PS - League Results

IMO C

Each team gets to play a total of 10 games. Whenever a team wins, another team loses. Therefore, the # of lose equal to # of win. The total# of games are 6p2*2=60, so there are 30 loses as well as 30 wins. If you add up all the given wins, u will get 24. total#of wins 30-24=6-wins for X. Same drill, u can get the #of lose for X, which is 4. In case GMAT ask u the same question in a different way.

Please let me know in case I am wrong.

I agree with u that the answer is 6 but not convinced that the number of matches played were 60

if team a played match against team b......its the same as team b playing against team a.....so its combinations rahter than permutations.

thus in IMO the number of games played is 30.thus if number of wins are 24 from a total of 30 matches played........x must have won 6 matches.

let me know if i am wrong.

first team plays 2 games * 5 teams = 10 games
second team plays 2 games * 4 teams = 8 games (exclude first team since they played)
....

in essence 2 (5+4+3+2+1) = 30 games total

All teams play the same number of matches. Take A it can play 5 games with the other team.

Similarly th3 6 teams can each play 5 matches making the total number of matches to be 30.

30- (numbers given for matches won by the various teams but x) = 6

x won 6 games

I think we may all be wrong with number 30. I agree with jeffxujian.

A plays 10 games, B play 10 games since each team plays the other team exactly 2 times.

Since we are given the number of wins column and not number of losses like jeffxujian pointed out it will be6 since number of wins must equal number of losses

The total number of matches = 30

There are 2 ways to know this:

1) Think of the 2 matches for each pair of teams as A plays B and B plays A.

Therefore total number of matches = 6P2 = 30

2) The other way is that we reduce the problem where each pair of the teams play each other only once:

i.e. A plays B and B plays A is the same (arrangement is not a concern)

Total number of matches if each pair play each other only once = 6C2 = 15

Therefore, the total number of matches if each pair play each other twice = 6C2 * 2 = 30


Hope the above helps.

BlueMentor