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A box of balls contains hollow balls and solid balls in the ratio 1:2.

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A box of balls contains hollow balls and solid balls in the ratio 1:2. [#permalink]

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A box of balls contains hollow balls and solid balls in the ratio 1:2. How many hollow balls are to be added to reverse this ratio?

I) The total number of balls in the box is 57.

II) The number of solid balls in the box is 18.
[Reveal] Spoiler: OA

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Re: A box of balls contains hollow balls and solid balls in the ratio 1:2. [#permalink]

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New post 24 Feb 2016, 09:51
Using either 1 or 2, we can find out the actual number of balls and therefore the number of balls required to reverse the ratio.
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Re: A box of balls contains hollow balls and solid balls in the ratio 1:2. [#permalink]

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New post 24 Feb 2016, 21:20
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

A box of balls contains hollow balls and solid balls in the ratio 1:2. How many hollow balls are to be added to reverse this ratio?

I) The total number of balls in the box is 57.

II) The number of solid balls in the box is 18.


In the original condition and the question, they become h(hollow balls' number)=k, s(solid balls' number)=2k, which makes 3 variables(h,s,k) and 2 equations(h=k, s=2k). In order to match with the number of equations, you need 1 more equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), k=19 is derived from k+2k=57, 3k=57, which is unique and sufficient.
For 2), k=9 is derived from s=2k=18, which is unique and sufficient.
Therefore, the answer is D.


 For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Re: A box of balls contains hollow balls and solid balls in the ratio 1:2. [#permalink]

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New post 12 Oct 2017, 06:55
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A box of balls contains hollow balls and solid balls in the ratio 1:2.   [#permalink] 12 Oct 2017, 06:55
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