JEE Math Practice Question

Let $$S_{K}=\frac{1+2+\ldots+K}{K}$$ and $$\sum\limits_{j=1}^{n} S_{j}^{2}=\frac{n}{A}\left(B n^{2}+C n+D\right)$$, where $$A, B, C, D \in \mathbb{N}$$ and $$A$$ has least value. Then

1. A.$$A+B+C+D$$ is divisible by 5
2. B.$$A+C+D$$ is not divisible by $$B$$
3. C.$$A+B=5(D-C)$$
4. D.$$A+B$$ is divisible by $$\mathrm{D}$$