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

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New post 04 Feb 2019, 05:30
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

Avoid removing two socks of the same color "while you can"... we call this the "Murphy´s Law argument": if something can (still) go wrong, it will!

Once one sock of each color was removed, the fourth´s removal cannot go wrong... hence the correct answer is (A).

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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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 04 Feb 2019, 11:35
Hi All,

The concept in these types of questions is based on the 'worst case scenario' - to guarantee that something will happen, you have to focus on the 'extreme/longest' way that it could happen. Here, we have 4 black socks, 3 gray socks and 2 orange socks. The question asks for the MINIMUM number of socks that would be need to be randomly removed from the drawer to guarantee that a matching pair of socks would drawn. Since we have the answer choices to work with, we could certainly start with the smallest answer and see if it "fits" the given information. Even if you didn't have the answers though, you can still work to the solution by TESTing some examples:

Let's start with 2 socks - is it possible that you could draw 2 socks and NOT get a matching pair? Certainly - there are several examples. If we pull one black sock and one gray sock, then we do NOT have a matching pair. Thus, 2 socks is NOT enough to guarantee a matching pair.

Next, let's try 3 socks - is it possible that you could draw 3 socks and NOT get a matching pair? Absolutely - if we pull one black sock, one gray sock and one orange sock, then we do NOT have a matching pair. Thus, 3 socks is NOT enough to guarantee a matching pair.

Finally, let's try 4 socks - is it possible that you could draw 4 socks and NOT get a matching pair? NO, and here's why - if we pull one black sock, one gray sock and one orange sock....we would still have to draw one more sock - and that 4th sock would match one of the 3 colors that we had already pulled. So we WOULD have a matching pair and 4 socks IS enough to guarantee a matching pair.

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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 04 Feb 2019, 17:12
1
Mansoor50 wrote:
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

Hi Mansoor50.

You ask a great question.

While everyone has answered in the same way, the choosing of the socks is indeed random.

The question asks us how many socks have to be chosen at random in order for us to be SURE that we chosen at least two socks of the same color.

So, consider the following.

We could choose two socks at random and get two socks of the same color. But if we were to choose only two socks at random, would we be sure to get two socks of the same color? Since there are three colors of socks in the drawer, we could draw two socks of two different colors. So, by drawing only two socks at random, we wouldn't be sure to get two of the same color.

What if we were to randomly draw three socks? We might get two socks of the same color, or even three socks of the same color, but since there are three different colors of socks, we might draw one of each. So, if we were to draw three socks at random, we wouldn't be sure to get two socks of the same color.

Now, what if we were to draw four socks? Well there are only three different colors. So, after the first three, we know that we would definitely have run out of colors. So, even none of the first three were to match, the fourth one would have to match one of the first three.

So, by drawing four socks at random, we can be sure that we will draw at least two of the same color. We may have drawn one pair and two singles. We may have drawn two pairs. In any case, we will definitely have drawn two that match.

The correct answer is A.
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Re: In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of   [#permalink] 04 Feb 2019, 17:12
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