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?

(A) 2 wins, 0 losses, 1 tie

(B) 1 win, 2 losses, 0 ties

(C) 0 wins, 1 loss, 2 ties

(D) 1 win, 1 loss, 1 tie

(E) 1 win, 0 losses, 2 ties
When Team A played Team B, if Team B won, then Team B scored more goals than Team A, and if the game ended in a tie, then Team A and Team B scored the same number of goals. Therefore, if a team has 0 wins, 1 loss, and 2 ties, then it scored fewer goals than its opponent once (the 1 loss) and the same number of goals as its oppponent twice (the 2 ties).

Combining this information, we see that the team must have scored fewer goals than were scored against them.

In other words, it is not possible for a team to have 0 wins, 1 loss, and 2 ties, and to have scored more goals than were scored against them.

We can also examine choices (A), (B), (D), (E) to see that, in each case, it is possible that the team scored more goals than it allowed.

This will eliminate each of these choices, and allow us to conclude that (C) must be correct.

(A): If the team won 2-0 and 3-0 and tied 1-1, then it scored 6 goals and allowed 1 goal.

(B): If the team won 4-0 and lost 1-2 and 2-3, then it scored 7 goals and allowed 5 goals.

(D): If the team won $4-0$, lost $1-2$, and tied 1-1, then it scored 6 goals and allowed 3 goals.

(E): If the team won 2-0, and tied 1-1 and 2-2, then it scored 5 goals and allowed 3 goals.

Therefore, it is only the case of 0 wins, 1 loss, and 2 ties where it is not possible for the team to score more goals than it allows.

ANSWER: (C)