Question

What is the two-digit number whose first digit is \( a \) and the second digit is \( b \)?
I. The number is a multiple of 6(2)
II. \( a + b = 9 \).

• A. If the statement I alone is sufficient to answer the question.
• B. If the statement II alone is sufficient to answer the question.
• C. If the statements I and II together are sufficient to answer the question but neither statement alone is sufficient.
• D. If the statements I and II together are not sufficient to answer the question and additional data is required.

Hint:

When solving for a specific number, use the given conditions to check possible values that satisfy both the mathematical conditions and logical constraints.

Answer 1

The Correct Option is A

Let the two-digit number be \( 10a + b \), where \( a \) is the tens digit and \( b \) is the ones digit. From condition I: The number is a multiple of 62, so we check the multiples of 62 within the two-digit range: \[ 62 \times 1 = 62 \quad \text{(valid two-digit number)} \] \[ 62 \times 2 = 124 \quad \text{(not a valid two-digit number)} \] So, the number must be 62. From condition II: \( a + b = 9 \), where \( a = 6 \) and \( b = 2 \). Thus, \( 6 + 2 = 9 \), which satisfies the condition. Therefore, the two-digit number is \( 62 \). Thus, the correct answer is \( \boxed{1} \).