The Will Rogers Effect

The problem
move one person from A to BGroup A90, 85, 80, 70avg = 81.3Group B60, 55, 50avg = 55.0can both group averages rise simultaneously?

You have two groups of people, each with a numerical value (IQ, salary, score). Each group has an average.

Move one person from group A to group B.

Can the average of both groups go up at the same time? Or does one average always have to fall when the other rises?