AMC 12 2025 Part B Problem 4

The value of the two-digit number \underline{a} \ \underline{b} in base seven equals the value of the two-digit number \underline{b} \ \underline{a} in base nine. What is a+b?

Answer Choices:

A. 7

B. 9

C. 10

D. 11

E. 14