Several students are seated at a large circular table.  They pass around a bag containing $100$ pieces of candy.  Each person receives the bag, takes one piece of candy and then passes the bag to the next person.  If Chris takes the first and last piece of candy, then the number of students at the table could be
$\text{(A)}\ 10 \qquad \text{(B)}\ 11 \qquad \text{(C)}\ 19 \qquad \text{(D)}\ 20 \qquad \text{(E)}\ 25$
If this is the case, then if there were only $99$ pieces of candy, the bag would have gone around the table a whole number of times.  Thus, the number of students is a divisor of $99$.  The only choice that satisfies this is choice $\boxed{\text{B}}$.