Each of A and B has a few marbles with them. If A gives 12 marbles to

Question

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

ThatDudeKnows · Accepted Answer

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.

GMATWhizTeam · Answer

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

Rohstar750 · Answer

Time Took: 1:02

Lets consider the initial ratio of marbles with A and B is 1:2

A gave 12 to B and the ratio became reverse so the new ratio is 2:1

If A gives 6 marbles to B the ratio becomes equal.

So ans is (A) 6.

Check:

Ratio of A to B is 2:1

Lets consider the initial marbles with A is 24 and 12 with B ( No. has to be such that the ratio can be reversed)

A gave 12 to B so new ratio is 1:2,

If A would give only 6 marbles to B ratio would be equal.

Ans A) 6

Kindly share your views on the approach.

prathammola1 · Answer

I believe the question asks if A gave 12, then how much more should he give again so that they have equal marbles now.

PSKhore · Answer

After we reach to A-B=12 
 We know that : A-x = B+x
A-B = 2x
A-B = 12
x=6

BadukMagician · Answer

I want to do efficient math.

A/B = Ma/Mb

A-12/B+12 = Mb/Ma

Hmm so if I give B 12 marbles, he now has the amount I had originally, and I have the amount he has originally!

so let's say I have 24 marbles and he has 12

A/B = 24/12

A-12/B+12 = 12/24

Ah so the answer must be less than 12

and after looking at my answer choices the only answer that's less than 12 is  A) 6

Each of A and B has a few marbles with them. If A gives 12 marbles to

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Each of A and B has a few marbles with them. If A gives 12 marbles to

Prep Toolkit

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