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A box contains 1 red ball, 3 green balls, 5 yellow balls, 7 blue balls

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Bunuel
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A box contains 1 red ball, 3 green balls, 5 yellow balls, 7 blue balls [#permalink] New post   28 Jun 2023, 07:00
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65% (hard)

Question Stats:

44% (02:00) correct 56% (01:59) wrong based on 45 sessions
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A box contains 1 red ball, 3 green balls, 5 yellow balls, 7 blue balls, 9 white balls, and 11 black balls. What is the minimum number of balls that must be drawn from the box without replacement to guarantee that at least 7 balls of the same color are drawn?

A. 7
B. 14
C. 15
D. 27
E. 28
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E
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TheBipedalHorse
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Re: A box contains 1 red ball, 3 green balls, 5 yellow balls, 7 blue balls [#permalink] New post   28 Jun 2023, 07:06
because we want to have at least 7 balls of the same color - red, green and yellow are omitted. There are 7 blue balls, 9 white and 11 black. Therefore, you must draw a ball from the bag for a minimum of 7 times to get all blue balls.
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RanonBanerjee
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Re: A box contains 1 red ball, 3 green balls, 5 yellow balls, 7 blue balls [#permalink] New post   28 Jun 2023, 07:30
IMO 28.

Blue is B and Black is O.

Number of draws shown below:

RGYBWO
GYBWO
GYBWO
YBWO
YBWO
BWO

Total =27

If we draw balls one by one this way, we see blue, white and black balls are all six in numbers. To ensure 7 balls of same color (can be either blue, white or black) we need to draw one more time, I.e., 27+1=28

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A box contains 1 red ball, 3 green balls, 5 yellow balls, 7 blue balls [#permalink] New post   28 Jun 2023, 09:46
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Bunuel wrote:
A box contains 1 red ball, 3 green balls, 5 yellow balls, 7 blue balls, 9 white balls, and 11 black balls. What is the minimum number of balls that must be drawn from the box without replacement to guarantee that at least 7 balls of the same color are drawn?

A. 7
B. 14
C. 15
D. 27
E. 28


Worst case scenario -

Take out 6 black balls, 6 white balls, 6 blue balls, 5 yellow balls, 3 green balls, and 1 red ball

The number of balls taken out = 18 + 9 = 27 balls.

However, we don't have 7 balls of the same color yet.

Taking out one more ball will ensure that 7 balls are of the same color.

27 + 1 = 28 balls.

Option E
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gmatclubot
A box contains 1 red ball, 3 green balls, 5 yellow balls, 7 blue balls [#permalink]
28 Jun 2023, 09:46
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