4. A. Xiao Qian and Xiao Ling each have several RMB notes with integer yuan denominations. Xiao Qian says to Xiao Ling: "If you give me 2 yuan, my money will be $n$ times yours"; Xiao Ling says to Xiao Qian: "If you give me $n$ yuan, my money will be 2 times yours", where $n$ is a positive integer. Then the number of possible values for $n$ is ( ).
(A) 1
(B) 2
(C) 3
(D) 4
4. A. D.

Let the amount of money Xiaolian has be $x$ yuan, and the amount of money Xiaoling has be $y$ yuan, where $x$ and $y$ are non-negative integers. From the problem, we have
$$
\left\{\begin{array}{l}
x+2=n(y-2), \\
y+n=2(x-n) .
\end{array}\right.
$$

Eliminating $x$, we get
$$
\begin{array}{l}
(2 y-7) n=y+4 \\
\Rightarrow 2 n=\frac{(2 y-7)+15}{2 y-7}=1+\frac{15}{2 y-7} .
\end{array}
$$

Since $\frac{15}{2 y-7}$ is a positive integer, the values of $2 y-7$ can only be $1, 3, 5, 15$. Therefore, the values of $y$ can only be $4, 5, 6, 11$. Thus, the values of $n$ are $8, 3, 2, 1$; and the values of $x$ are $14, 7, 6, 7$.