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M31-39

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Math Expert
Joined: 02 Sep 2009
Posts: 55277

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20 Jun 2015, 10:44
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Difficulty:

55% (hard)

Question Stats:

57% (02:17) correct 43% (02:27) wrong based on 23 sessions

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Certain jar contains a total of 300 marbles, out of which 125 are black and the remaining are white. How many white marbles should be taken from the jar in order the probability of picking a white marble to become $$\frac{1}{6}$$?

A. 25
B. 50
C. 125
D. 150
E. 165

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Math Expert
Joined: 02 Sep 2009
Posts: 55277

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20 Jun 2015, 10:44
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1
Official Solution:

Certain jar contains a total of 300 marbles, out of which 125 are black and the remaining are white. How many white marbles should be taken from the jar in order the probability of picking a white marble to become $$\frac{1}{6}$$?

A. 25
B. 50
C. 125
D. 150
E. 165

Since the probability of picking a white marble is $$\frac{1}{6}$$, then the ratio of white marbles to black marbles must be 1 to 5. So if we have 125 black marbles, we have 25 white marbles. We started with 175 white marbles, thus we need to remove 150 of them.

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Joined: 24 Oct 2012
Posts: 167

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21 Jun 2015, 21:51
1
Let X be the number of white marble that we need to remove from Jar.

As per the statement,
Currently Number of white Marble = 175
Total marble = 300

Hence required White marble = 175-x
Required total = 300-x

(175-x)/(300-x) = 1/6
Solving the above equation will give, X = 150

Option D
Intern
Joined: 23 Dec 2011
Posts: 36

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09 Apr 2018, 15:16
I followed the following approach and it took 1 minute, can someone confirm if my approach was correct -

1. to reduce the complexity, first I divided all the numbers by 25 -

So I got total 12 Marbles, in that - 5 black and 7 White. Black :White = 5:7

So I have to select at least 6 marbles to get 1 white. Multiplied 6 by 25 and got the answer 150.

Please let me know if my approach was correct or whether coincidentally the answer matched.
Intern
Joined: 19 Jan 2018
Posts: 49

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25 Feb 2019, 20:25
Please let me know if my approach is correct:

We know that there's 300 total marbles, and 125 of them are black. That means 175 marbles are white.

175/300.

If we remove 50 white marbles then: 175-50 = 125
Total: 300 - 50 = 250

125/250 = 1/2, which is larger than 1/6. So A and B out.

Let's try D:
If we remove 150 white marbles then: 175-150= 25
Total: 300 - 150 = 150

25/150 = 1/6.

Re: M31-39   [#permalink] 25 Feb 2019, 20:25
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M31-39

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