2023 AMC 10A Problem 14

A number is chosen at random from among the first 100 positive integers, and a positive integer divisor of that number is then chosen at random. What is the probability that the chosen divisor is divisible by 11?

\textbf{(A)} \dfrac{4}{100} \qquad \textbf{(B)} \dfrac{9}{200} \qquad \textbf{(C)} \dfrac{1}{20} \qquad \textbf{(D)} \dfrac{11}{200} \qquad \textbf{(E)} \dfrac{3}{50}

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