2009 Pascal Problem 23

A one-dollar coin should have a mass of 7.0 g. Each individual coin may be lighter or heavier by as much as 2.14\%. Joshua has a number of these coins and determines that they have a total mass of 1 kg. What is the difference between the greatest possible number and the least possible number of these coins that he could have?

\textbf{(A)}\ 4\quad \textbf{(B)}\ 5\quad \textbf{(C)}\ 6\quad \textbf{(D)}\ 7\quad \textbf{(E)}\ 8

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Pascal contests here.