these two equations,
f=4/5
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Re: In a corporation, 50 percent of the male employees and 40 [#permalink]

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06 Nov 2016, 19:47
I used the 2 way chart to help create the expression :

(50/100)x + (40/100)y = 42/100(x+y) .... where x is number of males, y is number of females and x+y is total.

Now when you simplify it, you will get 4x = y. Means for every 4 females there is 1 male... No of females is 80% or 4/5
Re: In a corporation, 50 percent of the male employees and 40   [#permalink] 06 Nov 2016, 19:47
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