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20 marbles were pulled out of a bag of only white marbles, p

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20 marbles were pulled out of a bag of only white marbles, p  [#permalink]

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New post Updated on: 02 Jun 2013, 04:31
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20 marbles were pulled out of a bag of only white marbles, painted black, and then put back in. Then, another 20 marbles were pulled out, of which 1 was black, afterwhich they were all returned to the bag. If the percentage of black marbles pulled out the second time represents their percentage in the bag, how many marbles in total does the bag currently hold?

A. 40
B. 200
C. 380
D. 400
E. 3200

Please explain confuesed how to form an equation for this problem...

Originally posted by fozzzy on 02 Jun 2013, 02:23.
Last edited by Bunuel on 02 Jun 2013, 04:31, edited 1 time in total.
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Re: 20 marbles were pulled out of a bag of only white marbles, p  [#permalink]

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New post 02 Jun 2013, 02:36
fozzzy wrote:
20 marbles were pulled out of a bag of only white marbles, painted black, and then put back in. Then, another 20 marbles were pulled out, of which 1 was black, afterwhich they were all returned to the bag. If the percentage of black marbles pulled out the second time represents their percentage in the bag, how many marbles in total does the bag currently hold?

A 40
B 200
C 380
D 400
E 3200


From a bag of all white marbles, 20 become black.
The second time 1 black is pulled out, and \(\frac{1}{20}=5%\) represents the percentage of black marble in the bag.
We know that \(5%=20 black\) , 20 is the number painted the first time (the ONLY black marble).

So there are a total of \(20*20=400\) marbles (\(20\) black and \(380\) white).
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Re: 20 marbles were pulled out of a bag of only white marbles, p  [#permalink]

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New post 02 Jun 2013, 02:41
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fozzzy wrote:
20 marbles were pulled out of a bag of only white marbles, painted black, and then put back in. Then, another 20 marbles were pulled out, of which 1 was black, afterwhich they were all returned to the bag. If the percentage of black marbles pulled out the second time represents their percentage in the bag, how many marbles in total does the bag currently hold?

A 40
B 200
C 380
D 400
E 3200

Please explain confuesed how to form an equation for this problem...


Ok. Lets do it with the help of ratio. 20 Black marbles in a bag of white marbles after 1st draw.
Second time, out of 20 there is one black marble. Ratio of Total:Black = 20:1
For every 1 black marble there are total of 20 marbles then
for 20 Black marbles we will have 20*20 = 400 Marbles in total.
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Re: 20 marbles were pulled out of a bag of only white marbles, p  [#permalink]

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New post 02 Jun 2013, 04:36
fozzzy wrote:
20 marbles were pulled out of a bag of only white marbles, painted black, and then put back in. Then, another 20 marbles were pulled out, of which 1 was black, afterwhich they were all returned to the bag. If the percentage of black marbles pulled out the second time represents their percentage in the bag, how many marbles in total does the bag currently hold?

A. 40
B. 200
C. 380
D. 400
E. 3200

Please explain confuesed how to form an equation for this problem...


We know that there are 20 black marbles in the bag and this number represent 1/20 th of the number of all marbles in the bag, thus there are total of 20*20=400 marbles.

Answer: D.
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Re: 20 marbles were pulled out of a bag of only white marbles, p  [#permalink]

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New post 20 Nov 2013, 20:44
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\(\frac{# of black marbles}{total in 2nd set pulled out of bag} =\frac{1}{20}=\frac{20}{x} = \frac{total black}{total marbles in bag}\) --- cross multiply

\(20*20=1*x\)

\(x=400\)
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Re: 20 marbles were pulled out of a bag of only white marbles, p  [#permalink]

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New post 09 Aug 2018, 08:37
When 20 marbles were pulled out we get 1 black that implies probability 1/20. As they mentioned this percentage ratio is valid for whole bag so if we have to get 20 black marbles we should make upper figure equal to "20".
1*20/20*20=20/400, there are 400 marbles in bag.

Answer(D)
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Re: 20 marbles were pulled out of a bag of only white marbles, p   [#permalink] 09 Aug 2018, 08:37
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