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30 Apr 2017, 09:20
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There are n people competing in a chess tournament. Each competitor must play every other competitor k times. If n > 1 and k > 0, what is the total number of games played in the tournament?
A) kn – k
B) (n² – 2k)/2
C) k(n² – n)/2
D) (n² – 2nk + k)/2
E) (kn – 2k)/2
*kudos for all correct solutions
A) kn – k
B) (n² – 2k)/2
C) k(n² – n)/2
D) (n² – 2nk + k)/2
E) (kn – 2k)/2
*kudos for all correct solutions
30 Apr 2017, 10:58
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GMATPrepNow
There are n people competing in a chess tournament. Each competitor must play every other competitor k times. If n > 1 and k > 0, what is the total number of games played in the tournament?
A) kn – k
B) (n² – 2k)/2
C) k(n² – n)/2
D) (n² – 2nk + k)/2
E) (kn – 2k)/2
*kudos for all correct solutions
A) kn – k
B) (n² – 2k)/2
C) k(n² – n)/2
D) (n² – 2nk + k)/2
E) (kn – 2k)/2
*kudos for all correct solutions
- • If each player plays with each other only once then the total number games is simply given by
- o \(^nC_2 = \frac{n!}{[2!(n-2)!]} = \frac{[n(n-1)]}{2}\)
o Where n is the number of players and we choose 2 players at a time to play a single game.
- o Hence the total number of games would be multiplied “k” times.
o Thus the total number of games = k * Total number of games played once \(= k*n*\frac{(n-1)}{2} = k*\frac{(n^2 – n)}{6}\)
01 May 2017, 06:21
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GMATPrepNow
There are n people competing in a chess tournament. Each competitor must play every other competitor k times. If n > 1 and k > 0, what is the total number of games played in the tournament?
A) kn – k
B) (n² – 2k)/2
C) k(n² – n)/2
D) (n² – 2nk + k)/2
E) (kn – 2k)/2
A) kn – k
B) (n² – 2k)/2
C) k(n² – n)/2
D) (n² – 2nk + k)/2
E) (kn – 2k)/2
I will do this logically
If I choose 3 teams to meet only 1 round. then total number of games =3
n= 3 & k=1 & total =3
Plug in the answer choices
A) kn – k ..................................3-1=2.............................Eliminate
B) (n² – 2k)/2......................... (9-2)/2.............................Eliminate
C) k(n² – n)/2...........................1 * (9-3)/2=3....................Keep
D) (n² – 2nk + k)/2..................(9-6+1)/2.........................Eliminate
E) (kn – 2k)/2..........................(3-2)/2.............................Eliminate
Answer: C
