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A box contains 3 red balls, 4 green balls, 5 yellow balls, 6 blue ball
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Updated on: 20 Mar 2019, 21:43
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A
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E
Difficulty:
65% (hard)
Question Stats:
57% (01:55) correct 43% (02:02) wrong based on 65 sessions
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[GMAT math practice question]
A box contains 3 red balls, 4 green balls, 5 yellow balls, 6 blue balls and 7 white balls. What is the minimum number of balls that must be drawn from the box without replacement to guarantee that at least 5 balls of a single color will be drawn?
A box contains 3 red balls, 4 green balls, 5 yellow balls, 6 blue ball
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Updated on: 20 Mar 2019, 23:20
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MathRevolution wrote:
[GMAT math practice question]
A box contains 3 red balls, 4 green balls, 5 yellow balls, 6 blue balls and 7 white balls. What is the minimum number of balls that must be drawn from the box without replacement to guarantee that at least 5 balls of a single color will be drawn?
A. 10 B. 12 C. 15 D. 18 E. 20
to draw min no of balls so as to get atleast 5 balls of single color we need to dram following balls red = 3 green= 4 yellow =4 blue = 4 white = 4 total ; 19 balls 1 ball more would be required to be removed so as to gurantee that atleast 5 balls of single color are drawn it could be yellow,blue or white so 19+1 = 20 IMO E
Originally posted by Archit3110 on 18 Mar 2019, 00:50.
Last edited by Archit3110 on 20 Mar 2019, 23:20, edited 1 time in total.
Re: A box contains 3 red balls, 4 green balls, 5 yellow balls, 6 blue ball
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18 Mar 2019, 01:55
This approach seems to be incorrect as if 15 balls are drawn then it might be a possibility that 3 red,4 green ,4 blue and 4 white are drawn which does not gurrantee 5 balls of same colour.
Re: A box contains 3 red balls, 4 green balls, 5 yellow balls, 6 blue ball
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18 Mar 2019, 07:10
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1
MathRevolution wrote:
[GMAT math practice question]
A box contains 3 red balls, 4 green balls, 5 yellow balls, 6 blue balls and 7 white balls. What is the minimum number of balls that must be drawn from the box without replacement to guarantee that at least 5 balls of a single color will be drawn?
A. 10 B. 12 C. 15 D. 18 E. 21
Determine the WORST-CASE-SCENARIO -- for each color of ball, the MAXIMUM number that can be removed WITHOUT removing 5 of the same color: 3 red 4 green 4 yellow 4 blue 4 white Sum = 3+4+4+4+4 = 19
Implication: It is possible to remove 19 balls without selecting 5 of the same color. Thus, to GUARANTEE that 5 of the same color are removed, we must remove ONE MORE ball: 19+1 = 20
The correct answer is not among the answer choices.
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Re: A box contains 3 red balls, 4 green balls, 5 yellow balls, 6 blue ball
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19 Mar 2019, 19:14
MathRevolution wrote:
[GMAT math practice question]
A box contains 3 red balls, 4 green balls, 5 yellow balls, 6 blue balls and 7 white balls. What is the minimum number of balls that must be drawn from the box without replacement to guarantee that at least 5 balls of a single color will be drawn?
A. 10 B. 12 C. 15 D. 18 E. 21
We could have 3 red balls, 4 green balls, 4 yellow balls, 4 blue balls, and 4 white balls drawn, that is, a total of 19 balls drawn, without 5 balls of a single color drawn. However, the next ball drawn will be yellow, blue or white, and we will have 5 balls of a single color drawn. Therefore, we need to draw 20 balls to guarantee that at least 5 balls of a single color will be drawn.
A box contains 3 red balls, 4 green balls, 5 yellow balls, 6 blue ball
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Updated on: 23 Mar 2019, 07:04
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=>
The maximum number of draws we can make without drawing 5 balls of a single color is 3 + 4 + 4 + 4 + 4 = 19. This occurs when we draw 3 red balls, 4 green balls, 4 yellow balls, 4 blue balls and 4 white balls. If we draw one more ball, then we will have drawn 5 balls of a single color.
Thus, to guarantee that we have drawn at least 5 balls of a single color, we must draw 19+1 = 20 balls.
Therefore, E is the answer. Answer: E
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57% (01:55) correct 
