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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] New post 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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Re: Percent Problem [#permalink] New post 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}.

Answer: D.
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Re: Percent Problem [#permalink] New post 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

Answer: 4/5 : D

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Corporation employees..... [#permalink] New post 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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Re: Percent Problem [#permalink] New post 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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Re: Percent Problem [#permalink] New post 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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GWD #1 Math 11 [#permalink] New post 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] New post 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


Merging similar topics. Please ask if anything remains unclear.
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: GWD #1 Math 11 [#permalink] New post 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] New post 02 Jun 2012, 18:06
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Re: In a corporation, 50 percent of the male employees and 40 [#permalink] New post 23 Sep 2013, 10:39
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Re: In a corporation, 50 percent of the male employees and 40 [#permalink] New post 28 Sep 2014, 12:36
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Re: In a corporation, 50 percent of the male employees and 40 [#permalink] New post 28 Sep 2014, 23:20
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}

Answer = E
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Re: In a corporation, 50 percent of the male employees and 40   [#permalink] 28 Sep 2014, 23:20
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