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.

https://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

pappueshwar 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.

OA IS E

(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.