For two positive integers x and y, we have:
(100*x + y)/(x+y) = 1 + (99*x)/(x+y) and,
(100*x + y)/(x+y) = 100-(99*y)/(x+y) . . . . (i)
Since both x and y are positive, we have: x+y > x and x+y > y
Accordingly, x+y does not divide either x or y, and, consequently from (i) we deduce that x+y divides (100*x + y) whenever, (x+y) divides 99.
Now, substituting (x, y) = (20, 16), we have: x+y = 36 which does not divide 99 and consequently we can conclude that 36 does not divide 2016.
However, in reality 2016/36 = 56 and, accordingly the above result is flawed.
Can you spot the error?