In Plutarch Enterprises, 70% of the employees are marketers, 20% are engineers, and the rest are managers. Marketers

[B BTGmoderatorDC]

In Plutarch Enterprises, 70% of the employees are marketers, 20% are engineers, and the rest are managers. Marketers make an average salary of $50,000 a year, and engineers make an average of $80,000. What is the average salary for managers if the average for all employees is also $80,000?

A. $80,000
B. $130,000
C. $240,000
D. $290,000
E. $320,000


OA D

Source: Magoosh

[Scott@TargetTestPrep]

In Plutarch Enterprises, 70% of the employees are marketers, 20% are engineers, and the rest are managers. Marketers make an average salary of $50,000 a year, and engineers make an average of $80,000. What is the average salary for managers if the average for all employees is also $80,000?

A. $80,000
B. $130,000
C. $240,000
D. $290,000
E. $320,000


OA D

Solution:

We can let the total number of employees at Plutarch Enterprises be 10. So 7 are marketers, 2 are engineers, and 1 is a manager. Letting n = the salary of the manager, we can create the equation:

(7 x 50,000 + 2 x 80,000 + n) / 10 = 80,000

350,000 + 160,000 + n = 800,000

510,000 + n = 800,000

n = 290,000

Answer: D

[Brent@GMATPrepNow]

In Plutarch Enterprises, 70% of the employees are marketers, 20% are engineers, and the rest are managers. Marketers make an average salary of $50,000 a year, and engineers make an average of $80,000. What is the average salary for managers if the average for all employees is also $80,000?

A. $80,000
B. $130,000
C. $240,000
D. $290,000
E. $320,000


OA D

Source: Magoosh

We can solve this using weighted averages

Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + . . .

We're told that:
The marketers (with an average annual salary of $50,000) comprise 7/10 of the group
The engineers (with an average annual salary of $80,000) comprise 2/10 of the group
The managers (with an average annual salary of $x) comprise 1/10 of the group
The average salary of all groups COMBINED = 80,000

Applying the formula we get: 80,000 = (7/10)($50,000) + (2/10)($80,000) + (1/10)(x)
Simplify: 80,000 = 35,000 + 16,000 + 0.1x
Simplify: 80,000 = 51,000 + 0.1x
We get: 29,000 = 0.1x
Solve: x = 290,000

Answer: D

[D deloitte247]

Marketers = 70%
Engineers = 20%
Total employees = 100%
Managers = 100 - (70+20) = 10%
Marketers average salary per year = $50000
Engineers average salary per year = $80000

Target question => What is the average salary for managers if the average salary of all employees = $80000
Using metered average:
Weighted average of combined terms = (proportion of 1st term) * (Average of 1st term) + (proportion of nth term) * (average of the nth term)
$$80000=\left(\frac{70}{100}\cdot50000\right)+\frac{20}{100}\cdot80000+\left(\frac{10}{100}\cdot x\right)$$
80000 = 35000 + 16000 + 0.1x
80000 = 51000 + 0.1x
0.1x = 29000
x = 29000/0.1 = 29000 (Answer = option D)