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26 May 2022, 03:00
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A
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Difficulty:
55%
(hard)
Question Stats:
69% (02:20) correct
31%
(02:45)
wrong
based on 275
sessions
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Not Attempted Yet
Each of A and B has a few marbles with them. If A gives 12 marbles to B, the ratio of the number of marbles with them becomes the reciprocal of the initial ratio. If they together have a total of N marbles, how many marbles should A give to B so that each of them has an equal number of marbles?
(A) 6
(B) 12
(C) 24
(D) 26
(E) 30
(A) 6
(B) 12
(C) 24
(D) 26
(E) 30
Updated on: 26 May 2022, 12:30
Originally posted by ThatDudeKnows on 26 May 2022, 12:22.
Last edited by ThatDudeKnows on 26 May 2022, 12:30, edited 2 times in total.
Last edited by ThatDudeKnows on 26 May 2022, 12:30, edited 2 times in total.
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Bunuel
This question is a great example of how GMAT quant is NOT a math test, it is a test of whether you can get math questions right!! Think through problems and you can avoid a ton of math, get the question right, and move on to the next one!!
If A gives 12 marbles to B, the relationship is flipped from where it was to begin. The question asks us how many A has to give to B to have them be equal. Equal is half way to having them flipped, so we need half of 12. Six.
Answer choice A.
If you aren't confident, go ahead and plug in. We just need to pick numbers such that wen we take from A and give to B, B ends up with A initially had. That just means B has 12 less than A.
If A starts with 12 and B with 0, they end up at A with 0 and B with 12. If A had given six to B, A would have 6 and B would have 6.
If A starts with 13 and B with 1, they end up at A with 1 and B with 13. If A had given six to B, A would have 7 and B would have 7.
If A starts with 14 and B with 2, they end up at A with 2 and B with 14. If A had given six to B, A would have 8 and B would have 8.
If A starts with 15 and B with 3, they end up at A with 3 and B with 15. If A had given six to B, A would have 9 and B would have 9.
General Discussion
26 May 2022, 11:32
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Let the number of marbles with A and B be x and y respectively.
The ratio of the number of marbles with them = \(\frac{ x }{ y}\)
It is also known that x + y = N
If A gives 12 marbles to B, the respective numbers of marbles with A and B are x – 12 and y + 12.
It is known that \(\frac{(x – 12) }{ (y + 12)}\) = \(\frac{y }{ x}\)
Simplifying the above equation, we get,
\(x^2\) – \(y^2\) = 12 (x + y)
Using standard algebraic identities, the equation above can be rewritten as,
(x – y) (x + y) = 12 (x + y)
From the equation above, x – y = 12 or x = y + 12
Since x + y = N, the value of x can be substituted in this equation. Upon doing so, we have,
y + 12 + y = N
2y + 12 = N
Solving for y, we have y = \(\frac{(N – 12)}{ 2}\)
Therefore, x = y + 12 = \(\frac{(N – 12)}{2}\) + 12 = \(\frac{(N + 12)}{2}\)
Let the number of marbles that A has to give B be k.
Then, x – k = y + k
\(\frac{(N + 12)}{2}\) – k = \(\frac{(N – 12)}{2}\) + k
Solving for k, we have,
N + 12 – 2k = N - 12 + 2k
4k = 24
k = 6
A should give 6 marbles to B so that each of them has an equal number of marbles
The correct answer option is A
The ratio of the number of marbles with them = \(\frac{ x }{ y}\)
It is also known that x + y = N
If A gives 12 marbles to B, the respective numbers of marbles with A and B are x – 12 and y + 12.
It is known that \(\frac{(x – 12) }{ (y + 12)}\) = \(\frac{y }{ x}\)
Simplifying the above equation, we get,
\(x^2\) – \(y^2\) = 12 (x + y)
Using standard algebraic identities, the equation above can be rewritten as,
(x – y) (x + y) = 12 (x + y)
From the equation above, x – y = 12 or x = y + 12
Since x + y = N, the value of x can be substituted in this equation. Upon doing so, we have,
y + 12 + y = N
2y + 12 = N
Solving for y, we have y = \(\frac{(N – 12)}{ 2}\)
Therefore, x = y + 12 = \(\frac{(N – 12)}{2}\) + 12 = \(\frac{(N + 12)}{2}\)
Let the number of marbles that A has to give B be k.
Then, x – k = y + k
\(\frac{(N + 12)}{2}\) – k = \(\frac{(N – 12)}{2}\) + k
Solving for k, we have,
N + 12 – 2k = N - 12 + 2k
4k = 24
k = 6
A should give 6 marbles to B so that each of them has an equal number of marbles
The correct answer option is A
