Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

There are 8 teams in a certain league and each team plays each of the [#permalink]

Show Tags

03 Dec 2009, 01:07

1

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

15% (low)

Question Stats:

76% (01:40) correct
24% (01:03) wrong based on 115 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?

Re: There are 8 teams in a certain league and each team plays each of the [#permalink]

Show Tags

03 Dec 2009, 07:35

its 8C2 that means [(Factorial 8)] / [ (Factorial 2)(Factorial 6) ] added OG tag

ro86 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?

1.15 2.16 3.28 4.56

OA is 28

I am not able to understand the explanation given to me in the OG. The OG has calculated the answer as (8x7)/2. has the og used some formula to arrive at the answer.

Tho i got the answer through manual counting. can any 1 explain the process used in the OG.

Re: There are 8 teams in a certain league and each team plays each of the [#permalink]

Show Tags

03 Dec 2009, 07:49

ro86 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?

1.15 2.16 3.28 4.56

OA is 28

I am not able to understand the explanation given to me in the OG. The OG has calculated the answer as (8x7)/2. has the og used some formula to arrive at the answer.

Tho i got the answer through manual counting. can any 1 explain the process used in the OG.

this is nothing but application of direct formulae i.e combination ( if one is aware of this) the formula is if we are asked to select r items out of n items then we can say nCr=n!/[(n-r)!*(n!)] now in this q to play a match we need 2(r) teams out of 8(n) teams substituting we get 8!/[2!*6!]=8*7*6!/[2!*6!]=8*7/2=28 HTH _________________

GMAT is not a game for losers , and the moment u decide to appear for it u are no more a loser........ITS A BRAIN GAME

Re: There are 8 teams in a certain league and each team plays each of the [#permalink]

Show Tags

03 Dec 2009, 07:54

2

This post received KUDOS

This is just applying the idea of choosing combinations i.e. in how many ways can you choose 2 teams from a total 8. You can readily apply the formula for choosing 2 out of 8 as \(= (8x7)/2 = 28\)

The explanation would be something like: Essentially, we need to find all possible pairs of teams from the 8.

So to create a pair, the first team can be chosen from the total of 8 - so 8 options/ways available. Now for each of this, we can choose the the opponent team for the pair from the 7 teams left. So the total will be \(8 x 7 = 56.\)

Now you can see that when we do the above, we will all possible pairs - (team1, team2), (team2, team3)....etc. We will also get the reverse pair (team2, team1), (team3, team2).... The order shouldn't matter since a game is just between 2 teams irrespective of the order.

So for every such pair of team, the reverse order is also included in the total of 56. So the total number of unique pairs we can have (which is the number of games) \(= 56/2 = 28\).

Re: There are 8 teams in a certain league and each team plays each of the [#permalink]

Show Tags

24 Jul 2011, 02:03

I was so confused by this line "If each game is played by 2 teams, what is the total number of games played?

I got 28 (coz 7!) then when I see this line "If each game is played by 2 teams, what is the total number of games played?" I took one extra step to divide 28/2 = 14......although 14 is not a choice but I wonder can ayone pls explain what does this line mean?

Re: There are 8 teams in a certain league and each team plays each of the [#permalink]

Show Tags

25 Jul 2011, 10:05

1

This post was BOOKMARKED

You can use combinations or you can do the following (note that this often comes up as something called "the handshake problem" as well as in counting the number of diagonals in convex polygons).

Team 1: plays 7 other teams - 7 games Team 2: plays 7 other teams, but you already counted their game against team 1 - 6 games Team 3: plays 7 other teams, but you already counted their games against teams 1 and 2 - 5 games And so on

7 + 6 + 5 + 4 + 3 + 2 + 1 = 28

If there are x people in a room, then for everyone to shake hands with everyone else exactly once there will be (x(x-1))/2 handshakes. Same method with the polygon problem.

Re: There are 8 teams in a certain league and each team plays each of the [#permalink]

Show Tags

05 Feb 2015, 03:49

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Re: There are 8 teams in a certain league and each team plays each of the [#permalink]

Show Tags

05 Feb 2015, 04:14

Expert's post

ro86 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?

Re: There are 8 teams in a certain league and each team plays each of the [#permalink]

Show Tags

05 Feb 2015, 04:14

Expert's post

1

This post was BOOKMARKED

Bunuel wrote:

ro86 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?

Excellent posts dLo saw your blog too..!! Man .. you have got some writing skills. And Just to make an argument = You had such an amazing resume ; i am glad...

So Much $$$ Business school costs a lot. This is obvious, whether you are a full-ride scholarship student or are paying fully out-of-pocket. Aside from the (constantly rising)...

London is the best kept secret of the corporate world. It is English speaking and time delayed by only 5 hours. That means when London goes home at 5...