CAT Quantitative Ability Questions | CAT Permutation, Combination and Probability questions
CAT/1998
Question . 61
A, B, C, D, ..................X, Y, Z are the players who participated in a tournament. Everyone played with every other player exactly once. A win scores 2 points, a draw scores 1 point and a loss scores 0 points. None of the matches ended in a draw. No two players scored the same score. At the end of the tournament, the ranking list is published which is in accordance with the alphabetical order. Then
Explanatory Answer
Method of solving this CAT Quantitative Ability Question from Permutation, Combination and Probability question
(a) Each one of the 26 players played 25 matches and none of the matches ended in a draw.
Hence, all the scores must be even. Also each one of them scored different from the other.
The maximum score possible is 50 and minimum score is 0.
There are exactly 26 possible scores, 50, 48, 46 .....0. The ranking is in a alphabetical order means A scored 50, B – 48, Z – 0.
This is possible if A wins all the matches B loses only to A win against all others etc.
In final rank, every player win only with all players who are below in final ranking .
Since M > N hence M wins over N.