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# There are 16 teams in a tournament. If during the first round, each te

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Director
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There are 16 teams in a tournament. If during the first round, each te  [#permalink]

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11 Jun 2016, 09:23
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Question Stats:

74% (01:10) correct 26% (01:01) wrong based on 188 sessions

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There are 16 teams in a tournament. If during the first round, each team plays every other team exactly once, how many games will be played in the first round?

A.15
B.30
C.120
D.240
E.256
Math Expert
Joined: 02 Aug 2009
Posts: 8753
Re: There are 16 teams in a tournament. If during the first round, each te  [#permalink]

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11 Jun 2016, 09:30
AbdurRakib wrote:
There are 16 teams in a tournament. If during the first round, each team plays every other team exactly once, how many games will be played in the first round?

A.15
B.30
C.120
D.240
E.256

this Q is a copy of VERITA's Q or verita's Q is a copy of this Q if the source have been mentioned correctly
http://gmatclub.com/forum/there-are-16-teams-in-a-soccer-league-and-each-team-plays-each-of-the-205437.html?fl=similar

Surprisingly whosoever copied has not even changed the number of teams .....

Choose two teams out of 16 -$$16C2 = \frac{16!}{14!2!}= \frac{16*15}{2}= 120$$
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Re: There are 16 teams in a tournament. If during the first round, each te  [#permalink]

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11 Jun 2016, 09:33
This is again a combinations questions since the order does not matter.

Number of ways to pick 2 teams from a total of 16 = 16C2 = 16!/14!*2! = 120. Hence C.
Director
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Re: There are 16 teams in a tournament. If during the first round, each te  [#permalink]

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11 Jun 2016, 10:08
chetan2u wrote:
AbdurRakib wrote:
There are 16 teams in a tournament. If during the first round, each team plays every other team exactly once, how many games will be played in the first round?

A.15
B.30
C.120
D.240
E.256

this Q is a copy of VERITA's Q or verita's Q is a copy of this Q if the source have been mentioned correctly
http://gmatclub.com/forum/there-are-16-teams-in-a-soccer-league-and-each-team-plays-each-of-the-205437.html?fl=similar

Surprisingly whosoever copied has not even changed the number of teams .....

Choose two teams out of 16 -$$16C2 = \frac{16!}{14!2!}= \frac{16*15}{2}= 120$$

Really!
However

This Question appeared to me on my Kaplan Test Prep CAT

Thanks
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Joined: 22 Mar 2017
Posts: 15
Re: There are 16 teams in a tournament. If during the first round, each te  [#permalink]

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27 May 2017, 11:23
Can someone explain to me why we divide the 16 * 15 by 2? Is it because two teams are playing?
Math Expert
Joined: 02 Sep 2009
Posts: 64951
Re: There are 16 teams in a tournament. If during the first round, each te  [#permalink]

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27 May 2017, 12:16
1
2
Nathanlambson wrote:
Can someone explain to me why we divide the 16 * 15 by 2? Is it because two teams are playing?

There are 16 teams in a tournament. If during the first round, each team plays every other team exactly once, how many games will be played in the first round?

A.15
B.30
C.120
D.240
E.256

Let me offer anothe solution, which might help to clear your doubt.

The total number of games played would be equal to the number of different pairs (groups of two) possible from 16 teams, which is $$C^2_{16}=\frac{16!}{2!14!}=120$$.

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Posts: 64951
Re: There are 16 teams in a tournament. If during the first round, each te  [#permalink]

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27 May 2017, 12:16
Intern
Joined: 26 Jun 2014
Posts: 18
Re: There are 16 teams in a tournament. If during the first round, each te  [#permalink]

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28 May 2017, 12:02
2
Nathanlambson wrote:
Can someone explain to me why we divide the 16 * 15 by 2? Is it because two teams are playing?

You divide by two because if A shakes hands with B, then B is also shaking hands with A, so 16*15 counts each handshake twice.
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Re: There are 16 teams in a tournament. If during the first round, each te  [#permalink]

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29 May 2017, 17:45
3
Hi All,

You can actually answer this question without any complex math, as long as you take the proper notes.

We're told that 16 teams each play one another once. We're asked for the total number of games played. For the sake of organization, I'm going to name the 16 teams...

ABCDE FGHIJ KLMNO P

Team A will play each of the other 15 teams = 15 games
Team B already played Team A, so Team B plays the other 14 teams = an additional 14 games
Team C already played Teams A and B, so Team C plays the other 13 teams = an additional 13 games
Etc.

Thus, the total number of games played will be... 15+14+13....+2+1+0. Using 'bunching' you end up with (15)(8) = 120 total games played.

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Re: There are 16 teams in a tournament. If during the first round, each te  [#permalink]

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19 Jun 2017, 04:23
If you don't know the combination formula you can still give a try. As I did with little bit logical reasoning.

Note: It's always good to use proper method / formula.

# of teams = 16.

We have 5 AC.

A.15
B.30
C.120
D.240
E.256

Eliminate option A and B as the number is too low.
Eliminate option E (16 * 16 = 256) max possible matches [if we consider double entry]

Options left C & D.

If we roughly guess double entries (e.g Team1 vs Team2 = Team2 vs Team1), the number is going to be more than 16.
Hence, eliminate option D.

Ans: Option C
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Re: There are 16 teams in a tournament. If during the first round, each te  [#permalink]

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20 Jun 2017, 17:42
AbdurRakib wrote:
There are 16 teams in a tournament. If during the first round, each team plays every other team exactly once, how many games will be played in the first round?

A.15
B.30
C.120
D.240
E.256

Since there are 16 teams and each team plays every other team once, the number of games played in the first round is 16C2 =16!/[2!(16-2)!] = (16 x 15)/2! = 8 x 15 = 120 games.

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Re: There are 16 teams in a tournament. If during the first round, each te  [#permalink]

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20 Jul 2018, 02:48
The total number of games played would be equal to two selecting two teams out of 16 team

16C2=16!14!2!=16∗152=120
Re: There are 16 teams in a tournament. If during the first round, each te   [#permalink] 20 Jul 2018, 02:48