1. Xiao Pei and Xiao Fo each have an integer amount of RMB. Xiao Pei says to Xiao Fo: "If you give me 2 yuan, my money will be $n$ times yours." Xiao Fo says to Xiao Pei: "If you give me $n$ yuan, my money will be 2 times yours." Here, $n$ is a positive integer. Then the number of possible values for $n$ is ( ).
(A) 1
(B) 2
(C) 3
(D) 4
- 1. D.

Let $x$ yuan and $y$ yuan represent the amounts of money Xiao Pei and Xiao Fo have, respectively. Thus,
$$
\left\{\begin{array}{l}
x+2=n(y-2), \\
y+n=2(x-n) .
\end{array}\right.
$$

From equation (1), we get $x=n y-2 n-2$.
Substituting the above equation into equation (2) yields
$$
(2 y-7) n=y+4 \text {, }
$$

which simplifies to $2 n=\frac{(2 y-7)+15}{2 y-7}=1+\frac{15}{2 y-7}$.
Therefore, $2 y-7=1,3,5,15, y=4,5,6,11$.
Correspondingly, $n$ is 8, 3, 2, 1, and $x$ is 14, 7, 6, 7.