CAYLEY 2016 Problem 24

What is the sum of all numbers q which can be written in the form \displaystyle q=\frac ab where a and b are positive integers with b\le10 and for which there are exactly 19 integers n that satisfy \sqrt q<n<q?

Answer Choices
A. 871.5
B. 743.5
C. 777.5
D. 808.5
E. 1106.5