A3 Tanya and Katya made an experiment and obtained two positive real numbers, each of which was between 4 and 100 inclusive. Tanya wrote the two numbers $x$ and $y$ and found their average while Katya wrote the second number twice and took the average of the three numbers $x, y$, and $y$. What is the maximum number by which their results may differ?
Answer: 16

Solution:
Tanya's calculation is $\frac{x+y}{2}$ and Katya's is $\frac{x+2 y}{3}$. We want the positive difference of these two quantities; after taking the common denominator of 6 , this is
$$
\left|\frac{3 x+3 y-2 x-4 y}{6}\right|=\left|\frac{x-y}{6}\right| \text {. }
$$

Since $x$ and $y$ are between 4 and 100, inclusive, the most they can differ is $100-4=96$; in this case, the difference between Tanya's calculation and Katya's calculation is $\frac{96}{6}=16$.