13. Let $n$ be a positive integer, $d$ be a digit from 0 to 9, the $n$-ary number $32 d$ converts to the decimal number $263$, and the $n$-ary number 324 converts to the base-6 number $11 d 1$. Then the value of $n+d$ is ( ).
(A) 10
(B) 11
(C) 13
(D) 15
(E) 16
13. B.

From the problem, we have
$$
\begin{array}{l}
\left\{\begin{array}{l}
3 n^{2}+2 n+d=263, \\
3 n^{2}+2 n+4=6^{3}+6^{2}+6 d+1
\end{array}\right. \\
\Rightarrow\left\{\begin{array}{l}
d=2 \\
n=9
\end{array}\right. \\
\Rightarrow n+d=11 .
\end{array}
$$