How many even numbers are there with three digits such that if 5 is one of the digits, then 7is the next digit?

Explanation

To solve the problem of how many even three-digit numbers exist such that if 5 is one of the digits, then 7 is the next digit, we can break it down into two cases: when 5 is present and when 5 is not present.

### Step-by-Step Solution:

**Step 1: Count the even numbers without the digit 5.**

1. **Identify the last digit:** Since we are looking for even numbers, the last digit can be one of the even digits: 0, 2, 4, 6, or 8. This gives us 5 options for the last digit.

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