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A box contains balls that are either yellow, black or brown in color.

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A box contains balls that are either yellow, black or brown in color.  [#permalink]

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New post 24 Nov 2018, 09:14
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Difficulty:

  55% (hard)

Question Stats:

40% (00:56) correct 60% (01:13) wrong based on 15 sessions

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GMATbuster's Weekly Quant Quiz#10 Ques #9


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A box contains balls that are either yellow, black or brown in color. One ball is chosen at random from the box. Is the probability that the chosen ball is black greater than 3/4?

(1) The probability that the chosen ball is not brown is less than 2/5.
(2) The probability that the chosen ball is not black is greater than 3/5.

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Re: A box contains balls that are either yellow, black or brown in color.  [#permalink]

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New post 24 Nov 2018, 09:54
(1) P(not brown) < 2/5
So, P(yellow or black) < 2/5
or P(yellow) + P(black) < 0.4

From this, we can gather that P(black) is definitely less than 0.4. Question asks if P(black) > 3/4 or 0.75, so answer is a definite NO. Hence Sufficient!

(2) P(not black) > 3/5
1 - P(black) > 3/5
1 - 3/5 > P(black)
P(black) < 2/5
P(black) < 0.4
Hence the answer to question is a definite NO. Hence Sufficient.

IMO, Option D
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Re: A box contains balls that are either yellow, black or brown in color.  [#permalink]

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New post 24 Nov 2018, 10:17
Option D.
Lets say total number of balls is 20.
Acc to stat 1, less than 8 balls are not brown i.e more than 12 balls are brown.
So prob of black balls cannot be greater than 2/5.

Acc to stat 2
Prob of not black ball is greater than 3/5 so prob of black is less than 2/5.

So both option are sufficient on their own to say that probablity of black ball cannot be more tha 3/4

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Re: A box contains balls that are either yellow, black or brown in color. &nbs [#permalink] 24 Nov 2018, 10:17
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A box contains balls that are either yellow, black or brown in color.

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