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# There are exactly 6 teams in league x. What was the total

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Senior Manager
Joined: 31 Oct 2011
Posts: 332
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Kudos [?]: 49 [0], given: 18

There are exactly 6 teams in league x. What was the total [#permalink]  06 Mar 2012, 22:36
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Difficulty:

25% (low)

Question Stats:

71% (01:52) correct 28% (01:01) wrong based on 109 sessions
There are exactly 6 teams in league x. What was the total number of games played by the 6 teams last season?

(1) Each team in league x played each of the other teams at least once.

(2) No team in league x played more than 7 games.
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 16878
Followers: 2776

Kudos [?]: 17634 [3] , given: 2233

Re: PT # 11 DS 9 [#permalink]  07 Mar 2012, 00:15
3
KUDOS
Expert's post
There are exactly 6 teams in league x. What was the total number of games played by the 6 teams last season?

(1) Each team in league x played each of the other teams at least once --> if each team played each of the other teams ONLY once then there was total of C^2_6=15 games played (notice that each team played 5 games) but if each team played each of the other teams TWICE then there was total of 2*C^2_6=30 games played (notice that each team played 10 games). Not sufficient.

(2) No team in league x played more than 7 games. Clearly insufficient.

(1)+(2) If each team played each of the other teams ONLY once then there was total of C^2_6=15 games played (each of the 6 teams played 5 games), but if after each team played each of the other teams ONLY once, some two teams played between each other once more then the total number of games played was 16 (4 teams played 5 games and 2 teams played 6 games). Not sufficient.

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Math Expert
Joined: 02 Sep 2009
Posts: 16878
Followers: 2776

Kudos [?]: 17634 [0], given: 2233

Re: There are exactly 6 teams in league x. What was the total [#permalink]  30 Jun 2013, 23:46
Expert's post
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Re: There are exactly 6 teams in league x. What was the total   [#permalink] 30 Jun 2013, 23:46
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