Question

Eleven members of the Middle School Math Club each paid the same amount for a guest speaker to talk about problem solving at their math club meeting. They paid their guest speaker $1⎯⎯A⎯⎯⎯2⎯⎯ $ 1 A 2 . What is the missing digit A A of this 3 3 -digit number?

Answer 1

A=3

Explanation:

This number, 1A2, must be divisible by 11. Using trial and error, we can quickly find that this number is 132.

BTW: Is this from AoPS by any chance? It looks quite familiar.

Answer 2

SINCE THEY ALL PAID EQUALLY, IT HAS TO BE A MULTIPLE OF 3. BY TRIAL AND ERROR, THE FIRST POSSIBLE MATCH IS 3.. SINCE 132 IS DIVISIBLE BY 11