3. From the 14 natural numbers $1,2, \cdots, 14$, take out $k$ numbers to ensure that there are two numbers, one of which is twice the other. Then the minimum value of $k$ is ( ).
(A) 8
(B) 9
(C) 10
(D) 11
3. C.

Divide $\{1,2, \cdots, 14\}$ into
$$
\{1,2\},\{3,6\},\{4,8\},\{5,10\},\{7,14\},\{9,11,12,13\} \text {. }
$$

If 10 numbers are taken from $\{1,2, \cdots, 14\}$, then at least 6 numbers must be taken from the first 5 groups, meaning that two numbers from the same group are taken, satisfying the problem's requirements.
Clearly, $\{1,3,4,5,7,9,11,12,13\}$ does not meet the requirements.
Therefore, $k_{\min }=10$.