Statistics And Sets Problems, Word Problems

[swerve]

In a company of only 20 employees, 10 employees make $80,000/yr, 6 employees make $150,000/yr, and the 4 highest-paid employees all make the same amount. If the average annual salary for the 20 employees is $175,000/yr, then what is the annual salary of each highest-paid employee?

A. $250,000
B. $300,000
C. $350,000
D. $400,000
E. $450,000

The OA is E

Source: Magoosh

[Brent@GMATPrepNow]

In a company of only 20 employees, 10 employees make $80,000/yr, 6 employees make $150,000/yr, and the 4 highest-paid employees all make the same amount. If the average annual salary for the 20 employees is $175,000/yr, then what is the annual salary of each highest-paid employee?

A. $250,000
B. $300,000
C. $350,000
D. $400,000
E. $450,000

The OA is E

Source: Magoosh

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

NOTE: To make things easier, let's drop the thousands and write $80 instead of $80,000

Let x = the annual salary of each highest-paid employee
Plug values into the formula to get: 175 = (10/20)(80) + (6/20)(150) + (4/10)(x)
Simplify: 175 = 40 + 45 + x/5
Simplify: 90 = x/5
Solve: x = 450

So, the annual salary of each highest-paid employee is $450,000
Answer: E