shortest "cut for finding the no of matches in a tourna

Expert replies

bblast: Legendary Member; Posts: 1077; Joined: Mon Dec 13, 2010 1:44 amFollowed by: 33 members; Thanked: 118 times; GMAT Score:710

by bblast » Wed Jul 06, 2011 12:10 am

1 > OG-12-PS-121 -
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?

In this question I did 8C2 which was correct.

2 > Team A, team B, team C, and team D take part in a tournament in which every team plays once with each of its opponents.

what is the total number of matches ?

answer is simple 4c2.

3>15 chess players take part in a tournament. If every player plays twice with each of his opponents, how many games will be played?

why is the answer 15P2 and not 15C something here ?

Cheers !!

Quant 47-Striving for 50
Verbal 34-Striving for 40

My gmat journey :
https://www.beatthegmat.com/710-bblast-s ... 90735.html
My take on the GMAT RC :
https://www.beatthegmat.com/ways-to-bbla ... 90808.html
How to prepare before your MBA:
https://www.youtube.com/watch?v=upz46D7 ... TWBZF14TKW_

Source: Beat The GMAT — Problem Solving | Wed Jul 06, 2011 12:10 am

GMAT/MBA Expert

Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Wed Jul 06, 2011 12:25 am

bblast wrote:1 > OG-12-PS-121 -
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?

In this question I did 8C2 which was correct.

2 > Team A, team B, team C, and team D take part in a tournament in which every team plays once with each of its opponents.

what is the total number of matches ?

answer is simple 4c2.

3>15 chess players take part in a tournament. If every player plays twice with each of his opponents, how many games will be played?

why is the answer 15P2 and not 15C something here ?

Hope you got the difference.
If not, read on...

If they played once with their opponent, number of games = 15C2
If they played twice with their opponent, number of games = 2*(15C2) = 2*(15!/[(15 - 2)!*2!]) = 15!/(15 - 2)! = 15P2

Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/

bblast: Legendary Member; Posts: 1077; Joined: Mon Dec 13, 2010 1:44 amFollowed by: 33 members; Thanked: 118 times; GMAT Score:710

by bblast » Wed Jul 06, 2011 12:34 am

perfect anurag, so the 15p2 was here was accidental. if each team plays other exactly thrice then we have the solution :

15C2 * 3. Correct ?

GMAT/MBA Expert

Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Wed Jul 06, 2011 12:42 am

bblast wrote:perfect anurag, so the 15p2 was here was accidental. if each team plays other exactly thrice then we have the solution :

15C2 * 3. Correct ?

I won't say 'accidental' because it is another way to write 2*(15C2). But yes the answer will of the form (Number of times they play)*(15C2).

Featured schoolRound 2 closes Jan 7, 2027 53 days left

Chicago Booth

Since 1982, 10 Booth faculty members have received the Nobel Prize in Economic Sciences, more than any other business school.

#3
U.S. News rank: $175,000
Median base salary: 670
Average GMAT Focus: 635
Students in the class

Apply to Booth Visit chicagobooth.edu See the full profile

Photo: Warren LeMay, CC BY-SA 2.0

GMAT Course Reviews

563 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (563 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review