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Initially, how many black chips are in a box containing only red chips

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Initially, how many black chips are in a box containing only red chips  [#permalink]

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New post 24 Apr 2018, 06:04
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  35% (medium)

Question Stats:

75% (01:32) correct 25% (01:24) wrong based on 59 sessions

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Initially, how many black chips are in a box containing only red chips and black chips, all identical except for color?

(1) Initially, the ratio of red chips to black chips in the box is 3/25.
(2) If 12 red chips and 80 black chips are removed from the box, the probability of randomly drawing a red chip from the box is 1/11.

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Re: Initially, how many black chips are in a box containing only red chips  [#permalink]

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New post 24 Apr 2018, 06:26
Bunuel wrote:
Initially, how many black chips are in a box containing only red chips and black chips, all identical except for color?

(1) Initially, the ratio of red chips to black chips in the box is 3/25.
(2) If 12 red chips and 80 black chips are removed from the box, the probability of randomly drawing a red chip from the box is 1/11.


We'll translate our data into equations to help us understand what we need to do.
This is a Precise approach..

(1) So r/b = 3/25. This is one equation with two variables and is insufficient.
Insufficient.

(2) We can write this as an equation to help us out:
(r - 12) / (r + b - 92) = 1/11
This is an equation with two variables and has infinite solutions.
Insufficient.

Combined:
We now have two equations with two variables we can solve. (But we won't bother!)
Sufficient

(C) is our answer.
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Re: Initially, how many black chips are in a box containing only red chips  [#permalink]

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New post 11 May 2018, 23:43
I) ratio is given so
R/B=3X/25X

On different values of x, different values appear so insufficient

II)R-12/B-80=1/11
Don't know relation between R and B so insufficient

Combining both
Putting value of I) in statement II)
We can get unique value for both R and B
Sufficient

Give kudos if it helps

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Re: Initially, how many black chips are in a box containing only red chips &nbs [#permalink] 11 May 2018, 23:43
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