3. A two-digit number $\overline{x y}$ added to the two-digit number $\overline{y x}$ after swapping positions results in a perfect square. Then the number of such two-digit numbers is ( ) .
(A) 8
(B) 4
(C) 2
(D) 1
3. A.

Given $1 \leqslant x \leqslant 9,1 \leqslant y \leqslant 9$, and
$$
\overline{x y}+\overline{y x}=10 x+y+10 y+x=11(x+y)
$$

is a perfect square, we know that $x+y=11$.
Therefore, the two-digit numbers sought are $29,38,47,56,65,74,83,92$, a total of 8.