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31 Oct 2024, 09:30
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The initial standing of the 16 teams coming into the football tournament is as follows:
These teams enter a football tournament where they are divided into four groups of four teams each. The format of the tournament consists of Group matches followed by Quarter Finals and Semi Finals. The winners of the Semi Finals then play for the trophy.
| Standing | Team Name |
| 1 | Team 1 |
| 2 | Team 2 |
| 3 | Team 3 |
| 4 | Team 4 |
| 5 | Team 5 |
| 6 | Team 6 |
| 7 | Team 7 |
| 8 | Team 8 |
| 9 | Team 9 |
| 10 | Team 10 |
| 11 | Team 11 |
| 12 | Team 12 |
| 13 | Team 13 |
| 14 | Team 14 |
| 15 | Team 15 |
| 16 | Team 16 |
These teams enter a football tournament where they are divided into four groups of four teams each. The format of the tournament consists of Group matches followed by Quarter Finals and Semi Finals. The winners of the Semi Finals then play for the trophy.
For each of the following, select Yes if it can be deduced from the information provided. Otherwise, select No.
| Yes | No | |
| Team 12 got fewer points in the Group stage than Team 14. | ||
| Team 13 won at least one match during the Group stage. | ||
| Team 4 lost all of its matches in the Group stage. |
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Official Answer
Team 12 got fewer points in the Group stage than Team 14.: No
Team 13 won at least one match during the Group stage.: Yes
Team 4 lost all of its matches in the Group stage.: No
31 Oct 2024, 09:31
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Official Solution:
Statement 1: Team 12 got less points in the Group stage than Team 14.
The only information we are given is the final positions of teams within their own groups and that all teams in each group finished with different point totals. This tells us the ranking order within each group but not the actual number of points earned.
Team 12 was the runner-up in Group 2, and Team 14 was the winner of Group 1. While it's likely that a group winner had more points than a runner-up, it is not guaranteed — the point totals are not comparable across groups without knowing the actual match results.
It is possible for a runner-up in one group to have more points than the winner of another group.
Example: Team 14 wins Group 1 with 6 points, and Team 12 finishes second in Group 2 with 6. This is valid and respects all constraints.
Group 1 (Teams: 14, 5, 10, 6):
Team 14 beats Team 10 and Team 6, loses to Team 5 → 6 points
Team 5 beats Team 14, draws with Team 10 and Team 6 → 5 points
Team 10 loses to Team 14, draws with Team 5, beats Team 6 → 4 points
Team 6 loses to Team 14 and Team 10, draws with Team 5 → 1 point
Group 2 (Teams: 13, 12, 8, 2):
Team 13 beats all → 9 points
Team 12 beats Team 8 and Team 2, loses to Team 13 → 6 points
Team 8 beats Team 2 only → 3 points
Team 2 loses all → 0 points
All teams have different point totals within their groups. Team 14 wins Group 1 with 6 points. Team 12 finishes second in Group 2 with 6 points.
Therefore, we cannot conclude that Team 12 got fewer points than Team 14. The answer is No.
Statement 2: Team 13 won at least one match during the Group stage.
Team 13 finished first in Group 2. If Team 13 had not won any matches, the maximum it could have earned is 3 points (from 3 draws).
But since all teams in the group had different point totals, the remaining teams would need to have 2, 1, and 0 points respectively — which is not possible within 3 matches per team.
Therefore, Team 13 must have won at least one match in the Group stage.
Statement 3: Team 4 lost all of its matches in the Group stage.
Team 4 finished last in its group, but that does not necessarily mean it lost all of its matches. A team can place fourth with 1 or even 2 points from draws if the other teams earned more and all teams had different point totals.
For example, Team 4 could have drawn one match and lost two, ending with 1 point, while the others had 6, 4, and 3 points respectively — all different.
Therefore, it is not certain that Team 4 lost all its matches.
Correct answer:
Team 12 got fewer points in the Group stage than Team 14. "No"
Team 13 won at least one match during the Group stage. "Yes"
Team 4 lost all of its matches in the Group stage. "No"
Bunuel
Statement 1: Team 12 got less points in the Group stage than Team 14.
The only information we are given is the final positions of teams within their own groups and that all teams in each group finished with different point totals. This tells us the ranking order within each group but not the actual number of points earned.
Team 12 was the runner-up in Group 2, and Team 14 was the winner of Group 1. While it's likely that a group winner had more points than a runner-up, it is not guaranteed — the point totals are not comparable across groups without knowing the actual match results.
It is possible for a runner-up in one group to have more points than the winner of another group.
Example: Team 14 wins Group 1 with 6 points, and Team 12 finishes second in Group 2 with 6. This is valid and respects all constraints.
Group 1 (Teams: 14, 5, 10, 6):
Team 14 beats Team 10 and Team 6, loses to Team 5 → 6 points
Team 5 beats Team 14, draws with Team 10 and Team 6 → 5 points
Team 10 loses to Team 14, draws with Team 5, beats Team 6 → 4 points
Team 6 loses to Team 14 and Team 10, draws with Team 5 → 1 point
Group 2 (Teams: 13, 12, 8, 2):
Team 13 beats all → 9 points
Team 12 beats Team 8 and Team 2, loses to Team 13 → 6 points
Team 8 beats Team 2 only → 3 points
Team 2 loses all → 0 points
All teams have different point totals within their groups. Team 14 wins Group 1 with 6 points. Team 12 finishes second in Group 2 with 6 points.
Therefore, we cannot conclude that Team 12 got fewer points than Team 14. The answer is No.
Statement 2: Team 13 won at least one match during the Group stage.
Team 13 finished first in Group 2. If Team 13 had not won any matches, the maximum it could have earned is 3 points (from 3 draws).
But since all teams in the group had different point totals, the remaining teams would need to have 2, 1, and 0 points respectively — which is not possible within 3 matches per team.
Therefore, Team 13 must have won at least one match in the Group stage.
Statement 3: Team 4 lost all of its matches in the Group stage.
Team 4 finished last in its group, but that does not necessarily mean it lost all of its matches. A team can place fourth with 1 or even 2 points from draws if the other teams earned more and all teams had different point totals.
For example, Team 4 could have drawn one match and lost two, ending with 1 point, while the others had 6, 4, and 3 points respectively — all different.
Therefore, it is not certain that Team 4 lost all its matches.
Correct answer:
Team 12 got fewer points in the Group stage than Team 14. "No"
Team 13 won at least one match during the Group stage. "Yes"
Team 4 lost all of its matches in the Group stage. "No"
