T'm thinking of a number. The number is odd. The number is a multiple of 3 . The number is less than \( 5 \cdot 8+17 \). The number is greater than \( 4^{2} \). The sum of its digits is divisible by 12 . What is the number? A. 39 B. 48 C. 57 D. Not enough information to know

1. Determine the upper bound: - The number is less than \( 5\cdot 8 + 17 \). Calculate: \[ 5\cdot 8+17 = 40+17 = 57. \] - Thus, the number is less than \( 57 \). 2. Determine the lower bound: - The number is greater than \( 4^{2} \): \[ 4^{2}=16. \] - Thus, the number is greater than \( 16 \). 3. List additional conditions: - The number is odd. - The number is a multiple of \( 3 \). - The sum of its digits is divisible by \( 12 \). 4. Find candidates that meet the first set of conditions: - The odd multiples of \( 3 \) between \( 16 \) and \( 57 \) are: \[ 21,\, 27,\, 33,\, 39,\, 45,\, 51. \] 5. Check the sum of the digits for each candidate: - For \( 21 \): \( 2 + 1 = 3 \) (not divisible by \( 12 \)). - For \( 27 \): \( 2 + 7 = 9 \) (not divisible by \( 12 \)). - For \( 33 \): \( 3 + 3 = 6 \) (not divisible by \( 12 \)). - For \( 39 \): \( 3 + 9 = 12 \) (divisible by \( 12 \)). - For \( 45 \): \( 4 + 5 = 9 \) (not divisible by \( 12 \)). - For \( 51 \): \( 5 + 1 = 6 \) (not divisible by \( 12 \)). 6. Conclusion: - The only number that meets all the conditions is \( 39 \). Answer: A. 39