During a certain game, after each turn, a player’s points are doubled

A straight logical answer is YES..
since we have a term being multiplied by 2, there will be only one term which will be a non-multiple of 2, because a term prior to it will be a decimal.

other way..
nth term = \(2^nx-80*(2^n-1)=0........2^n(80-x)=80\)
x is an ODD integer, and 80-x has to be a multiple of 5, so 80-x can be 5, 15 , 25 ....
Only \(2^n*5 = 80\) when n is 4, so \(80-x=5...x=80-5=75\)

Bunuel VeritasKarishma Pls help to solve statement B.

When the player completes the game (reaches a score of 0), we know what if his number of points before that were N,

2N - 80 = 0
N = 40

Now, can we say what the score was in the previous turn? Sure. We got 40 by doubling the previous score and subtracting 80.

2M - 80 = 40
M = 60

Now, can we say what the score was in the previous turn? Sure. We got 60 by doubling the previous score and subtracting 80.

2L - 80 = 60
L = 70

Now, can we say what the score was in the previous turn? Sure. We got 70 by doubling the previous score and subtracting 80.

2K - 80 = 70
K = 75
(not an even score)

Now, can we say what the score was in the previous turn? Sure. We got 75 by doubling the previous score and subtracting 80.

2J - 80 = 75
J = 77.5

The reason we did not need to do all this calculation backwards was this - Every time, we are adding 80 to the current score and dividing by 2. As long as our current score is even,
(Even + 80) = Even, so on dividing by 2 we get an integer.
The moment out current score becomes odd (75 in our case), the previous score will not be an integer because Odd + 80 = Odd. So on dividing by 2, we get a decimal. But every score must be an integer. This tells us that there is only one odd score that anyone can have and that is in the beginning of the game and it is 75 only (as calculated above). But since this is a DS question, we didn't really need to do the calculation as long as we know that we will get a single unique value of the starting score.

Just wondering, how could this possibly even be a game? I mean, all you can do is starting with 75 points and ending with 0 points. And no points can be awarded? This question doesnt fit the logic of reality, that is, answering the question why people play games?

That's not the point. If you want to tie this question to logic of reality, you need to do it in a different way. What if you need to analyse a game or a point system. You need to decide whether it works or not. This is the closest you can get to relating the real world to this question. Also, the logic does not lie in the statements but in the process that you are doing to arrive at the answer and that skill of deriving an answer logically works everywhere. And the purpose of many games is to arrive at 0. While playing 8 ball pool, you should have 0 balls on the table in order to win. But anyway, I don't think that's the point.

I got this question wrong though LOL.

Of course the purpose of a game can be to arrive at 0. I instantly thought of dart when I read the question. The confusing part here is just that points did not get awarded or withdrawn or anything during the game. But ok, we can think of a game where you always start with 75 points and if you dont make any mistakes, the least number of turns to arrive at 0 will be four turns. During a turn then, if you lose or make a mistake, your score will only decrease by 20, or 40, or 60 by the end of the turn. Or maybe there can be some penalty if you lose one turn and then your score will get back to what you had in the end of the last turn.

So well, there might actually be a game that fits the description. One thing though is for sure: I already hate this game.

I hear what you're saying. But the takeaway from this question is the approach to logical thinking, of course hardly any of us would be calculating how long it takes for 2 trains to pass each other or how many people have been vaccinated. Such situations would obviously be much more complex than STD formulas or a simple sets matrix. The objective of this section is to test our reasoning skills. I think we're both on the same page though. Good luck with your prep!

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