ykaiim 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

A) III only

B) I and II only

C) I and III only

D) II and III only

E) I, II, and III

OA is D and OE is:

From the stem it follows that there were only 4 games in which whites had the last move. These 4 games were responsible for the difference in the total number of moves made by whites and blacks during the tournament. We know that these 4 games were not won by blacks (but they could well have ended in a draw). All the other games could have been won by blacks or ended in a draw. Thus, scenarios II and III are possible.

Scenario I is impossible. It means that there were at least 5 games in which whites had the last move. If this were true then the difference between the total number of moves of whites and blacks should be at least 5. In fact, it's only 4.

So, either II or III is possible.

I want to know if how II case is possible as we dont have any other data to find that.

If white wins then white has more moves

If black wins black has the same moves as white

Let's say black wins 6 games so the number of moves are equal. For argument's sake let's say it took two moves for black and two moves for white for each game. Total = 12 each

Let's say white wins 4 games and for argument's sake white wins in 2 moves so black only has 1 move: total moves, 8 for white and 4 for black

Total moves of all 10 games: white = 20 and black = 16

So it's possible black wins more games than white. The question asks what can be possible. That doesn't mean black definitely won all games, however, it is possible.