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M31-39

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M31-39 [#permalink]

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New post 20 Jun 2015, 10:44
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Question Stats:

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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
[Reveal] Spoiler: OA

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Re M31-39 [#permalink]

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New post 20 Jun 2015, 10:44
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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.


Answer: D
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: M31-39 [#permalink]

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New post 21 Jun 2015, 21:51
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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
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Re: M31-39 [#permalink]

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New post 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. :-)
Re: M31-39   [#permalink] 09 Apr 2018, 15:16
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