M14-09

In order for whites to avoid losing the game, they must have the last move, and therefore, the move must be one more move than the number of black moves. For blacks to avoid losing the game, they only need an equal amount of moves as the number of white moves. However, it's impossible to determine whether blacks won the games or tied them.

Thanks

I think this is a high-quality question and I agree with explanation. Wow but looks like critical reasoning question in verbal section rather than a quant question!

In a game of chess, the moves of whites and blacks alternate with whites having the first move.

Two Possible Scenarios:

i) Starts with White and ends with Black ............... eg: W -> B or W -> B -> W -> B
This means there will be equal number of black and white moves


ii) Starts with White and ends with White............... eg: W -> B -> W or W -> B -> W -> B ->W
This means there will be 1 more move of White than moves of Black

We are given that Whites have made 2319 moves altogether while Blacks have made 2315 moves.
==> The above statement means "There must be some cases where scenario 2 is applicable"


For understanding purpose, let's assume There were 5 Games with following scenarios:

Game 1: w->b.......w->b (2309 moves by each) [1 game in which white and black moved equal number of moves = 2309]
(There can be n number of games with multiple scenarios, what we care about is : "Equal number of white and black moves" )]

[ Now, remaining White moves = 10 and Black moves = 6]

As we are given that : "White made additional 4 number of moves", there can be 4 games in which White made last move
We can assume following cases:
Game 2: w->b->w
Game 3: w->b->w
Game 4: w->b->w
Game 5: w->b->w->b->w->b->w

We are given that "If in any game the side that made the last move did not lose"
Results of Games :
Game 1: Black Last move = Black did not lose = Black won or Match draw
Game 2: White Last move = White did not lose = White won or Match draw
Game 3: White Last move = White did not lose = White won or Match draw
Game 4: White Last move = White did not lose = White won or Match draw
Game 5: White Last move = White did not lose = White won or Match draw
----------------------------------
Question is asking "What can be true" [ not what "must" be true]
I. Blacks lost 5 games

--> Black can lose at most 4 games

II. Blacks won more games than whites

Let's say : Game 1 resulted in win and Game 2,3,4,5 resulted in Draw
We can say that YES blacks won more games than whites ( In our case, Blacks wins =1 and White wins = 0)

III. All games ended in a draw
--> Game 1,2,3,4,5 can resulted in draw

Hence II and III are possible

I agree with explanation.

Hi Xylan

Can you please assist me on this?

While i do understand from the Q stem that BLACK has lost 4 games since WHITE has 4 points more than BLACK. This information definitely negates the Statement that Blacks lost 5 games.

However, the other 2 Statements are way too confusing or i'm unable to get the logic.

Would really appreciate your help!
Thanks

JIAA In a game of chess, the moves of whites and blacks alternate with whites having the first move.

Two Possible Scenarios:

1) Starts with White and ends with Black ............... eg: W -> B or W -> B -> W -> B
This means there will be an equal number of black and white moves

2) Starts with White and ends with White............... eg: W -> B -> W or W -> B -> W -> B ->W
This means there will be 1 more move of White than moves of Black

We are given that Whites have made 2319 moves altogether while Blacks have made 2315 moves.

The above statement means "There must be some cases where scenario 2 is applicable"

We clearly know because of the difference in 4 points: \(2319 - 2315 = 4\)

W could have either WON or DRAW the 4 matches.

Inference: B could have either LOST or DRAW the 4 matches. - The maximum number of macthes that can be lost by B: \(4\) - Read this slowly

For understanding purpose, let's assume: There were 5 Games: {1, 2, 3, 4, 5}

Question is asking "What CAN be true" [ not what "MUST" be true] - Q is looking for a possibility, NOT a certainity

I. Blacks lost 5 games

Black can lose AT MOST 4 games

II. Blacks won more games than whites
Let's say: Game 1 resulted in win and Game 2,3,4,5 resulted in Draw
We CAN say that YES blacks won more games than whites ( In our case, Blacks wins =1 and White wins = 0) - A possible scenario

III. All games ended in a draw

Game 1,2,3,4,5 CAN result in a draw - A possible scenario

Hence, ONLY II and III CAN be possible.

One thing imp in this question is that Black will never exceed White even if it wins.
To Demonstrate:
Black win : W-B-W-B-W-B
Black Draw : W-B-W-B or W-B-W-B-W
So black is never exceeding white's count in an individual game.
So black can at most lose 4 games.
Black Can win more than 5 games
And all games may end in draw.

Please give Kudos if you like my answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.