(B) $n+1$
We need a state for strings of length $0, 1, 2, ... n$ (and their respective multiples with $k$). Each of these set of strings form an equivalence class as per Myhill-Nerode relation and hence needs a separate state in min-DFA.
$$\begin{array}{|c|c|c|c|}\hline \textbf{Myhill-Nerode} & \textbf{Myhill-Nerode} & \textbf{Myhill-Nerode} & \textbf{Myhill-Nerode}\\\textbf{Class 1} & \textbf{Class 2} & \textbf{Class n} & \textbf{Class n+1}
\\\hline \text{$\epsilon$} & \text{a,} & \text{#a=n-1,}& \text{#a=n,}\\ & \text{#a=n+1,}& \text{#a=2n-1,} &\text{#a=2n,}\\ & \text{#a=2n+1,}& \text{#a=3n-1,} &\text{#a=3n,}\\ &\text{...}&\text{...}& \text{...} \\\hline \end{array}$$One thing to notice here is $k > 0$. Because of this we are not able to combine Class $1$ and Class $n+1$. Had it been $k \geq 0$, we would have had only $n$ equivalent classes and equivalently $n$ states in the minimal DFA.