In the department of Mathematics at Green University, more than half o

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 ?

let's say there are 10 professors:

more than half is 6, if they are earning 80,000 than there earnings combined reaches 4,80,000 and lets say there rest 4 do not make any money, then in such a case total would be 480000.

and the average would be 4,80,000/10 = 48000, thus there are two options answer now, 45000 and 40,000.

I believe there is some issue with the questions.