2016 Cayley Problem 7

A soccer team played three games. Each game ended in a win, loss, or tie. (If a game finishes with both teams having scored the same number of goals, the game ends in a tie.) In total, the team scored more goals than were scored against them. Which of the following combinations of outcomes is not possible for this team?

\textbf{(A)}\ 2 wins, 0 losses, 1 tie\quad \textbf{(B)}\ 1 win, 2 losses, 0 ties\quad \textbf{(C)}\ 0 wins, 1 loss, 2 ties\quad \textbf{(D)}\ 1 win, 1 loss, 1 tie\quad \textbf{(E)}\ 1 win, 0 losses, 2 ties

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.