Question

For a certain set of five numbers, the mean of all but the largest is 80, and the mean of all but the smallest number is 90. What is the range of the set of five numbers?

Answer 1

if the numbers a,b,c,d,e are sorted in increasing order, then

(a+b+c+d)/4 = 80
(b+c+d+e)/4 = 90

equating the expressions for (b+c+d)/4, we have

80 - a/4 = 90 - e/4
e/4 - a/4 = 10
e-a = 40

the range is thus 40

Answer 2

320,360