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

Question

In a chess tournament, each player in the tournament plays every other player exactly once. Each time a player wins a match, she receives 2 points, while 1 point is deducted from the loser’s score; if the match is a draw, no points are awarded or deducted. Player X has 4 points after 6 matches.

From the available options, select a number of wins and a number of losses that would result in Player X’s score. The answers must be jointly consistent with the outcome. Make only one choice in each column.

archiemuty · Answer

Hello,

I don't quite understand this system. The explanations given are clear but not on how to eliminate 3 wins

⃝ | ⃝ |0
⃝ | ⃝ |1
⃝ | ⃝ |3
⃝ | ⃝ |4
⃝ | ⃝ |5

Kurtosis · Answer

Let X be the number of wins, Y be the number of draws and Z be the number of losses.

2x + 0.5Y - Z = 4

Correct Answer: 2(1) + 0.5(4) - 0 = 4 --> X = 1; Y + Z = 4

If you have 3 wins: 2(3) + 0.5(0) - 2 = 4 --> X = 3; Y + Z = 2 --> Can you select this option? No. This is a probable answer choice but the answer choice is missing in the given options.

thuyduong91vnu · Answer

Hi archiemuty & Vyshak I have one question here. For such kind of problem, do we have another way to resolve other than testing possibilities? I mean, in case of the given data, testing possibilities could be a quick approach, but in case that we were given larger data (e.g got 100 points and participated in 70 matches..), this approach could be quite time-consuming and may incur inaccuracy, right? Thanks for help

Kurtosis · Answer

Hi,

There are 3 unknowns. The 3 unknowns can take multiple values. Answer can be found only by substituting the given values.

fanniedelavelle · Answer

Hello,
My issue with this problem is that it mentions: "Player X has 4 points after 6 matches", which implies that 6 matches have actually been played, however the only way to get to the correct answer is to assume that the player has skipped one of the games. Isn't it illogical to count a game that hasn't been played? I didn't get to the correct answer because I assumed that we shouldn't count the games that the player chooses to sit out.

Sajjad1994 · Answer

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).

bumpbot · Answer

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

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Wins	Losses	Number
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