Re: GMAT CLUB OLYMPICS: The ratio of the number of marbles in boxes X and
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27 Aug 2021, 00:27
Answer: E
The ratio of the number of marbles in boxes X and Y was 5 to 8. After some number of marbles were transferred from box Y to box X, the ratio of the number of marbles in boxes X and Y became 7 to 6. What is the total number of marbles in the two boxes?
Let the number of marbles in box X be 5A and box Y be 8A.
Let the number of marbles transferred from box Y to box X be T.
A and T will be integers because number of marbles will be integer values
Therefore, (5A+T) / (8A-T) = 7/6
This will give us T = 2A.
We need to find total number of marbles in two boxes i.e. 5A+8A = 13A = 13T/2
Therefore, we also need to make sure that T needs to be even integer.
Statement 1: Initially the number of marbles in box Y was between 45 and 100.
This means 45 < 8A < 100.
i.e. 8A can be multiple of 8 between 45 and 100
i.e. 8A = 48, 56, 64, 72, 80, 88, or 96
i.e. A = 6, 7, 8, 9, 10, 11, 12
Since A has multiple values, therefore, we will have multiple values 13A i.e. total number of marble in two boxes.
Hence insufficient.
Statement 2: After the transfer, the number of marbles in box X became between 45 and 100.
This means 45 < 5A+T < 100
i.e. 45 < 7A < 100
i.e. 7A = 49, 56, 63, 70, 77, 84, 91, or 98
i.e. A = 7, 8, 9, 10, 11, 12, 13, or 14
Since A has multiple values, therefore, we will have multiple values 13A i.e. total number of marble in two boxes.
Hence insufficient.
Both statements together:
We still end up with A = 7, 8, 9, 10, 11 or 12
Since A has multiple values, therefore, we will have multiple values 13A i.e. total number of marble in two boxes.
[color=#00a651]Hence both statements together as well are insufficient.[/color]