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Last year at an accounting firm, accountants made up 40% of

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by hazelnut01 » Sun Apr 02, 2017 2:58 pm
Last year at an accounting firm, accountants made up 40% of the total employees. This year, 50% of these accountants left for another company, and new accountants, which amounts to 50% of the total employees left, joined the company. What percent of the total employees are accountants this year?

A. 10%     
B. 20%      
C. 25%       
D. 30%     
E. 50%

Source : Math Revolution
Official Answer : E
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by [email protected] » Sun Apr 02, 2017 6:47 pm
Hi ziyuenlau,

This is an awkwardly-worded question, but it can be solved by TESTing VALUES.

To start, let's set the TOTAL number of employees at 100. Since 40% of those employees are accountants, we have 40 accountants (out of 100 employees).

Next, we're told that 50% of the ACCOUNTANTS left for another company - thus 20 (of the 40) left. This leaves 80 total employees, of which 20 are accountants.

Then a group of NEW accountants, equal to 50% of the CURRENT number of employees, joined the company. Since there were 80 current total employees, that 50% increase represents 40 NEW accountants. This brings the total number of employees up to 120 and the total number of accountants up to 60. The question asks for the percentage of total employees that are now accountants....

60/120 = 1/2 = 50%

Final Answer: E

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by Jeff@TargetTestPrep » Tue Apr 11, 2017 11:22 am
ziyuenlau wrote:Last year at an accounting firm, accountants made up 40% of the total employees. This year, 50% of these accountants left for another company, and new accountants, which amounts to 50% of the total employees left, joined the company. What percent of the total employees are accountants this year?

A. 10%     
B. 20%      
C. 25%       
D. 30%     
E. 50%
We can let the total number of employees = E. Thus, the number of accountants is 0.4E.

We are given that this year, 50% of these accountants left for another company, so 0.5(0.4E) = 0.2E of the accountants left for another company.Thus, there are 0.8E left at the company.

Now since the number of new accountants who joined the company amounts to 50% of the total employees left, the number of new accountants added to the company is 0.5(0.8E) = 0.4E.

Thus, this year we have a total of 0.4E - 0.2E + 0.4E = 0.6E accountants and a total of E - 0.2E + 0.4E = 1.2E employees. So the percent of the total employees who are accountants this year is:

0.6E/1.2E = 0.6/1.2 = 1/2 = 50%

Answer: E

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