Math Gold Medalist

Lor

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 $5$.

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

General Form of Divisibility Rule

Hundreds digit = 5

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   Solution