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A box contains 3 red balls, 4 green balls, 5 yellow balls, 6 blue ball

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A box contains 3 red balls, 4 green balls, 5 yellow balls, 6 blue ball  [#permalink]

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New post Updated on: 20 Mar 2019, 21:43
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Question Stats:

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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  [#permalink]

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New post 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.
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Re: A box contains 3 red balls, 4 green balls, 5 yellow balls, 6 blue ball  [#permalink]

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New post 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  [#permalink]

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New post 18 Mar 2019, 07:10
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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. 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  [#permalink]

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New post 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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A box contains 3 red balls, 4 green balls, 5 yellow balls, 6 blue ball  [#permalink]

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New post 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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Originally posted by MathRevolution on 20 Mar 2019, 01:54.
Last edited by MathRevolution on 23 Mar 2019, 07:04, 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  [#permalink]

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New post 20 Mar 2019, 11:15
MathRevolution

The basic calculation is wrong.
You shared 3 + 4 + 4 + 4 + 4 = 14

Please fix the typo in your comment.
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A box contains 3 red balls, 4 green balls, 5 yellow balls, 6 blue ball  [#permalink]

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New post 23 Mar 2019, 07:04
sanpreetsingh wrote:
MathRevolution

The 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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A box contains 3 red balls, 4 green balls, 5 yellow balls, 6 blue ball   [#permalink] 23 Mar 2019, 07:04
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