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In Dives Corporation, 75% of the employees are customer service repres

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In Dives Corporation, 75% of the employees are customer service repres [#permalink]

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In Dives Corporation, 75% of the employees are customer service representatives, 15% are programmers, and 10% are managers. The customer service representatives have an average salary of $60,000, and the programmers have an average salary of $100,000. If the average salary of all employees is also $100,000, what is the average salary of the managers?

A. $140,000
B. $180,000
C. $260,000
D. $400,000
E. $560,000
[Reveal] Spoiler: OA

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Re: In Dives Corporation, 75% of the employees are customer service repres [#permalink]

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New post 04 Dec 2017, 04:20
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imo D
let total # of employees be 100 & the average salary of the managers be x
sum of salaries = average salary* number of employees
\(10^7\)= (60,000*75) +(\(10^5\) *15) + 10x
\(10^7\)= 45*\(10^5\) + 15*\(10^5\) +10x
\(10^5\)(100-60)=10x
x= 400,000
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Re: In Dives Corporation, 75% of the employees are customer service repres [#permalink]

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Bunuel wrote:
In Dives Corporation, 75% of the employees are customer service representatives, 15% are programmers, and 10% are managers. The customer service representatives have an average salary of $60,000, and the programmers have an average salary of $100,000. If the average salary of all employees is also $100,000, what is the average salary of the managers?

A. $140,000
B. $180,000
C. $260,000
D. $400,000
E. $560,000


40....100....x (Distance from Mean)

75 * 40 = x * 10
x = 30
Salary of manager = 30 + 10 = 40
D
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In Dives Corporation, 75% of the employees are customer service repres [#permalink]

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New post 11 Dec 2017, 10:30
Bunuel wrote:
In Dives Corporation, 75% of the employees are customer service representatives, 15% are programmers, and 10% are managers. The customer service representatives have an average salary of $60,000, and the programmers have an average salary of $100,000. If the average salary of all employees is also $100,000, what is the average salary of the managers?

A. $140,000
B. $180,000
C. $260,000
D. $400,000
E. $560,000

Weighted average approach.* For easier calculation, remove three zeros from salaries (divide all by 1,000). Obviously, put them back for the answer.

Percentages sum to 100, in decimal form, = 1. They are the weight.
Salaries are the average for each group.
Let $x = managers' average salary

Customer service: .75($60)
Programmers: .15($100)
Managers: .10($x)
Total weight: (.75 + .15 + .10 = 1)
Overall average salary: $100

.75($60) + .15($100) + .10($x) = (1)($100)

$45 + $15 + .10x = $100
.10x = $40
\(x = \frac{40}{.10}=$400\)
(put three zeros back, i.e., $400 * 1,000)
x = $400,000

Answer D

*\((W_1)(A_1) + (W_2)(A_2) + (W_3)(A_3) = (W{1+2+3})(A_{overall})\)
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Re: In Dives Corporation, 75% of the employees are customer service repres [#permalink]

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New post 12 Jan 2018, 07:29
Bunuel wrote:
In Dives Corporation, 75% of the employees are customer service representatives, 15% are programmers, and 10% are managers. The customer service representatives have an average salary of $60,000, and the programmers have an average salary of $100,000. If the average salary of all employees is also $100,000, what is the average salary of the managers?

A. $140,000
B. $180,000
C. $260,000
D. $400,000
E. $560,000


We can let n = the average salary of the managers and create the equation:

0.75(60,000) + 0.15(100,000) + 0.1n = 100,000

45,000 + 15,000 + 0.1n = 100,000

0.1n = 40,000

n = 400,000

Answer: D
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Re: In Dives Corporation, 75% of the employees are customer service repres   [#permalink] 12 Jan 2018, 07:29
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