In the Group stage, each team in a group plays against every other

Question

In the Group stage, each team in a group plays against every other team in that group. A win earns the winning team 3 points, while a draw gives 1 point to each team. The losing team gets no points. The top two teams from each group advance to the Quarter Finals. In each group, all teams finished with different point totals, so there were no ties in the final group standings.

The position of the teams at the end of the Group stage is as given below:

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 16In the Group stage, each team in a group plays against every other team in that group. A win earns the winning team 3 points, while a draw gives 1 point to each team. The losing team gets no points. The top two teams from each group advance to the Quarter Finals. In each group, all teams finished with different point totals, so there were no ties in the final group standings.

The position of the teams at the end of the Group stage is as given below:

Position  Group 1  Group 2  Group 3  Group 4  
  1  Team 14  Team 13  Team 7  Team 9  
  2  Team 5  Team 12  Team 16  Team 11  
  3  Team 10  Team 2  Team 1  Team 3  
  4  Team 6  Team 8  Team 15  Team 4Format of the matches in the knockout stage is as given below:

Quarter-finals:

Match A: Winner of Group 1 vs Runner-up of Group 2

Match B: Runner-up of Group 1 vs Winner of Group 2

Match C: Winner of Group 3 vs Runner-up of Group 4

Match D: Runner-up of Group 3 vs Winner of Group 4

Semi-finals:

SF1: Winner of Match A vs Winner of Match D

SF2: Winner of Match B vs Winner of Match C

Final:  Winner of SF1 vs Winner of SF2

In the knockout stage, there were no upsets — that is, a team with a better initial standing (as shown in the Introduction tab) always won against a team with a lower standing.

Bunuel · Answer

Official Solution:

Question 1: How many of the top 8 teams in the initial standings advanced to the Quarter Finals?

We know that the teams in the Quarter Finals are the top two teams from each group.

These teams are: Team 14, Team 13, Team 7, Team 9, Team 5, Team 12, Team 16, Team 11.

The top 8 teams based on the initial standings are: Team 1, Team 2, Team 3, Team 4, Team 5, Team 6, Team 7, Team 8.

The teams common to both lists are: Team 5 and Team 7. So, only 2 of the top 8 teams reached the Quarter Finals.

Thus, this question can be answered.

Question 2: Which team won the tournament?

Since there were no upsets in the knockout stage, the team with the better initial standing always won.

Following the bracket and applying this rule:

Quarter-finals:

– Match A: Team 14 (Winner of Group 1) vs Team 12 (Runner-up of Group 2) → Team 12 wins (Team 12 has better initial standing)

– Match B: Team 5 (Runner-up of Group 1) vs Team 13 (Winner of Group 2) → Team 5 wins

– Match C: Team 7 (Winner of Group 3) vs Team 11 (Runner-up of Group 4) → Team 7 wins

– Match D: Team 16 (Runner-up of Group 3) vs Team 9 (Winner of Group 4) → Team 9 wins

Semi-finals:

– SF1: Team 12 vs Team 9 → Team 9 wins

– SF2: Team 5 vs Team 7 → Team 5 wins

Final:

– Final: Team 5 vs Team 9 → Team 5 wins (as Team 5 had a better initial standing)

Therefore, Team 5 won the tournament.

Thus, this question can be answered.

Question 3: Did Team 5 remain unbeaten throughout the tournament?

We know that Team 5 won the tournament and that there were no upsets in the knockout stage, meaning Team 5 won all of its knockout matches.

However, we do not have the results of individual group-stage matches. It's possible that Team 5 could have drawn or even lost a match in the group stage and still advanced as one of the top two teams in its group.

Therefore, we cannot determine whether Team 5 remained unbeaten throughout the tournament.

Thus, this question cannot be answered.

Correct answer:

How many of the top 8 teams in the initial standings advanced to the Quarter Finals?  "Yes"

Which team won the tournament?  "Yes"

Did Team 5 remain unbeaten throughout the tournament?  "No"

Bunuel · Answer

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 · Answer

Official Solution:

Team 10 drew all three of its group-stage matches, so it earned 3 points.
 
Team 5 finished second in the group, so it must have had more than 3 points, and Team 14, which finished first, had more than Team 5.
 
Since both Team 14 and Team 5 drew against Team 10, Team 14 must have had 7 points (1 draw with Team 10 and 2 wins), and Team 5 must have had 4 points (1 draw with Team 10, 1 loss to Team 14, and 1 win against Team 6).
 
 Therefore, Team 5 got 4 points in the Group stage.

Correct answer:

If Team 10 drew all three of its group-stage matches, how many points did Team 5 get in the Group stage?

"4"

In the Group stage, each team in a group plays against every other

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

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

Yes	No
		How many of the top 8 teams in the initial standings advanced to the Quarter Finals?
		Which team won the tournament?
		Did Team 5 remain unbeaten throughout the tournament?

GMAT Multi-Source Reasoning (MSR) Questions

In the Group stage, each team in a group plays against every other

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards