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The number must be 42.
The secret number must be a two-digit number greater than 25 and less than 50. Since the tens digit is odd, it can be 3, 5, or 7. However, the sum of the digits must be less than 10, so the only possible tens digit is 3. The units digit can be any number from 0 to 9 that, when added to 3, results in a sum less than 10. Therefore, the secret number is 31.