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# A bag contains r red, g green, and w white marbles, where r, g and w

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Manager
Joined: 20 Feb 2017
Posts: 164
Location: India
Concentration: Operations, Strategy
WE: Engineering (Other)
A bag contains r red, g green, and w white marbles, where r, g and w  [#permalink]

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14 Aug 2018, 20:42
1
00:00

Difficulty:

55% (hard)

Question Stats:

47% (01:26) correct 53% (01:47) wrong based on 36 sessions

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A bag contains r red, g green, and w white marbles, where r, g and w are all positive integers. If one marble is picked randomly, is the probability that the marble is red higher than the probability that the marble is either green or white?
1) The probability of selecting a green marble is 4/9
2) The total number of marbles in the bag is less than 15.

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Math Expert
Joined: 02 Aug 2009
Posts: 7764
Re: A bag contains r red, g green, and w white marbles, where r, g and w  [#permalink]

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14 Aug 2018, 21:03
1
A bag contains r red, g green, and w white marbles, where r, g and w are all positive integers. If one marble is picked randomly, is the probability that the marble is red higher than the probability that the marble is either green or white?

Basically the question asks " Whether the number of Red marbles is more than number of green and white combined.

1) The probability of selecting a green marble is 4/9
So probability of red and white is 5/9..
Say total are 90... 40 are green. If white is <5, Ans is YES, otherwise NO
Insufficient

2) The total number of marbles in the bag is less than 15.
Clearly insufficient..

Combined..
Total has to be a multiple of 9, as ratio of green is 4/9.
Since total <15, total is 9..
4 are green, so white + red = 5..
But white is a positive number so at least 1
Thus red is 4 at the maximum..
Hence it is less than the number of green and white combined..
Sufficient

C
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Re: A bag contains r red, g green, and w white marbles, where r, g and w   [#permalink] 14 Aug 2018, 21:03
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