10.32 Among the following numbers, which can be the sum of 100 consecutive positive integers?
(A) 1627384950.
(B) 2345678910.
(C) 3579111300.
(D) 4692581470.
(E) 5815937260.
(48th American High School Mathematics Examination, 1997)
[Solution] The sum of the first term being $k$ of 100 consecutive natural numbers is
$$
S_{100}=\frac{[n+(n+99)] \cdot 100}{2}=50(2 n+99) \text{.}
$$

Obviously, $50 \mid S_{100}$, but $100 \nmid S_{100}$.
Therefore, the answer is $(A)$.