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 Answer: C Source: www.gmatprepnow.com Difficulty level: 650

Brent@GMATPrepNow wrote: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 Answer: C Source: www.gmatprepnow.com Difficulty level: 650 Here's one approach (there are several others): Let's say a MATCH is when two competitors sit down to play their k games against each other. If we ask each of the n competitors, "How many MATCHES did you have?", the answer will be n-1, since each competitor plays every other competitor, but does not play against him/herself. So, n(n-1) = the total number of MATCHES IMPORTANT: There's some duplication here. For example, when Competitor A says that he/she played n-1 other competitors, this included the match played against Competitor B. Likewise, when Competitor B said he/she played n-1 other competitors, this included the match played against Competitor A. So, in our calculation of n(n-1) = the total number of MATCHES, we included the A vs B match twice. In fact, we counted every match two times. To account for this duplication, we'll take n(n-1) and divide by 2 to get n(n-1)/2 MATCHES. Since each match consists of k games, the total number of games = kn(n-1)/2 Check the answer choices....not there! However, we can take kn(n-1)/2 and rewrite it as k(n² - n)/2 Answer: C Cheers, Brent