$10 \cdot 4$ Find the digits $x, y, z$ that satisfy the equation $\overline{x 5} \cdot \overline{3 y z}=7850$.
(13th All-Russian Mathematical Olympiad, 1987)
[Solution] Since $5 \cdot 400=200010000>7850$.

Therefore,
$$
x \neq 5,6,7,8,9 \text{. }
$$

Thus, only $x=2$, in which case we have the equation
$$
25 \cdot 314=7850.
$$

That is,
$$
x=2, \quad y=1, \quad z=4.
$$