The code of Ethan's home lock is simple: it is a two-digit number. The problem is, Ethan forgot what the number is! He still remembers, however, that the first digit is 2, 3, or 4, and the second digit is 5, 6, 7, or 8. List all numbers that might be the lock code.

All numbers that might be the lock code are: 25, 26, 27, 28, 35, 36, 37, 38, 45, 46, 47, and 48.

Step-by-step explanation:

All the numbers that might be the lock code can be determined by combining one of the possible first digits with all of the possible second digits at a time.

From the question,

The first digit is 2, 3, or 4; and the second digit is 5, 6, 7, or 8.

Therefore,

If the first digit is 2, then the lock code might be

25, 26, 27, or 28

If the first digit is 3, then the lock code might be

35, 36, 37, or 38

If the first digit is 4, then the lock code might be

45, 46, 47, or 48.

Hence, all numbers that might be the lock code are:

25, 26, 27, 28, 35, 36, 37, 38, 45, 46, 47, and 48.

the answer to this question is yes