3. Reverse the order of the four digits of a four-digit number, and add the resulting number to the original number. If the sum obtained is divisible by 35, then this four-digit number is called a "good number". Then, among all four-digit numbers, the number of good numbers is ( ).
(A) 234
(B) 252
(C) 270
(D) 369
3. A.

Let the four-digit number be $\overline{a_{1} a_{2} a_{3} a_{4}}$. Then
$$
\begin{array}{l}
A=\overline{a_{1} a_{2} a_{3} a_{4}}+\overline{a_{4} a_{3} a_{2} a_{1}} \\
=1001\left(a_{1}+a_{4}\right)+110\left(a_{2}+a_{3}\right) .
\end{array}
$$

Since $1001=7 \times 143$, we have
$$
\begin{array}{l}
7 \mid A \Leftrightarrow 7 \mid 110\left(a_{2}+a_{3}\right) \Leftrightarrow 7 \mid \left(a_{2}+a_{3}\right), \\
5 \mid A \Leftrightarrow 5 \mid \left(a_{1}+a_{4}\right) . \\
\text { Then }\left(a_{1}, a_{4}\right) \\
=(1,4),(1,9),(2,3),(2,8),(3,2) \text {, } \\
(3,7),(4,1),(4,6),(5,0),(5,5) \text {, } \\
(6,4),(6,9),(7,3),(7,8),(8,2) \text {, } \\
(8,7),(9,1),(9,6) \text {. } \\
\left(a_{2}, a_{3}\right) \\
=(0,7),(1,6),(2,5),(3,4),(4,3) \text {, } \\
(5,2),(5,9),(6,1),(6,8),(7,0) \text {, } \\
(7,7),(8,6),(9,5) \text {. } \\
\end{array}
$$

Therefore, the number of numbers that satisfy the conditions is $18 \times 13=234$.