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

[BTGmoderatorDC]

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

OA A

Source: Magoosh

[Jay@ManhattanReview]

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

OA A

Source: Magoosh

It's already answered at the BTG. Pl. find it here: https://www.beatthegmat.com/probability-t99931.html

Hope this helps!

-Jay
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[Brent@GMATPrepNow]

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

OA A

Source: Magoosh

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

[fskilnik@GMATH]

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
Source: Magoosh

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

Excellent approach!

In our method we call it the "Murphy´s Law argument": if something can (still) go wrong, it will!

(Brent´s wording is perfect: three socks may go wrong, but the fourth´s cannot. That´s why the answer is 4, indeed.)

Regards,
Fabio.

[[email protected]]

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.

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

[Scott@TargetTestPrep]

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

OA A

Source: Magoosh

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