<s>[INST] Let $[a]$ denote the greatest integer less than or equal to $a$. If $x$ is a real number and $n$ is an integer, then the expression $[nx] - [nx - [x]]$ equals:
A) $2[x]$.
B) $n[x]$.
C) $\left\{ \begin{array}{ll}
n[x] & \mbox{ if } x -[x] < 1/n \\
2[x] & \mbox{ if } x -[x] \ge 1/n \end{array} \right.$
D) $\left\{ \begin{array}{ll}
1 & \mbox{ if } x -[x] < 1/n \\
2[x] & \mbox{ if } x -[x] \ge 1/n \end{array} \right.$[/INST]