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# A city is hosting a Swiss-system chess tournament called Chessmaster

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Intern
Joined: 06 Nov 2015
Posts: 23
GMAT 1: 690 Q49 V35
A city is hosting a Swiss-system chess tournament called Chessmaster  [#permalink]

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18 Apr 2016, 20:58
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A city is hosting a Swiss-system chess tournament called Chessmaster. In a Swiss-system tournament, every player plays every other player, and no one is eliminated. At Chessmaster, each player who wins a match receives two points; those who draw a match each receive half a point; those who lose a match each lose one point; and every player can choose to sit out one match (and neither receive nor lose points). Player X has 4 points after 6 matches.

From the available options, select a number of wins and a number of combined draws and 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.

Wins| Draws + Losses| Number
⃝ | ⃝ |0
⃝ | ⃝ |1
⃝ | ⃝ |3
⃝ | ⃝ |4
⃝ | ⃝ |5

This is an IR question from MGMAT test. Could someone help to give some other ways to resolve such kind of question rather than testing possibilities? Thanks

The explanation given by Manhattan is as below:
The only way to answer this question is to quickly work out all the possible patterns of 6 rounds that would result in a score of 4 points. Basically, Player X could have won 1, 2, or 3 games (any more than that and the score is too big, while draws alone can’t bring the score up to 4 points in only 6 games). Let’s consider these three possibilities:

1 Win: With only 1 win, the only way to get up to 4 points would be to draw the next 4 games, and sit the last one out. This will turn out to be the situation that the answer choices fit.

2 Wins: Looking at the answer choices, we can see that 2 isn’t an option. However, with 2 wins, the only way to reach 4 points is to draw twice and then lose once (and sit the final round out).

3 Wins: With three wins (adding up to six points), the only way to get down to 4 points is to lose two matches in a row (and sit out the final round). While 3 is an option in the answer choices, we already know that 2 isn’t, so this can’t be the correct situation.

Answer: Wins: 1, Draws + Losses: 4
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Re: A city is hosting a Swiss-system chess tournament called Chessmaster  [#permalink]

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19 Apr 2016, 11:42
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
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Joined: 13 Apr 2015
Posts: 1710
Location: India
Concentration: Strategy, General Management
GMAT 1: 200 Q1 V1
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Re: A city is hosting a Swiss-system chess tournament called Chessmaster  [#permalink]

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19 Apr 2016, 11:48
archiemuty wrote:
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

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.
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Re: A city is hosting a Swiss-system chess tournament called Chessmaster  [#permalink]

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19 Apr 2016, 18:38
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
_________________

"Chance favors the prepared mind"

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Re: A city is hosting a Swiss-system chess tournament called Chessmaster  [#permalink]

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19 Apr 2016, 19:13
1
thuyduong91vnu wrote:
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

Hi,

There are 3 unknowns. The 3 unknowns can take multiple values. Answer can be found only by substituting the given values.
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Re: A city is hosting a Swiss-system chess tournament called Chessmaster  [#permalink]

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09 Dec 2017, 09:19
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.
Re: A city is hosting a Swiss-system chess tournament called Chessmaster &nbs [#permalink] 09 Dec 2017, 09:19
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