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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
Question Stats:
46% (02:02) correct 54% (02:07) wrong based on 41 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. 10 B. 12 C. 15 D. 18 E. 20
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Originally posted by MathRevolution on 18 Mar 2019, 00:38.
Last edited by Bunuel on 20 Mar 2019, 21:43, edited 1 time in total.
Edited the OA.



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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, 23:20
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
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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.



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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.
The answer should be 21
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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
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 WORSTCASESCENARIO  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. Answer: 20
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Updated on: 23 Mar 2019, 07:04
=> 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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Re: A box contains 3 red balls, 4 green balls, 5 yellow balls, 6 blue ball
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20 Mar 2019, 11:15
MathRevolutionThe basic calculation is wrong. You shared 3 + 4 + 4 + 4 + 4 = 14 Please fix the typo in your comment.
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23 Mar 2019, 07:04
sanpreetsingh wrote: MathRevolutionThe basic calculation is wrong. You shared 3 + 4 + 4 + 4 + 4 = 14 Please fix the typo in your comment. It is fixed. Thank you for your correction.
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