siddreal wrote:
Bunuel wrote:
During a certain game, after each turn, a player’s points are doubled and then reduced by 80. Players can only have a whole number of points and take turns until their score reaches exactly zero. Assuming no other points are gained or earned, how many points did player A start with?
(1) Player A takes exactly 4 turns.
(2) Player A’s starting score was not a multiple of 2.
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.
_________________
Karishma
Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >