Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 12 May 2012
Posts: 17
Location: United States
Concentration: Technology, Human Resources

There are 8 teams in a certain league and each team plays each of the
[#permalink]
Show Tags
Updated on: 26 Feb 2019, 03:29
Question Stats:
79% (01:03) correct 21% (01:04) wrong based on 2402 sessions
HideShow timer Statistics
There are 8 teams in a certain league and each team plays each of the other teams exactly once. 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
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by sarb on 17 Jun 2012, 02:52.
Last edited by Bunuel on 26 Feb 2019, 03:29, edited 2 times in total.
Renamed the topic.




Math Expert
Joined: 02 Sep 2009
Posts: 61192

Re: There are 8 teams in a certain league and each team plays each of the
[#permalink]
Show Tags
16 Nov 2012, 03:19
Sachin9 wrote: Bunuel wrote: sarb wrote: There are 8 teams in a certain league and each team plays each of the other teams exactly once. 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 The total # of games played would be equal to the # of different pairs possible from 8 teams, which is \(C^2_{8}=28\). Answer: C. P.S. Please read and follow: http://gmatclub.com/forum/rulesforpos ... 33935.html Pay attention ot the points #3 and #8. I would like to learn about \(C^2_{8}=28\). Manhattan Book doesn't discuss this approach. They have anagram approach. Well, the game is played by 2 teams. How many games are needed if there are 8 teams and each team plays each of the other teams exactly once? The number of games will be equal to the number of different pairs of 2 teams we can form out of 8 teams (one game per pair). How else? Similar questions to practice: http://gmatclub.com/forum/howmanydiag ... 01540.htmlhttp://gmatclub.com/forum/if10persons ... 10622.htmlhttp://gmatclub.com/forum/10businesse ... 26163.htmlhttp://gmatclub.com/forum/howmanydiff ... 29992.htmlhttp://gmatclub.com/forum/15chessplay ... 55939.htmlhttp://gmatclub.com/forum/thereare5c ... 27235.htmlhttp://gmatclub.com/forum/ifeachparti ... 42222.htmlHope it helps.
_________________




Director
Joined: 08 Jun 2010
Posts: 682

Re: There are 8 teams in a certain league and each team plays each of the
[#permalink]
Show Tags
31 Jan 2013, 00:37
it is not easy and is harder if we are on the test date.
there are 8 team to take out 2 teams, IF ORDER MATTERS we have 8*7 but in fact order does not matter
8*7/2=28
princeton gmat book explain this point wonderfully.




EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 16104
Location: United States (CA)

Re: There are 8 teams in a certain league and each team plays each of the
[#permalink]
Show Tags
12 Jan 2015, 13:46
Hi All, Using the Combination Formula IS one way to approach these types of questions, but it's not the only way. Sometimes the easiest way to get to a solution on Test Day is to just draw a little picture and keep track of the possibilities.... Let's call the 8 teams: ABCD EFGH We're told that each team plays each other team JUST ONCE. Start with team A.... A plays BCD EFGH = 7 games total Team B has ALREADY played team A, so those teams CANNOT play again... B plays CD EFGH = 6 more games Team C has ALREADY played teams A and B, so the following games are left... C plays D EFGH = 5 more games At this point, you should notice a pattern: the additional number of games played is reduced by 1 each time. So what we really have is: 7 + 6 + 5 + 4 + 3 + 2 + 1 + 0 = 28 games played Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Intern
Joined: 18 Oct 2012
Posts: 4

Re: There are 8 teams in a certain league and each team plays each of the
[#permalink]
Show Tags
18 Nov 2012, 20:09
These type of problems can be solved with a simple diagram.
1. Draw a table consisting of 8 columns and 8 rows. 2. Divide the table by a diagonal and count the number of spaces including the half spaces only on one side of the diagonal. 3. The number should be 28.
I tried uploading the diagram but unsuccessful.



Math Expert
Joined: 02 Sep 2009
Posts: 61192

Re: There are 8 teams in a certain league and each team plays each of the
[#permalink]
Show Tags
17 Jun 2012, 02:57
sarb wrote: There are 8 teams in a certain league and each team plays each of the other teams exactly once. 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 The total # of games played would be equal to the # of different pairs possible from 8 teams, which is \(C^2_{8}=28\). Answer: C. P.S. Please read and follow: rulesforpostingpleasereadthisbeforeposting133935.html Pay attention ot the points #3 and #8.
_________________



Intern
Joined: 20 Sep 2014
Posts: 7

Re: There are 8 teams in a certain league and each team plays each of the
[#permalink]
Show Tags
Updated on: 13 Jan 2015, 06:51
SreeViji wrote: Hi Bunnel,
I would also like to learn this approach. Can u help me?
Sree Hey SreeViji, I think i have something to help you. The answer here is the combination 8C2 ( 8 teams Choose 2) which mean \frac{8!}{6!x2!} > \frac{8x7}{2} To understand that we just have to think that each of the 8 team plays against 7 other (8x7) but they play each team exactly once so we divide the total by 2. We divide by 2 because "TEAM A VS TEAM B" is the same as "TEAM B VS TEAM A" So we end up with \frac{8x7}{2}= 28 If you still have trouble with combination and permutation check out this website it's well done, http://www.mathsisfun.com/combinatorics ... tions.htmlhope it helps.



Math Expert
Joined: 02 Sep 2009
Posts: 61192

Re: There are 8 teams in a certain league and each team plays each of the
[#permalink]
Show Tags
27 Dec 2013, 02:08



eGMAT Representative
Joined: 04 Jan 2015
Posts: 3239

Re: There are 8 teams in a certain league and each team plays each of the
[#permalink]
Show Tags
20 May 2015, 02:10
onedayill wrote: pranav123 wrote: These type of problems can be solved with a simple diagram.
1. Draw a table consisting of 8 columns and 8 rows. 2. Divide the table by a diagonal and count the number of spaces including the half spaces only on one side of the diagonal. 3. The number should be 28.
I tried uploading the diagram but unsuccessful. Hi, I don;t think we need to count the half spaces. with half space count is 36. without half space  count: 28. Dear onedayillYou're right! The boxes along the diagonal (these are the boxes that contribute to half spaces) represent a team playing with itself. Since that is not possible, these boxes should not be included in the counting. I noticed in the thread above that a few students had doubts about the expression 8C2. If any of the current students too have such a doubt, here's how this question could be solved visually: There are 7 ways in which Team 1 can play with another team. Similarly, there are 7 ways for each of the 8 teams to choose its playing opponent. But it's easy to see that the red zone is essentially a duplication of the blue zone. For example, (Team 1 playing with Team 2) is the same case as (Team 2 playing with Team 1) So, the correct answer will be: 8(that is, the number of teams)*7(that is, the number of ways in which each team can choose its playing opponent)/2 = 28 Hope this was useful! Best Regards Japinder
_________________



Math Expert
Joined: 02 Sep 2009
Posts: 61192

Re: There are 8 teams in a certain league and each team plays each of the
[#permalink]
Show Tags
16 May 2013, 03:33
mywaytomba wrote: Bunuel wrote: The total # of games played would be equal to the # of different pairs possible from 8 teams, which is \(C^2_{8}=28\).
Hi Bunuel, I have seen that you are using this formula/approach to solve most of the combination questions. Could you please explain, in general, how do you use this formula? Thanks a lot. Check combinatorics chapter of Math Book for theory: mathcombinatorics87345.html Also check some questions on combinations to practice: DS: search.php?search_id=tag&tag_id=31PS: search.php?search_id=tag&tag_id=52Hard questions on combinations and probability with detailed solutions: hardestareaquestionsprobabilityandcombinations101361.html (there are some about permutation too) Hope it helps.
_________________



Director
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 717
Location: United States (CA)
Age: 40
GMAT 1: 770 Q47 V48 GMAT 2: 730 Q44 V47 GMAT 3: 750 Q50 V42
WE: Education (Education)

Re: There are 8 teams in a certain league and each team plays each of the
[#permalink]
Show Tags
25 May 2016, 21:25
Attached is a visual that should help.
Attachments
Screen Shot 20160525 at 9.41.57 PM.png [ 75.15 KiB  Viewed 112796 times ]



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9417
Location: United States (CA)

Re: There are 8 teams in a certain league and each team plays each of the
[#permalink]
Show Tags
16 Jun 2016, 05:00
sarb wrote: There are 8 teams in a certain league and each team plays each of the other teams exactly once. 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 We are given that there are 8 teams in a league and that each game is played by 2 teams. Note that each team does not play itself, and the order of pairing each team with its opponent doesn't matter. [For example, the pairing of (Team A vs. Team B) is identical to the pairing of (Team B vs. Team A).] The situation can therefore be solved by finding the number of combinations of 8 items taken 2 at a time, or 8C2, as follows: 8C2 = 8! / [2! x (82)!] (8 x 7 x 6!) / (2! x 6!) (8 x 7)/2! (8 x 7)/ 2 4 x 7 = 28 Answer C
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



Retired Moderator
Joined: 25 Feb 2013
Posts: 1141
Location: India
GPA: 3.82

Re: There are 8 teams in a certain league and each team plays each of the
[#permalink]
Show Tags
19 Mar 2018, 10:00
dave13 wrote: Bunuel wrote: sarb wrote: There are 8 teams in a certain league and each team plays each of the other teams exactly once. 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 The total # of games played would be equal to the # of different pairs possible from 8 teams, which is \(C^2_{8}=28\). Answer: C. P.S. Please read and follow: http://gmatclub.com/forum/rulesforpos ... 33935.html Pay attention ot the points #3 and #8. Bunuel you know I got confused by your shortcut solution until figured out all possible combinations in details . you know what surprises how this expression \(C^2_{8}=28\) excludes the possibility of playing more than one game by two distinct teams, also it exludes repeated games like AB and BA.... let 8 teams be A, B, C, D, E, F, G, H NUMBER OF GAMES PLAYES BY TWO TEAMS AS FOLLOWS: AB BC CD DE EF AC BD CE DF EG AD BE CF DG EH AE BF CG DH AF BG CH AG BH AH niks18 your comments are always appreciated have a great day Hi dave13it is clearly mentioned in the question that each team plays against other team only Once. Hence you can safely use the formula provided by Bunuel. and if we say A plays against B then its same as saying B plays against A so order does not matter here. Hence there will be only one combination with A & B taken together and not two different combinations as stated by you AB & BA.



Senior Manager
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 417
Location: India
GMAT 1: 640 Q43 V34 GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)

Re: There are 8 teams in a certain league and each team plays each of the
[#permalink]
Show Tags
14 Nov 2012, 05:23
Bunuel wrote: sarb wrote: There are 8 teams in a certain league and each team plays each of the other teams exactly once. 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 The total # of games played would be equal to the # of different pairs possible from 8 teams, which is \(C^2_{8}=28\). Answer: C. P.S. Please read and follow: rulesforpostingpleasereadthisbeforeposting133935.html Pay attention ot the points #3 and #8. I would like to learn about \(C^2_{8}=28\). Manhattan Book doesn't discuss this approach. They have anagram approach.
_________________
hope is a good thing, maybe the best of things. And no good thing ever dies.Who says you need a 700 ?Check this out : http://gmatclub.com/forum/whosaysyouneeda149706.html#p1201595My GMAT Journey : http://gmatclub.com/forum/endofmygmatjourney149328.html#p1197992



Intern
Joined: 14 Jan 2013
Posts: 3
Location: Austria

Re: There are 8 teams in a certain league and each team plays each of the
[#permalink]
Show Tags
16 May 2013, 00:13
Bunuel wrote: The total # of games played would be equal to the # of different pairs possible from 8 teams, which is \(C^2_{8}=28\).
Hi Bunuel, I have seen that you are using this formula/approach to solve most of the combination questions. Could you please explain, in general, how do you use this formula? Thanks a lot.



Manager
Joined: 13 Jul 2013
Posts: 59

Re: There are 8 teams in a certain league and each team plays each of the
[#permalink]
Show Tags
26 Dec 2013, 22:04
Lets assume the question asks 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?
Then is 28*2 the correct approach?



Senior Manager
Status: Math is psychological
Joined: 07 Apr 2014
Posts: 399
Location: Netherlands
GMAT Date: 02112015
WE: Psychology and Counseling (Other)

Re: There are 8 teams in a certain league and each team plays each of the
[#permalink]
Show Tags
12 Jan 2015, 11:48
I also used a table to do this, like that:
1_2_3_4_5_6_7_8 1_1_1_1_1_1_1_1 2_2_2_2_2_2_2_2 3_3_3_3_3_3_3_3 4_4_4_4_4_4_4_4 5_5_5_5_5_5_5_5 6_6_6_6_6_6_6_6 7_7_7_7_7_7_7_7 8_8_8_8_8_8_8_8
Then you delete the same team pairs: e.g. 11, 22, 33 and then 21 (because you have 12), 32 (because you have 23). After you cross out the first 2 columns you then see that you cross out everything from the diagonal and below. The remaining is 28.
However, the 8!/2!*6! approach is better, because if you have many numbers the table will take forever to draw. In case there is sth similar though and your brain gets stuck, use the table...



Senior Manager
Joined: 25 Feb 2010
Posts: 260

Re: There are 8 teams in a certain league and each team plays each of the
[#permalink]
Show Tags
19 May 2015, 06:31
pranav123 wrote: These type of problems can be solved with a simple diagram.
1. Draw a table consisting of 8 columns and 8 rows. 2. Divide the table by a diagonal and count the number of spaces including the half spaces only on one side of the diagonal. 3. The number should be 28.
I tried uploading the diagram but unsuccessful. Hi, I don;t think we need to count the half spaces. with half space count is 36. without half space  count: 28.
_________________
GGG (Gym / GMAT / Girl)  Be Serious
Its your duty to post OA afterwards; some one must be waiting for that...



GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4318
Location: Canada

Re: There are 8 teams in a certain league and each team plays each of the
[#permalink]
Show Tags
Updated on: 06 Dec 2018, 10:46
sarb wrote: There are 8 teams in a certain league and each team plays each of the other teams exactly once. 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 There are 8 teams. If we ask each team, "How many teams did you play?" we'll find that each team played 7 teams, which gives us a total of 56 games (since 8 x 7 = 56). From here we need to recognize that each game has been COUNTED TWICE. For example, if Team A and Team B play a game, then Team A counts it as a game, and Team B ALSO counts it as a game. So, to account for the DUPLICATION, we'll divide 56 by 2 to get 28 Answer: C Cheers, Brent
_________________
Test confidently with gmatprepnow.com
Originally posted by GMATPrepNow on 27 Jun 2017, 05:43.
Last edited by GMATPrepNow on 06 Dec 2018, 10:46, edited 1 time in total.



Manager
Joined: 09 Apr 2017
Posts: 79
GPA: 3.99

Re: There are 8 teams in a certain league and each team plays each of the
[#permalink]
Show Tags
25 Aug 2017, 23:46
Try this watch this, similar examples Try pick up from Khan academy to built the foundation for permutations and combinations. The questions are very interesting too. Similar questions found in: https://www.khanacademy.org/math/precal ... mbinationsPosted from my mobile device




Re: There are 8 teams in a certain league and each team plays each of the
[#permalink]
25 Aug 2017, 23:46



Go to page
1 2
Next
[ 30 posts ]



