2019 AMC 12B Problem 14

Let S be the set of all positive integer divisors of 100,000. How many numbers are the product of two distinct elements of S?

\textbf{(A) }98\qquad\textbf{(B) }100\qquad\textbf{(C) }117\qquad\textbf{(D) }119\qquad\textbf{(E) }121

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