For some positive integer k, the repeating bas-k representation of the (base-ten) fraction \dfrac{7}{51} is 0.\overline{23}_k =0.23232323\cdots_k. What is k?

**Answer Choices**

A. 13

B. 14

C. 15

D. 16

E. 17

For some positive integer k, the repeating bas-k representation of the (base-ten) fraction \dfrac{7}{51} is 0.\overline{23}_k =0.23232323\cdots_k. What is k?

**Answer Choices**

A. 13

B. 14

C. 15

D. 16

E. 17