At the last soccer world championships, group A ended with the following standings: Austria 7, Brazil 5, Cameroon 4, Denmark 0.
Austria and Cameroon each conceded one goal.
Brazil and Cameroon scored only once, while Austria scored three goals.
What was the score of Austria-Denmark?
Note: Recall that, in every match played in the group, the winning team earns 3 points, the losing team 0 points; in case of a draw each of the two teams earns 1 point.
Pick one
Solution
Solution:
The answer is (B). In a group of 4 teams, each plays 3 matches, for a total of 6 matches overall. Since a win is worth 3 points, while a draw is worth only 1, in order to obtain the final standings given in the text it is necessary that Austria won 2 matches and drew one; that Brazil won one match and drew two; that Cameroon won, drew, and lost once.
Cameroon scored only one goal, so its only win was by a score of 1-0 and necessarily against Denmark, which lost all its matches. Cameroon conceded only one goal: having lost one match, it lost by 0-1. The draw was consequently by a score of .
Brazil suffered no defeats, so it won against Denmark and drew with Austria and Cameroon. On the other hand, Austria drew only once (with Brazil). Therefore Austria-Cameroon ended 1-0. Brazil scored only one goal, necessarily in the match it won against Denmark. Consequently Austria-Brazil ended 0-0.
We know that Austria scored three goals and conceded one. By difference, the score of Austria-Denmark is 2-1.
Note that it is possible to establish the final score of each of the six matches in the group:
| Austria-Brazil | Austria-Cameroon | Austria-Denmark | |||
|---|---|---|---|---|---|
| Brazil-Cameroon | Brazil-Denmark | Cameroon-Denmark |
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