The harmonic mean of two positive integers is the reciprocal of the arithmetic mean of their reciprocals. For how many ordered pairs $(x,y)$ of positive integers is the harmonic mean of $x$ and $y$ equal to $20$?
There are 5 pairs: (12,60), (15,30), (20,20), (30,15), (60,12).
x y
110 11 60 12 35 14 30 15 20 20 15 30 14 35 12 60 11 110
Just count them.
