11. When the positive integer $b$ has the value $(\quad)$, $(2021)_{b}-(221)_{b}$ in base $b$ is not divisible by 3.
(A) 3
(B) 4
(C) 6
(D) 7
(E) 8
11. E.
$$
\begin{aligned}
& (2021)_{b}-(221)_{b} \\
= & 2 \times b^{3}+0 \times b^{2}+2 \times b+1 \times b^{0}- \\
& \left(2 \times b^{2}+2 \times b+1 \times b^{0}\right) \\
= & 2 b^{2}(b-1) \not \equiv 0(\bmod 3) .
\end{aligned}
$$

Thus, \( b \not \equiv 0(\bmod 3) \), \( b \neq \equiv 1(\bmod 3) \). Therefore, \( b \equiv 2(\bmod 3) \).