1. Determine the digits $x, y$ so that the number $\overline{x 74 y}$ is divisible by 15.
Solution. Since the number $\overline{x 74 y}$ is divisible by 15, it is divisible by 3 and by 5, so $y$ can be 0 or 5.

If $y=0$, then from divisibility by 3 it follows that the sum of the digits $x+7+4+0=x+11$ is divisible by 3, which is possible if $x=1$ or $x=4$ or $x=7$, thus we get the numbers 1740, 4740, and 7740.

If $y=5$, then again from divisibility by 3 it follows that the sum of the digits $x+7+4+5=x+16$ is divisible by 3, which is possible if $x=2$ or $x=5$ or $x=8$, so we get the numbers 2745, 5745, and 8745.