In a chess tournament, each player in the tournament plays every other

Official Explanation

Rather than consider all of the possible combinations of wins, losses, and draws that might result in this outcome, use the answer choices. Since winning is the only way to receive positive points, start there.

(A) Because Player X has 4 points, she must have won at least two matches; eliminate A for the first column.

(B) If Player X wins 2 games, she will have 4 points. In order to stay at 4 points, she must draw all 4 of the remaining matches and lose no matches. There is no option for 0 losses so this cannot be the correct answer.

(C) If Player X wins 3 games, she will have 6 points. In order to return to 4 points, she must lose 2 of the remaining 3 games and draw on 1 game. This combination is possible in the answer choices: win 3 and lose 2.

You don’t need to check the remaining answers because you have found a pair that works. Just to check the logic: the player can’t have won 4 or 5 matches because she will earn too many points. If she wins 4 matches, she’ll earn 8 points. If she loses the other 2 matches, she’ll drop only 2 points to 6, but the problem requires her score to finish at 4. If she wins 5 matches, her final score will be even higher.

Column 1: The correct answer is (C).
Column 2: The correct answer is (B).