There are seven team and each team has to play with three other teams

Question

There are seven team and each team has to play with three other teams in the first round of tournament. What is the minimum number of matches that can happen in the first round?
A) 10
B) 11
C) 12
D) 21
E) 22

Weekly Quant Quiz #6 Question No 6

GMATBusters · Answer

Each match is between two teams.. say A B C D E F G.. so for every match two alphabets will appear.. we need each alphabet thrice (three matches per team).. 7*3 = 21 .. but each match has two alphabets so total appearance of alphabets can only be even.. 21 is not possible but 22 is possible (with 11 matches).

Answer = 11 (B)

Answer = 11 (B)

pudu · Answer

someone please explain this...there is no clear solution here

pudu · Answer

1,2,3,4,5,6 and 7

1->2,3,4
5->6,7,2
6->2,3
7->4,3
4 can take any number so that it too has 3 matches. So total=3+3+2+2+1=11.Hence B

Vivek1707 · Answer

The wording of this quesiton is a bit off. When the question says that each team has to play with 3 other team. It kinda implies that each team has to play exactly 3 matches.

But that would be impossible!

Since whenever there are two teams playing a match, If you add up the matches played by individual teams it will  ALWAYS  add up to an even number.

Eg: Say there are three teams A , B , C

If I say that A has played 3 matches that means if I add up the matches played by B and C those should also add up to 3.

So each match requires 2 teams i.e an even number of teams.

So here, the if there are 7 teams and each team plays 3 games, then there are 21 games. But 21 is an odd number. We need an even number.

The closest even number would be 22. Hence the minimum number of matches would be  11

There are seven team and each team has to play with three other teams

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There are seven team and each team has to play with three other teams

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