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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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24 Nov 2018, 10:14
4
00:00

Difficulty:

65% (hard)

Question Stats:

44% (01:37) correct 56% (01:24) wrong based on 63 sessions

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GMATbuster's Weekly Quant Quiz#10 Ques #9

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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24 Nov 2018, 10:54
1
(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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24 Nov 2018, 11:17
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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A box contains balls that are either yellow, black or brown in color.  [#permalink]

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06 Apr 2019, 05:42
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?

I. The probability that the chosen ball is not brown is less than 2/5

II. The probability that the chosen ball is not black is greater than 3/5
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Posts: 1530
Re: A box contains balls that are either yellow, black or brown in color.  [#permalink]

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06 Apr 2019, 15:14
When you're picking just one thing, a probability is just a proportion. The question is just saying:

Are more than 3/4 of the balls black?
1. Less than 2/5 of the balls are not brown
2. More than 3/5 of the balls are not black

From Statement 1, if less than 2/5 are not brown, then less than 2/5 of the balls are either yellow or black, so it is certainly true that less than 2/5 of the balls are black, and Statement 1 is sufficient to give a 'no' answer.

Statement 2 tells us that less than 2/5 of the marbles are black, so it is also sufficient to give a 'no' answer, and the answer is D.
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Re: A box contains balls that are either yellow, black or brown in color.  [#permalink]

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07 Apr 2019, 00:00
kiran120680 wrote:
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?

I. The probability that the chosen ball is not brown is less than 2/5

II. The probability that the chosen ball is not black is greater than 3/5

Merging topics. Please search before posting. Thank you.
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Re: A box contains balls that are either yellow, black or brown in color.   [#permalink] 07 Apr 2019, 00:00
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