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32 teams compete in the World Cup of Soccer. They are divided into ei 18 Jan 2019, 05:12
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C
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[Math Revolution GMAT math practice question]

32 teams compete in the World Cup of Soccer. They are divided into eight groups of four teams (groups A to H) to compete in the ‘group stage’. Teams in each group play one another in a round-robin competition, with the top two teams of each group advancing to the knockout stage. What is the total number of matches played at the group stage?

A. 24
B. 36
C. 48
D. 56
E. 64
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C
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32 teams compete in the World Cup of Soccer. They are divided into ei 18 Jan 2019, 05:41
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MathRevolution
[Math Revolution GMAT math practice question]

32 teams compete in the World Cup of Soccer. They are divided into eight groups of four teams (groups A to H) to compete in the ‘group stage’. Teams in each group play one another in a round-robin competition, with the top two teams of each group advancing to the knockout stage. What is the total number of matches played at the group stage?

A. 24
B. 36
C. 48
D. 56
E. 64
Show more


total matches one team plays in each group : 4c2 = 6
total groups = 8
total group matches : 8 * 6 = 48 IMO C
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32 teams compete in the World Cup of Soccer. They are divided into ei 18 Jan 2019, 07:44
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MathRevolution
[Math Revolution GMAT math practice question]

32 teams compete in the World Cup of Soccer. They are divided into eight groups of four teams (groups A to H) to compete in the ‘group stage’. Teams in each group play one another in a round-robin competition, with the top two teams of each group advancing to the knockout stage. What is the total number of matches played at the group stage?

A. 24
B. 36
C. 48
D. 56
E. 64


total matches one team plays in each group : 4c2 = 6
total groups = 8
total group matches : 8 * 6 = 48 IMO C
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I arrived at C as well, but am confused by your combination. How would the number of matches a team plays in each group =6 and why would the combo = 4c2?

e.g.
Group A Pairings: (1 v 2, 1 v 3, 1 v 4), (2 v 1, 2 v 3, 2 v 4), (3 v 1, 3 v 2, 3 v 4) (4 v 1, 4 v 2, 4 v 3) and then subtract redundant combinations... leaving you with (1 v 2, 1 v 3, 1 v 4), (2 v 3, 2 v 4) and (3 v 4)


6 unique matches in each group * 8 groups =48


Thanks in advance for your help!
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32 teams compete in the World Cup of Soccer. They are divided into ei 18 Jan 2019, 07:50
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nch2024
Archit3110
MathRevolution
[Math Revolution GMAT math practice question]

32 teams compete in the World Cup of Soccer. They are divided into eight groups of four teams (groups A to H) to compete in the ‘group stage’. Teams in each group play one another in a round-robin competition, with the top two teams of each group advancing to the knockout stage. What is the total number of matches played at the group stage?

A. 24
B. 36
C. 48
D. 56
E. 64


total matches one team plays in each group : 4c2 = 6
total groups = 8
total group matches : 8 * 6 = 48 IMO C

I arrived at C as well, but am confused by your combination. How would the number of matches a team plays in each group =6 and why would the combo = 4c2?

e.g.
Group A Pairings: (1 v 2, 1 v 3, 1 v 4), (2 v 1, 2 v 3, 2 v 4), (3 v 1, 3 v 2, 3 v 4) (4 v 1, 4 v 2, 4 v 3) and then subtract redundant combinations... leaving you with (1 v 2, 1 v 3, 1 v 4), (2 v 3, 2 v 4) and (3 v 4)


6 unique matches in each group * 8 groups =48


Thanks in advance for your help!
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nch2024
4c2 : means that in a group of 4 teams , each team would play each other once so total no. of matches in the group would played would be 6 or 4c2..
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32 teams compete in the World Cup of Soccer. They are divided into ei 18 Jan 2019, 07:58
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Ahh I see now! 4c2 states how many possible pairs can be created from the 4 teams in each group... Thank you!
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32 teams compete in the World Cup of Soccer. They are divided into ei 20 Jan 2019, 18:42
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=>

Each group plays 4C2 = 6 games and we have 8 groups.
Thus, the group stage includes 6*8 = 48 games.

Therefore, the answer is C.
Answer: C
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32 teams compete in the World Cup of Soccer. They are divided into ei 27 Sep 2024, 08:06
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Using the handshake formula for combinations

n(n-1)/2
where n is the total number of people in a group

For each group the number of 'handshakes' (aka matches played)
= 4(4-1)/2
= 4(3)/2
= 6

Total of 6 games is played per group

There are eight groups

Total games played = 6*8
= 48
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