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In a game of chess the moves of whites and blacks alternate

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Manager
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Joined: 22 May 2007
Posts: 220

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In a game of chess the moves of whites and blacks alternate [#permalink]

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New post 26 Jul 2008, 19:58
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In a game of chess the moves of whites and blacks alternate with whites having the first move. During a certain chess tournament whites have made 2319 moves altogether while blacks have made 2315 moves. If in any game the side that made the last move did not lose, which of the following can be true about the tournament?

I. Blacks lost 5 games

II. Blacks won more games than whites

III. All games ended in a draw


* III only
* I and II only
* I and III only
* II and III only
* I, II, and III

Kudos [?]: 113 [0], given: 0

Director
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Joined: 14 Aug 2007
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Re: Like Chess ?- Try this [#permalink]

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New post 26 Jul 2008, 20:35
IMO D.

Whites - Blacks = 2319 - 2315= 4..Whites have made 4 more moves than blacks

Since Whites start the game, then :
When Whites win the game -> they have 1 more move than blacks
When Blacks win the game -> the number of moves by whites and blacks equals
When there's a draw -> either the number of moves made by whites and blacks equal OR whites have one more move than blacks. [ because either white or black can draw the game]

Considering above 3 scenerios
I. Untrue, Because blacks could have won maximum of 5 games given the difference is 4

II. Possible, Consider the underlined part of possibility of draw above; whites could have done 4+ more moves to draw the game and still blacks have won more games.

III. This is also possible; Consider the underlined part of possibility of draw above; considering that the +4 moves by whites were to draw the game

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Director
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Re: Like Chess ?- Try this [#permalink]

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New post 26 Jul 2008, 21:52
Not a very well thought out question. Any statement "can" be true.

A Black can lost 5 games (and win 0 or 1 or 5 or whatever games).
B it is possible that black won more games than white
C It is also possible that all games ended in a tie.

aaron22197 wrote:
In a game of chess the moves of whites and blacks alternate with whites having the first move. During a certain chess tournament whites have made 2319 moves altogether while blacks have made 2315 moves. If in any game the side that made the last move did not lose, which of the following can be true about the tournament?

I. Blacks lost 5 games

II. Blacks won more games than whites

III. All games ended in a draw


* III only
* I and II only
* I and III only
* II and III only
* I, II, and III

Kudos [?]: 225 [0], given: 0

Senior Manager
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Joined: 06 Apr 2008
Posts: 432

Kudos [?]: 164 [0], given: 1

Re: Like Chess ?- Try this [#permalink]

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New post 26 Jul 2008, 22:30
aaron22197 wrote:
In a game of chess the moves of whites and blacks alternate with whites having the first move. During a certain chess tournament whites have made 2319 moves altogether while blacks have made 2315 moves. If in any game the side that made the last move did not lose, which of the following can be true about the tournament?

I. Blacks lost 5 games

II. Blacks won more games than whites

III. All games ended in a draw


* III only
* I and II only
* I and III only
* II and III only
* I, II, and III


Will go with E)

Black can end up losing 5 games
Black can won more than whites since white taking last move can also mean that game ended in draw.
All games can end in draw as well since draw does not gurantee who made last move.

Kudos [?]: 164 [0], given: 1

Re: Like Chess ?- Try this   [#permalink] 26 Jul 2008, 22:30
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In a game of chess the moves of whites and blacks alternate

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