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# A student is asked to pick marbles from a bag that contains

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A student is asked to pick marbles from a bag that contains [#permalink]

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03 Nov 2008, 07:18
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A student is asked to pick marbles from a bag that contains 18 marbles. Eight marbles are red, 4 are green, and 6 are black. What is the minimum number of marbles that a blindfolded student would have to draw from the bag to be certain of having at least three marbles of the same color?

A. 5
B. 6
C. 7
D. 13
E. 14
[Reveal] Spoiler: OA

Last edited by Bunuel on 22 Mar 2013, 02:53, edited 1 time in total.
Edited the question and added the OA.
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03 Nov 2008, 07:50
I think the answer is (C) 7. Because at worst case the student can draw 2 from each color and still he has to draw at least one more marble so that the third one of any color will constitute a color with three marbles.

What is OA?
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03 Nov 2008, 07:57
i get 7...he takes out 2 of each..so the 7th one will be of the 3rd color
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03 Nov 2008, 08:26
you all are right, it is 7

although, i really have hard time understanding why??? What if he keeps taking red ones... Or minimum no means that he's "lucky", keeps pulling different color each time
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03 Nov 2008, 10:28
linau1982 wrote:
you all are right, it is 7

although, i really have hard time understanding why??? What if he keeps taking red ones... Or minimum no means that he's "lucky", keeps pulling different color each time

What you are saying is right for the best case. However, in order to be certain, worst case has to be considered.
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Re: A student is asked to pick marbles from a bag that contains [#permalink]

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22 Mar 2013, 02:04
It should b R+G+B and then again R+G+B and then on 7th draw,he might pick either of R/G/B thus satisfying our condition.
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Re: A student is asked to pick marbles from a bag that contains [#permalink]

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22 Mar 2013, 02:33

There is no way we can have 7 marbles without picking at least 3 of the same color, infact we cannot write 7 as the combination of only 2 marbles of the same color:

$$2G+2B+2R+1?=7$$ marbles

The last one that is missing must be G or B or R so we have at LEAST 3 of a color.
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Re: A student is asked to pick marbles from a bag that contains [#permalink]

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22 Mar 2013, 03:11
Expert's post
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linau1982 wrote:
A student is asked to pick marbles from a bag that contains 18 marbles. Eight marbles are red, 4 are green, and 6 are black. What is the minimum number of marbles that a blindfolded student would have to draw from the bag to be certain of having at least three marbles of the same color?

A. 5
B. 6
C. 7
D. 13
E. 14

The worst case scenario would be if we remove 2 marbles of each color, so 6 marbles, and we still won't have 3 marbles of the same color. The 7th marble will be red, green or black, thus after 7 draws we are guaranteed to have at least three marbles of the same color.

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Hope it helps.
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Re: A student is asked to pick marbles from a bag that contains   [#permalink] 22 Mar 2013, 03:11
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