Chairs set out in rows of 3 leave 2 over, and in rows of 5 leave 3 over. What is the least number of chairs?

Explanation

1. 01

   We need $x \equiv 2 \pmod{3}$ and $x \equiv 3 \pmod{5}$.

2. 02

   Numbers $\equiv 3 \pmod{5}$: 3, 8, 13, … The first that leaves 2 on division by 3 is 8.