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# From a drawer containing black, blue and gray solid-color

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Manager
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Joined: 21 Nov 2009
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WE: Project Management (Manufacturing)
From a drawer containing black, blue and gray solid-color [#permalink]

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23 Dec 2009, 10:23
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Question Stats:

55% (00:43) correct 45% (00:40) wrong based on 268 sessions

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From a drawer containing black, blue and gray solid-color socks, including at least three socks of each color, how many matched pairs can be removed?

(1) The drawer contains 11 socks.

(2) The drawer contains an equal number of black and gray socks.
[Reveal] Spoiler: OA

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Manager
Joined: 09 May 2009
Posts: 198
Re: From a drawer containing black, blue and gray solid-color [#permalink]

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23 Dec 2009, 10:32
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IMO E
s1) possiblities are
blue=5;black=3,grey=3
blue=3,black=4;grey=4
like this there are more possiblities and no ways differ

s2) as said above

s1)+s2) 5,3,3 or 3,4,4 no. of ways differ
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Manager
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Re: From a drawer containing black, blue and gray solid-color [#permalink]

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15 Feb 2012, 21:40
IMO E. sock pairs are still uncertain
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Manager
Joined: 17 Sep 2011
Posts: 184
Re: From a drawer containing black, blue and gray solid-color [#permalink]

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16 Feb 2012, 00:36
The correct answer is E as there are multiple possibilities for statement A and B.
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Manager
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GMAT 1: 720 Q49 V40
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Re: From a drawer containing black, blue and gray solid-color [#permalink]

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17 Feb 2012, 20:07
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The answer has to be E.

We know there are "ATLEAST" 3 socks for each color. We do not know the actual number of socks for each of the colors so therefore there is no way to find out. Socks could be more than $$100[/] even! Statement A: There are a total of [m]11$$ socks and we know that there are at least $$3$$ socks of each color. Lets try and distribute these:

Possibility $$A$$
Blue $$=5$$
Black $$=3$$
Grey $$=3$$
So matched pairs that can be removed $$=4$$

Possibility $$B$$
Blue $$=3$$
Black $$=4$$
Grey $$=4$$
So matched pairs that can be removed $$=5$$

Since there are Two different answers, this statement alone is insufficient.

Statement B: The drawer contains an equal number of Black and Grey socks.

Multiple possibilities. If you revert back to the solution provided for Statement A, in both those possibilities, the number of Black and Grey socks is equal and we have two different answers. This should also answer your concern as to why both statements together are also insufficient to answer the question.

Hence E should be the correct answer.
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Senior Manager
Status: May The Force Be With Me (D-DAY 15 May 2012)
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Re: From a drawer containing black, blue and gray solid-color [#permalink]

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17 Feb 2012, 20:47
+1 E....
I'm not good with probability but the probability of the outcome can change when the number of black, Blue or grey socks changes

You can have only 1 Blue 1 Black & the rest grey for example
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Re: From a drawer containing black, blue and gray solid-color [#permalink]

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05 Jun 2016, 14:20
msunny wrote:
From a drawer containing black, blue and gray solid-color socks, including at least three socks of each color, how many matched pairs can be removed?

(1) The drawer contains 11 socks.

(2) The drawer contains an equal number of black and gray socks.

If we know exactly how many socks of each color are present, then we can tell the possibility of removing matching pair.

(1) The drawer contains 11 socks.

Possibilities:-
Blue- 3/4/5
Black- 3/4/5
Grey- 3/4/5

Not sufficient.

(2) The drawer contains an equal number of black and gray socks.
Possibilities:-

Blue + black + grey= 3+5+3

Blue + black + grey= 4+3+4

Not sufficient

Statement 1 and 2 together do not give exact number of socks for each color.

E is the answer
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Re: From a drawer containing black, blue and gray solid-color [#permalink]

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06 Aug 2017, 10:04
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Re: From a drawer containing black, blue and gray solid-color   [#permalink] 06 Aug 2017, 10:04
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# From a drawer containing black, blue and gray solid-color

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