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There are 8 teams in a certain league and each team plays

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Manager
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There are 8 teams in a certain league and each team plays [#permalink] New post 10 May 2012, 20:45
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

61% (02:22) correct 38% (00:40) wrong based on 57 sessions
There are 8 teams in a certain league and each team plays each of the other teams exactly twice. If each game is played by 2 teams, what is the total number of games played?

A. 15
B. 16
C. 28
D. 56
E. 64
[Reveal] Spoiler: OA
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Kudos [?]: 12 [0], given: 10

Re: There are 8 teams in a certain league and each team plays... [#permalink] New post 10 May 2012, 21:16
IMO 54 matches

Let's say first team plays with 7 other teams - resulting in 7 matches, taking this further in the similar way, the number of matches between 8 teams would be 7+6+5+4+3+2+1 = 28.. as in this case each team is playing with other twice, the no of matches would be 28*2 = 56

Last edited by gmihir on 11 May 2012, 00:13, edited 1 time in total.
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Re: There are 8 teams in a certain league and each team plays... [#permalink] New post 10 May 2012, 21:19
Every team plays with 7 teams...so total no of matches = 8 x 7 = 56.
Now, each match is played twice => 56 x 2
But 2 teams play a match => 56 x 2 /2 = 56.
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Re: There are 8 teams in a certain league and each team plays... [#permalink] New post 10 May 2012, 21:31
Bunuel, can you please comment on this?
1 KUDOS received
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Re: There are 8 teams in a certain league and each team plays [#permalink] New post 10 May 2012, 21:37
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Expert's post
Smita04 wrote:
There are 8 teams in a certain league and each team plays each of the other teams exactly twice. If each game is played by 2 teams, what is the total number of games played?

A. 15
B. 16
C. 28
D. 56
E. 64


# of different pairs possible from 8 teams is C^2_{8}=28, since each pair plays twice between each other than total # of games is 2*28=56.

Answer: D.
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Re: There are 8 teams in a certain league and each team plays [#permalink] New post 13 Sep 2013, 10:11
But the official answer is C, and I got that using combination [8!/(2!6!)]. Did I miss anything? Please help.
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Re: There are 8 teams in a certain league and each team plays [#permalink] New post 13 Sep 2013, 10:55
Expert's post
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Re: There are 8 teams in a certain league and each team plays [#permalink] New post 14 Sep 2013, 09:44
Thanks Bunuel! I caught my mistake. I was looking for other ways of solving question 133 OG 13th edi (121 in 12th edi), and that is how I landed here. Similar version of this question in the 13th and 12th edi OGs has the word 'once' instead of 'twice', as in the above question. My bad :( !!
Is my approach at solving the question correct?
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Re: There are 8 teams in a certain league and each team plays [#permalink] New post 14 Sep 2013, 09:55
Expert's post
vjns wrote:
Thanks Bunuel! I caught my mistake. I was looking for other ways of solving question 133 OG 13th edi (121 in 12th edi), and that is how I landed here. Similar version of this question in the 13th and 12th edi OGs has the word 'once' instead of 'twice', as in the above question. My bad :( !!
Is my approach at solving the question correct?


Yes, for that question you solved correctly. Discussed here: there-are-8-teams-in-a-certain-league-and-each-team-plays-134582.html

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All OG13 questions with solutions: the-official-guide-quantitative-question-directory-143450.html

Hope it helps.
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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: There are 8 teams in a certain league and each team plays   [#permalink] 14 Sep 2013, 09:55
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