socks

[j_shreyans]

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.

[Brent@GMATPrepNow]

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.

Target question: How many matched pairs can be removed?

Given: There are least three socks of each color

Statement 1: The drawer contains 11 socks.
Since there must be at least 3 socks of each color, there are two possible cases to consider:
Case a: there are 3 of one color (meaning that 1 matched pair can be removed), 3 of another color (meaning that 1 matched pair can be removed) and 5 of another color (meaning that 2 matched pairs can be removed). So, we can remove 4 matched pairs
Case b: there are 3 of one color (meaning that 1 matched pair can be removed), 4 of another color (meaning that 2 matched pairs can be removed) and 4 of another color (meaning that 2 matched pairs can be removed). So, we can remove 5 matched pairs
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The drawer contains an equal number of black and gray socks.
Here, there is no limit to the number of socks in the drawer.
So, there might be 3 black, 3 gray and 4 blue (for a total of 4 matched pairs), or there might be 300 black, 300 gray and 4 blue (for a total of 302 matched pairs)
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that there are only 2 possible scenarios: 3-3-5 or 3-4-4
Statement 2 tells us that there's an equal number of black and gray socks.
Notice that statement 2 does not help narrow down the options.
To see what I mean, consider these two cases:
Case a: 3 black, 3 gray and 5 blue (for a total of 4 matched pairs)
Case b: 4 black, 4 gray and 3 blue (for a total of 5 matched pairs)
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent

[Matt@VeritasPrep]

S1: We know that 9 of the socks are BBBBBBGGG. If we add a black sock and a gray sock, we'll have a total of FIVE matched pairs. If we add two blue socks, however, we'll have a total of FOUR matched pairs. INSUFFICIENT!

S2: We could have 100 black and 100 gray or 4 black and 4 gray: INSUFFICIENT.

Taking the two together, we still have the two possibilities I mentioned in S1, so the two statements together remain INSUFFICIENT.

This sort of trick works really well in DS: cheat a bit by using S2 as one of your scenarios in S1, and if S1 is insufficient in that case, you know the answer must be E.