A student makes the following claim:\\
For all integers $n$, the expression $4 \left( \frac { 9 n + 1 } { 2 } - \frac { 3 n - 1 } { 2 } \right)$ is divisible by 3 .\\
Here is the student's argument:

$$\begin{aligned}
4 \left( \frac { 9 n + 1 } { 2 } - \frac { 3 n - 1 } { 2 } \right) & = 2 \left( 2 \left( \frac { 9 n + 1 } { 2 } - \frac { 3 n - 1 } { 2 } \right) \right) \\
& = 2 ( 9 n + 1 - 3 n - 1 ) \\
& = 2 ( 6 n ) \\
& = 12 n \\
& = 3 ( 4 n )
\end{aligned}$$

which is always a multiple of 3 .

So the expression $4 \left( \frac { 9 n + 1 } { 2 } - \frac { 3 n - 1 } { 2 } \right)$ is always divisible by 3 .

Which one of the following is true?

A The argument is correct.\\
B The argument is incorrect, and the first error occurs on line (I).\\
C The argument is incorrect, and the first error occurs on line (II).\\
D The argument is incorrect, and the first error occurs on line (III).\\
E The argument is incorrect, and the first error occurs on line (IV).\\
F The argument is incorrect, and the first error occurs on line (V).\\
G The argument is incorrect, and the first error occurs on line (VI).