In Plutarch Enterprises, 70% of the employees are marketers,

If the overall average is $80,000, and the engineers' average is $80,000, we can just ignore the engineers, because including them won't change the average. Since 70% of employees are marketers and 10% are managers, the ratio of marketers to managers is 7 to 1. So, by alligation principles, the distance from the managers' average salary to the overall average will be 7 times as big as the distance from the marketers' salary to the overall average. Since the marketers are $30,000 below average, the managers will be $210,000 above average, so they'll make $290,000.

BTGmoderatorDC wrote: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 let the total number of employees in 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

BTGmoderatorDC wrote: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

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

For more information on weighted averages, watch this video: https://www.gmatprepnow.com/module/gmat- ... ics?id=805