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Q4

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bacali: Master | Next Rank: 500 Posts; Posts: 245; Joined: Thu Aug 16, 2007 12:41 pm

by bacali » Mon Dec 01, 2008 3:24 pm

If each of the 12 teams participating in a certain tournament plays exactly one game

with each of the other teams, how many games will be played?
A. 144 B. 132 C. 66 D. 33 E. 23

OA: C

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Source: Beat The GMAT — Problem Solving | Mon Dec 01, 2008 3:24 pm

dmateer25: Community Manager; Posts: 1049; Joined: Sun Apr 06, 2008 5:15 pmFollowed by: 27 members; Location: Pittsburgh, PA; Thanked: 113 times; GMAT Score:710

by dmateer25 » Mon Dec 01, 2008 3:38 pm

Team 1 plays: 2,3,4,5,6,7,8,9,10,11,12 (11 games)
Team 2 plays: 3,4,5,6,7,8,9,10,11,12 (10 games)
Team 3 plays: 4,5,6,7,8,9,10,11,12 (9 games)
etc...

11+10+9+8+7+6+5+4+3+2+1+0=66

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muzali: Senior | Next Rank: 100 Posts; Posts: 95; Joined: Fri Sep 28, 2007 10:16 am; Thanked: 6 times; GMAT Score:710

by muzali » Mon Dec 01, 2008 3:55 pm

Total teams = 12
Each team plays with all but itself, so 12 teams play with (12-1) = 11 teams
So, total number of games = 12*11
But each game like A plays B and B plays A is actually just one game, i.e., 12*11 includes duplicates.

Therefore, the actual number o fgames = 12*11/2 = 66

In general, for such questions of teams playing or handshakes, the formula is n(n-1)/2.

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