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In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of

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In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of  [#permalink]

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New post 17 Oct 2018, 04:08
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Question Stats:

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In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of gray socks and 2 pairs of orange socks. If socks are removed at random without replacement, what is the minimum number of socks that must be removed in order to ensure that two socks of the same color have been removed?

A. 4
B. 7
C. 9
D. 10
E. 11

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In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of  [#permalink]

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New post 17 Oct 2018, 04:55
Black socks = 8, Gray socks = 6, Orange socks = 4

If 3 socks are removed, then it can be 2 of one colour and 1 other colour OR 3 of one colour OR 1 of each colour.
Since 1 of each colour is possible, we might not get a pair.

If 4 socks are removed, then it can be 1 of each colour and the 4th one removed has to form a pair with one of the three colours. Any other case will also have a pair.
Hence 4 should be the minimum.

Option A
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Re: In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of  [#permalink]

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New post 17 Oct 2018, 05:45
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Bunuel wrote:
In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of gray socks and 2 pairs of orange socks. If socks are removed at random without replacement, what is the minimum number of socks that must be removed in order to ensure that two socks of the same color have been removed?

A. 4
B. 7
C. 9
D. 10
E. 11


If we remove 1 black sock, 1 gray sock, and 1 orange sock, then we still don't have a matching sock. So, we can select 3 socks WITHOUT having a matching pair.
However, if we pick ANY sock for our fourth sock, that sock MUST match one of the first 3 socks selected.

Answer: A

Cheers,
Brent
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Re: In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of  [#permalink]

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New post 17 Oct 2018, 08:52
Bunuel wrote:
In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of gray socks and 2 pairs of orange socks. If socks are removed at random without replacement, what is the minimum number of socks that must be removed in order to ensure that two socks of the same color have been removed?

A. 4
B. 7
C. 9
D. 10
E. 11



8, 6, and 4 socks respectively.

If we take 1 of each we then have 1, 1, 1

In order to have a pair we need one more.

4

Answer choice A

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Re: In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of  [#permalink]

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New post 18 Oct 2018, 17:14
Bunuel wrote:
In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of gray socks and 2 pairs of orange socks. If socks are removed at random without replacement, what is the minimum number of socks that must be removed in order to ensure that two socks of the same color have been removed?

A. 4
B. 7
C. 9
D. 10
E. 11


We can remove 1 black, 1 gray, and 1 orange sock first. The next sock selection of any color would ensure that at least one pair of socks of the same color has been removed.

Answer: A
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Re: In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of  [#permalink]

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New post 16 Nov 2018, 00:01
GMATPrepNow wrote:
Bunuel wrote:
In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of gray socks and 2 pairs of orange socks. If socks are removed at random without replacement, what is the minimum number of socks that must be removed in order to ensure that two socks of the same color have been removed?

A. 4
B. 7
C. 9
D. 10
E. 11


If we remove 1 black sock, 1 gray sock, and 1 orange sock, then we still don't have a matching sock. So, we can select 3 socks WITHOUT having a matching pair.
However, if we pick ANY sock for our fourth sock, that sock MUST match one of the first 3 socks selected.

Answer: A

Cheers,
Brent


Hi.

the problem i have with these questions is as follows:

when it says 'randomly pick' .. does this mean we are picking WITHOUT looking? meaning i put my hand into the drawer and pick one - in which case i do not know which color i will get

OR

am i allowed to pick any color i want...in which case, its not random?

all the answers are deliberately picking one sock of each color....is that random?

help will be greatly appreciated
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Re: In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of &nbs [#permalink] 16 Nov 2018, 00:01
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