3. The line $l: y=p x$ (where $p$ is an integer not equal to 0)
intersects the line $y=x+10$ at exactly an integer point. Then, the number of lines $l$ that satisfy this condition is ( ).
(A) 6
(B) 7
(C) 8
(D) infinitely many
(2007, National Junior High School Mathematics Competition, Zhejiang Province Preliminary)
(Solve the system of equations $y=p x$ and $y=x+10$ to get $x=\frac{10}{p-1}$. For $x$ to be an integer, $p-1= \pm 1, \pm 2$, $\pm 5, \pm 10$. Therefore, $p=2,3,-1,6,-4,11,-9$. Hence, there are 7 such lines.)