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

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Joined: 25 Jun 2014
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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, 10:41
1
1
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

88% (00:49) correct 12% (01:18) wrong based on 93 sessions

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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.

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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, 10:51
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, 22:20
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 28 May 2018, 09:35
Mesto wrote:
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.


Although the answer is D

According to statement 1 , solid balls are 38
According to statement 2, solid balls are 18

There is discrepancy here, both statements should give same number of solid balls .

Please correct me , if there is any error from my part.
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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 02 Jun 2018, 04:11
Ans D

Both the statement gives enough data to find total or individual no of each type of ball.
Hence each of them is sufficient
Re: A box of balls contains hollow balls and solid balls in the ratio 1:2. &nbs [#permalink] 02 Jun 2018, 04:11
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