2021 Fall AMC 12B Problem 25

For n a positive integer, let R(n) be the sum of the remainders when n is divided by 2, 3, 4, 5, 6, 7, 8, 9, and 10. For example, R(15) = 1+0+3+0+3+1+7+6+5=26. How many two-digit positive integers n satisfy R(n) = R(n+1)\,?

\textbf{(A) }0\qquad\textbf{(B) }1\qquad\textbf{(C) }2\qquad\textbf{(D) }3\qquad\textbf{(E) }4

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.