2023 AMC 10A Problems/Problem 12

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

• The number is divisible by .

• The number formed by reversing the digits of is divisble by .

Solution 1

Multiples of 5 always end in 0 or 5 and since it is a three digit number, it cannot start with 0. All possibilities have to be in the range from 7 x 72 to 7 x 85 inclusive. 85 - 72 + 1 = 14. .

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