AIMO 2021 Primary 5 — Preliminary (Open Trial 1) Question 19

If $=\frac{1000\times1003}{1001\times1002}$; $B=\frac{1000\times1002}{1001\times1003}$; $C=\frac{1000\times1001}{1002\times1003}$, then which has the greatest value?