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16 Sep 2014, 01:02
Kudos
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Half of the company's employees work in manufacturing. If 20% of the employees who do not work in manufacturing are women, what percent of the company's employees are men?
(1) 50% of the company's male employees work in manufacturing.
(2) 20% of the company's employees working in manufacturing are women.
(1) 50% of the company's male employees work in manufacturing.
(2) 20% of the company's employees working in manufacturing are women.
16 Sep 2014, 01:02
Kudos
Bookmarks
Official Solution:
Half of the company's employees work in manufacturing. If 20% of the employees who do not work in manufacturing are women, what percent of the company's employees are men?
Assume the total number of employees is 100. Then 50 employees work in manufacturing, and the remaining 50 employees do not work in manufacturing. Out of the 50 employees who do not work in manufacturing, \(0.2*50=10\) are women and 40 are men.
(1) 50% of the company's male employees work in manufacturing.
Therefore, the remaining 50% of the company's male employees do not work in manufacturing. So, the 40 men who do not work in manufacturing represent 50% of the total male employees: \(0.5* \{\text{total male employees} \} = 40\), which gives \(\{\text{total male employees} \} = 80\). Thus, men constitute 80% of the company's total employees. Sufficient.
(2) 20% of the company's employees working in manufacturing are women.
Therefore, the remaining 80% of the company's employees who work in manufacturing are men. So, \(0.8*50=40\) men work in manufacturing, meaning the total number of male employees is \(40+40=80\), which is 80% of 100. Sufficient.
Answer: D
Half of the company's employees work in manufacturing. If 20% of the employees who do not work in manufacturing are women, what percent of the company's employees are men?
Assume the total number of employees is 100. Then 50 employees work in manufacturing, and the remaining 50 employees do not work in manufacturing. Out of the 50 employees who do not work in manufacturing, \(0.2*50=10\) are women and 40 are men.
(1) 50% of the company's male employees work in manufacturing.
Therefore, the remaining 50% of the company's male employees do not work in manufacturing. So, the 40 men who do not work in manufacturing represent 50% of the total male employees: \(0.5* \{\text{total male employees} \} = 40\), which gives \(\{\text{total male employees} \} = 80\). Thus, men constitute 80% of the company's total employees. Sufficient.
(2) 20% of the company's employees working in manufacturing are women.
Therefore, the remaining 80% of the company's employees who work in manufacturing are men. So, \(0.8*50=40\) men work in manufacturing, meaning the total number of male employees is \(40+40=80\), which is 80% of 100. Sufficient.
Answer: D
General Discussion
06 Nov 2019, 01:11
Kudos
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From the stem, derive the following:
------------------Work------Don't Work
-------Men---------------------40%------------|
---Women---------------------10%------------|
____________________________________
------Total-------50%---------50%------------|100%
In (1) we know that 1/2 males don't work in mfg, which means the 40% in Men(Don't Work) = 1/2 of all men --> Men = 80% of all employees.
In (2), we know that 20% of 50% = 10% of all employees are women who work in mfg. Therefore, only 40% of all employees are men who work in mfg. Therefore, total percentage of employees who are men = 40% who work in mfg + 40% who don't work in mfg (from stem).
From (2), the matrix should look like this:
------------------Work------Don't Work
-------Men-------40%------------40%--------|--80%
---Women-------10%------------10%-------|
____________________________________
------Total--------50%----------50%--------|100%
------------------Work------Don't Work
-------Men---------------------40%------------|
---Women---------------------10%------------|
____________________________________
------Total-------50%---------50%------------|100%
In (1) we know that 1/2 males don't work in mfg, which means the 40% in Men(Don't Work) = 1/2 of all men --> Men = 80% of all employees.
In (2), we know that 20% of 50% = 10% of all employees are women who work in mfg. Therefore, only 40% of all employees are men who work in mfg. Therefore, total percentage of employees who are men = 40% who work in mfg + 40% who don't work in mfg (from stem).
From (2), the matrix should look like this:
------------------Work------Don't Work
-------Men-------40%------------40%--------|--80%
---Women-------10%------------10%-------|
____________________________________
------Total--------50%----------50%--------|100%
