Đáp án đúng: B
Giải chi tiết:Ta có: \(\left\{ \begin{array}{l}3n + 4\,\, \vdots \,\,n - 3\\n - 3\,\, \vdots \,\,n - 3\end{array} \right. \Rightarrow \left\{ \begin{array}{l}3n + 4\,\, \vdots \,\,n - 3\\3n - 9\,\, \vdots \,\,n - 3\end{array} \right.\)
\(\begin{array}{l} \Rightarrow \left( {3n + 4} \right) - \left( {3n - 9} \right)\,\, \vdots \,\,n - 3 \Rightarrow 13\,\, \vdots \,\,n - 3.\\ \Rightarrow n - 3 \in U\left( {13} \right) = \left\{ { - 13; - 1;\,\,1;\,\,13} \right\}.\end{array}\)
\( \Rightarrow \left[ \begin{array}{l}n - 3 = - 13\\n - 3 = - 1\\n - 3 = 1\\n - 3 = 13\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}x = - 13 + 3\\n = - 1 + 3\\n = 1 + 3\\n = 13 + 3\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}n = - 10\\n = 2\\n = 4\\n = 16\end{array} \right..\)
Vậy \(n \in \left\{ { - 10; - 2;\,\,4;\,\,16} \right\}.\)
Chọn B.