2023 AMC 10A Problem 12

How many three-digit positive integers N satisfy the following properties?

• The number N is divisible by 7.

• The number formed by reversing the digits of N is divisible by 5.

\textbf{(A)} 13 \qquad \textbf{(B)} 14 \qquad \textbf{(C)} 15 \qquad \textbf{(D)} 16 \qquad \textbf{(E)} 17

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.