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

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

by swerve » Mon May 07, 2018 11:04 am

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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 move 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

A. III only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III

The OA is D.

Please, can anyone explain this PS question for me? I can't get the correct answer. I need help. Thanks.
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by deloitte247 » Sat Jun 02, 2018 4:27 pm
4 games end with white being the last player 2315 end with black being the last player.
Let number of white moves =NW , Number of black moves= NB For a single game of chess
Since the white starts, black can either win or draw on their turn.
Therefore, NB=NW
Similarly, white can win or draw in their turn , Therefore NW=NB+1
We are given sum total of all white and black wins in a tournament, clearly whites have only won or drawn 4 more games (2319-2315).
Black on the other hand have won or drawn as many as 2315 games. It is certain that blacks didn't lose more than 4 games,
blacks won more than whites all games probably ended in a draw
Answer is Option D = II and III
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