A student was given a piece of rope and told to cut it into two equal pieces, keep one piece, and pass the other piece to the next student. Each student was to repeat this process until every student in the class had exactly one piece of rope. Which of the following could be the fraction of the original rope that one of the students had?
(A) $\displaystyle\frac{1}{4}$
(B) $\displaystyle\frac{1}{15}$
(C) $\displaystyle\frac{1}{16}$
(D) $\displaystyle\frac{1}{17}$
My answer sheet tells me the answer, which is (C). But why? This question is basically asking how many kids are in the classroom. There could be a random amount of students as far as the question goes, so why does it have to (C) that's correct?