ScottTargetTestPrep wrote:

duahsolo wrote:

In the department of Mathematics at Green University, more than half of the professors have an income in excess of $80,000 a year. Which of the following cannot be the average (arithmetic mean) annual income of the professors in the department?

A) $160,000

B) $120,000

C) $50,000

D) $45,000

E) $40,000

Let’s assume that exactly half of the professors make exactly $80,000 a year. Even if the other half of the professors do not make a penny, the average annual income of all of the professors would be exactly $40,000. However, since we are given that more than half of the professors make more than $80,000 a year, even if the other half of the professors do not make a penny, the average annual income would still be more than $40,000. Thus, answer choice E can’t be the average annual income.

Answer: E

sorry, the solutions are not clear .

lets say there are 6 professors.( more than half is 4.)

now if the average is 50,000 then the total is(6 *50,000) 300,000

more than half earn in excess of 80,000 but even if they earn just 80,000 then half their salary totals :

4*80,000= 320,000, which is already more than the total of 6 professors hence even 50,000 cannot be the average.

lets say there are 6 professors.( more than half is 4.)

now if the average is 45,000 then the total is(6 *45,000) 270,000

more than half earn in excess of 80,000 but even if they earn just 80,000 then half their salary totals :

4*80,000= 320,000, which is already more than the total of 6 professors hence even 45,000 cannot be the average.

hence 3 options seem to satisfy this question.

Am i missing anything ?

_________________

- Stne