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At a certain company, the average (arithmetic mean) salary of 10 of

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At a certain company, the average (arithmetic mean) salary of 10 of  [#permalink]

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New post 30 Jun 2017, 02:34
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At a certain company, the average (arithmetic mean) salary of 10 of the employees is $30,000, the average salary of 30 other employees is $40,000, and the average salary of the remaining 20 employees is $60,000. What is the average salary of the 60 employees at the company?

(A) $40,000
(B) $43,000
(C) $45,000
(D) $50,000
(E) $55,000

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Re: At a certain company, the average (arithmetic mean) salary of 10 of  [#permalink]

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New post 30 Jun 2017, 03:12
Bunuel wrote:
At a certain company, the average (arithmetic mean) salary of 10 of the employees is $30,000, the average salary of 30 other employees is $40,000, and the average salary of the remaining 20 employees is $60,000. What is the average salary of the 60 employees at the company?

(A) $40,000
(B) $43,000
(C) $45,000
(D) $50,000
(E) $55,000


Average salary of \(10\) employees \(= $30,000\)

Total Salary of \(10\) employees \(= 30,000 * 10 = 300,000\)

Average salary of \(30\) employees \(= $40,000\)

Total Salary of \(30\) employees \(= 40,000 * 30 = 1,200,000\)

Average salary of \(20\) employees \(= $60,000\)

Total Salary of \(20\) employees \(= 60,000 * 20 = 1,200,000\)

Total number of employees \(= 60\)

Total Salary of \(60\) employees \(= 1,200,000 + 1,200,000 + 300,000 = 2,700,000\)

Average salary of \(60\) employees \(= \frac{2,700,000}{60} = $45,000\)

Answer (C)...
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Re: At a certain company, the average (arithmetic mean) salary of 10 of  [#permalink]

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New post 30 Jun 2017, 09:21
Bunuel wrote:
At a certain company, the average (arithmetic mean) salary of 10 of the employees is $30,000, the average salary of 30 other employees is $40,000, and the average salary of the remaining 20 employees is $60,000. What is the average salary of the 60 employees at the company?

(A) $40,000
(B) $43,000
(C) $45,000
(D) $50,000
(E) $55,000

\(\frac{(10*30000) + (30*40000) + (20*60000)}{10 + 30 + 20}\)

= \(\frac{300000 + 1200000 + 1200000}{60}\)

= \(\frac{2700000}{60}\)

= \(45000\)

Thus, the answer must be (C)
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Re: At a certain company, the average (arithmetic mean) salary of 10 of  [#permalink]

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New post 30 Jun 2017, 09:35
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10*30 + 30*40 + 20*60 = 2700. The only option that has a perfect divisor of 2700 is (C) (since 45 * 60 = 2700). Eliminate others. Answer is Option (C).
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Re: At a certain company, the average (arithmetic mean) salary of 10 of  [#permalink]

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New post 02 Jul 2017, 09:06
Since every number is very round, therefore, we can easily reduce to case to one digit number for employees and two digit numbers for income and just multiply to a 1000 when the final average is gotten.

\(\frac{1*30+3*40+2*60}{6} = \frac{270}{6}=45 * 1000\)

Therefore, option C
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Re: At a certain company, the average (arithmetic mean) salary of 10 of  [#permalink]

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New post 04 Jul 2017, 08:15
Bunuel wrote:
At a certain company, the average (arithmetic mean) salary of 10 of the employees is $30,000, the average salary of 30 other employees is $40,000, and the average salary of the remaining 20 employees is $60,000. What is the average salary of the 60 employees at the company?

(A) $40,000
(B) $43,000
(C) $45,000
(D) $50,000
(E) $55,000


We can create the following equation for a weighted average:

(10 x 30,000 + 30 x 40,000 + 20 x 60,000)/60

(300,000 + 1,200,000 + 1,200,000)/60

2,700,000/60

45,000

Answer: C
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Re: At a certain company, the average (arithmetic mean) salary of 10 of   [#permalink] 04 Jul 2017, 08:15
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