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20 marbles were pulled out of a bag of only white marbles...

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by swerve » Mon Mar 12, 2018 10:04 am
20 marbles were pulled out of a bag only white marbles, painted black, and then put back in. Then another 20 marbles were pulled out, of which 1 was black, after which 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

The OA is D.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer and I would like to know how can I form an equation for this problem. I need your help. Thanks.
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by DavidG@VeritasPrep » Mon Mar 12, 2018 10:35 am
swerve wrote:20 marbles were pulled out of a bag only white marbles, painted black, and then put back in. Then another 20 marbles were pulled out, of which 1 was black, after which 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

The OA is D.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer and I would like to know how can I form an equation for this problem. I need your help. Thanks.
We know that 20 marbles were painted black after the first selection.
We know that 1 of the 20 marbles from the second selection was black. If this represents the proportion of black marbles in the whole bag, it means that 1/20 of the marbles in the bag are black.
Well, if we have 20 black marbles and this represents 1/20 of the total marbles, then 20 = (1/20) *T, and T = 400. The answer is D
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by Scott@TargetTestPrep » Wed Mar 14, 2018 3:34 pm
swerve wrote:20 marbles were pulled out of a bag only white marbles, painted black, and then put back in. Then another 20 marbles were pulled out, of which 1 was black, after which 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
We can let x = the number of (white) marbles originally in the bag and create the following equation:

(# of black marbles in the bag)/(total # of marbles) = (# of black marbles pulled out 2nd time)/(total # of marbles pulled out 2nd time)

20/x = 1/20

x = 400

Answer: D

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