3. (10 points) On the table, there are 20 cards numbered $1 \sim 20$. Each time, Xiao Ming takes out 2 cards, with the requirement that one card's number is 2 more than twice the number of the other card. What is the maximum number of cards Xiao Ming can take out?
A. 12
B. 14
C. 16
D. 18
【Analysis】Since 2 cards are drawn each time, and it is required that one card's number is 2 more than twice the other, the larger number of the drawn cards cannot exceed 20. Let the other card number be $x$, then $2 x+2 \leqslant 20$, and $x \geqslant 1$. Solve accordingly.

【Solution】Let the other card number be $x$, then:
$$
\begin{array}{l}
2 x+2 \leqslant 20 \\
2 x+1-2 \leqslant 20-2 \\
2 x \leqslant 18 \\
2 x \div 2 \leqslant 18 \div 2 \\
x \leqslant 9
\end{array}
$$

Since $x \geqslant 1$
$$
9 \times 2=18 \text { (cards) }
$$
$\because 4, 6, 8$ can serve as both the single quantity and the quantity that is 2 more than twice,
$\therefore$ the total number of cards that can be drawn is: $18-3 \times 2=12$ cards;
Answer: Xiao Ming can draw a maximum of 12 cards.
Therefore, the correct choice is: $A$.