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Hi, there. I'm happy to help with this.

Prompt: 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?

Statement #1: The drawer contains 11 socks.

Here are the only two possibilities:

Case One:
color #1 = 5 socks ---> 2 pairs
color #2 = 3 socks ---> 1 pair
color #3 = 3 socks ---> 1 pair
TOTAL = 4 pairs

Case One:
color #1 = 4 socks ---> 2 pairs
color #2 = 4 socks ---> 2 pairs
color #3 = 3 socks ---> 1 pair
TOTAL = 5 pairs

Because two cases are possible, we don't know how many pairs, 4 or 5. Statement #1 is insufficient.

Statement #2: The drawer contains an equal number of black and gray socks. .

There could be ten socks or a million socks. We have no idea given this piece of information. Statement #2 is insufficient.

Combined Statements #1&#2:

Here are the only two possibilities:

Case One:
blue = 5 socks ---> 2 pairs
black = 3 socks ---> 1 pair
grey = 3 socks ---> 1 pair
TOTAL = 4 pairs

Case One:
black = 4 socks ---> 2 pairs
grey = 4 socks ---> 2 pairs
blue = 3 socks ---> 1 pair
TOTAL = 5 pairs

Even with both statements, we don't know how many pairs, 4 or 5. Combined, the statements are insufficient.

Answer = E

Here's another DS question about socks.

http://gmat.magoosh.com/questions/1038

When you submit your answer to that question, the following page will have a video explanation.

Does all this make sense? Please let me know if you have any further questions.

Mike

_________________
Magoosh GMAT Instructor
http://gmat.magoosh.com/

(1) The drawer contains 11 socks.
There can be may possibilities like black = 3, blue = 3, and grey = 5 OR black = 3, blue = 4, and grey = 4
No definite answer; NOT sufficient.

(2) The drawer contains an equal number of black and gray socks.
Again there can be many possibilities.
No definite answer; NOT sufficient.

Combining (1) and (2), we can take the same examples as in statement 1; NOT sufficient.

The correct answer is E.

_________________
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

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