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:
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
