The number 52A8 is divisible by 12, where A is a single digit. Which of the following can A be?

Explanation

1. 01

   Divisible by 12 means divisible by both 3 and 4.

2. 02

   For 3: $5 + 2 + A + 8 = 15 + A$ must be a multiple of 3, so A is 0, 3, 6 or 9.

3. 03

   For 4: the last two digits A8 must be divisible by 4; 38 is not, 68 is. (4 and 5 already fail the test for 3.)

4. 04

   So $A = 6$ $(5{,}268 = 12 \times 439)$.