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

Question

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

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

TaN1213 · Answer

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

Luckisnoexcuse · Answer

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

75 * 40 = x * 10
x = 30
Salary of manager = 30 + 10 = 40
D

generis · Answer

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})

ScottTargetTestPrep · Answer

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

EMPOWERgmatRichC · Answer

Hi All,

We're told that in the 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. We're asked if the average salary of ALL employees is also $100,000, then what is the average salary of the MANAGERS. This question can be approached in a variety of different ways - using some variation on the Average Formula. Here's how you can use the concept of a 'Weighted Average' against this prompt.

Since the average salary of ALL employees is $100,000, we can ignore the programmers (since they have an average salary of $100,000 already). This allows us to focus on the customer service representatives and the managers. 75% of the employees are customer service representatives and 10% are managers, so that is a ratio of 7.5 to 1 (meaning for every 1 manager, there are 7.5 customer service reps).

Customer service reps have an average salary of $60,000, so each rep is essentially $40,000 BELOW the average. This difference has to be 'made up' by the managers. For every 7.5 customer service reps, we'll be (7.5)($40,000) = $300,000 total below what the average is supposed to be, so the 1 manager will have to 'make up' that $300,000 AND have a $100,000 salary to match the average. This means that each manager would need to earn $300,000 + $100,000 = $400,000 to balance out the average.

Final Answer:  D

GMAT assassins aren't born, they're made, 
Rich

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

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