24. Use the digits $1, 2, 3, 4, 5$ to form a five-digit number $\overline{P Q R S T}$ without repeating any digit, and $4|\overline{P Q R}, 5| \overline{Q R S}$, $3 \mid \overline{R S T}$. Then the digit $P$ is ( ).
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
24. A.

From $5 \mid \overline{Q R S} \Rightarrow S=5$.
From $4|\overline{P Q R} \Rightarrow 4| \overline{Q R}$
$\Rightarrow R=2$ or 4.
When $R=2$, by
$$
\begin{array}{l}
3|\overline{R S T} \Rightarrow 3| \overline{25 T} \\
\Rightarrow 2+5+T \equiv 0(\bmod 3) \\
\Rightarrow T \equiv 2(\bmod 3) .
\end{array}
$$

Thus, $T=2$ or 5.
Since the five-digit number has no repeated digits, we discard these.
Similarly, when $R=4$,
$$
\begin{array}{l}
4+5+T \equiv 0(\bmod 3) \\
\Rightarrow T=3 .
\end{array}
$$

Therefore, $\overline{P Q R S T}=12453$.
Hence, $P=1$.