If each participant of a chess tournament plays exactly one game with each of the remaining participants, then 153 games will be played during the tournament. Find the number of participants. Choose one:
A) 15  B) 16  C) 17  D) 18  E) 19

Rationale: "if the number of participants is 3 ( say a , b , c ) the number of games played will be 2 ( a plays against b and c ) + 1 ( b plays against c ) = 3 using the same logic , if the number of participants is n , the number of games played will be ( n - 1 ) + ( n - 2 ) + ( n - 3 ) + . . . 3 + 2 + 1 given that this sum = 153 = 1 + 2 + 3 + . . . ( n - 1 ) sum of first m positive integers is given by m ( m + 1 ) / 2 . so sum of first ( n - 1 ) positive integers is ( n - 1 ) * n / 2 153 = ( n - 1 ) * n / 2 ( n - 1 ) * n = 306 17 * 18 = 306 ( we know that 15 ^ 2 = 225 so the two consecutive numbers must be greater than 15 . also , 20 ^ 2 = 400 so the two numbers must be less than 20 . the pair of numbers in between 15 and 20 whose product ends with 6 is 17 and 18 ) so n = 18 answer ( d )"
Answer: D