Let S be the statement 
"If the sum of the digits of the whole number $n$ is divisible by $6$, then $n$ is divisible by $6$."
A value of $n$ which shows $S$ to be false is
$\textbf{(A)}\ 30 \qquad \textbf{(B)}\ 33 \qquad \textbf{(C)}\ 40 \qquad \textbf{(D)}\ 42 \qquad \textbf{(E)}\ \text{ none of these}$
For a counterexample, we need a number whose digit sum is divisible by $6$, but which is not itself divisible by $6$. $33$ satisfies these conditions, as $3+3=6$ but $6$ does not divide $33$, so the answer is $\boxed{B}$.