Hi All,
This DS question revolves around a ratio. In these situations, it's important to remember that ratio questions often come down to "multiples."
We're given a starting ratio of Brown gloves to Black gloves = 5/6. We're told that Left-handed and Right-handed gloves are ordered individually (which means that there's NO ratio governing the number of Left or Right). We're asked if the total number of gloves is at least 250? This is a YES/NO question.
From the prompt, we KNOW that the number of Brown gloves MUST be a multiple of 5 and the number of Black gloves MUST be a multiple of 6…
Fact 1: 44% of left-handed gloves are Black.
44/100 = 11/25 left-handed gloves are Black, so the minimum number of this type = 11
This means….
56/100 = 14/25 left-handed gloves are Brown, so the minimum number of this type = 14
We don't know the number (or color) of Right-handed gloves, which is a significant missing piece of information, so we could have ANY NUMBER of Right-handed Black and Right-handed Brown gloves (as long as those number properly complete the given ratio). For example:
Brown Left = 14
Black Left = 11
Brown Right = 1
Black Right = 7
Total = 33 and the answer to the question is NO
Brown Left = 14
Black Left = 11
Brown Right = 101
Black Right = 127
Total = 253 and the answer to the question is YES
Fact 1 is INSUFFICENT
Fact 2: 84 Black Right-handed Gloves
Using the original ratio, this info tells us that there are a MINIMUM of 70 Brown gloves, so the MINIMUM TOTAL = 154 (answer is NO), but the total could be higher (e.g. in the 1000s, so the answer is YES.
Fact 2 is INSUFFICIENT
Combined, we know:
Black Right-handed = 84
Brown Rightt-handed = ???
Black Left-handed = multiple of 11
Brown Left-handed = multiple of 14
Total Brown = multiple of 5
Total Black = multiple of 6
Here's where things get a bit more complex:
Since the Total Black must be a multiple of 6….84 + (multiple of 11) = (multiple of 6)
The MINIMUM multiple of 11 that "fits" this factoid would be 66, so we'd have 84 + 66 = 150 Black gloves AT THE MINIMUM
With those 150 Black gloves, we'd have to match the ratio in the prompt, so the Total number of Brown gloves would be 125 AT THE MINIMUM.
So, we end up with a MINIMUM of 275 gloves; the answer to the question is ALWAYS YES.
Final Answer:
GMAT assassins aren't born, they're made,
Rich