2025 AMC 8 Problem 16

Five distinct integers from 1 to 10 are chosen, and five distinct integers from 11 to 20 are chosen. No two numbers differ by exactly 10. What is the sum of the ten chosen numbers?

\textbf{(A)} 95 \qquad \textbf{(B)} 100 \qquad \textbf{(C)} 105 \qquad \textbf{(D)} 110 \qquad \textbf{(E)} 115

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