Hi sana.noor,

This DS question focuses on probability math, but there's a "question behind the question" hidden within it:

The original prompt asks about the probability of mixing 3 bottles and having NO ALCOHOL.

The Q behind the Q asks "what's the probability of randomly grabbing 3 "mixers"? Let's call L the number of Liquor Bottles and M the number of Mixer Bottles.

Fact 1 tells us that there's twice as many liquor bottles as mixer bottles. TESTing values, we could have:

L = 2
M = 1
In this scenario, there is a 0% chance of getting 3 mixers.

L = 6
M = 3
Here, there's clearly a chance that's GREATER THAN 0%

Inconsistent answers = INSUFFICIENT


Fact 2 gives us a range of possibilities, but not enough info to give us a specific answer, so...

Fact 2 is INSUFFICIENT.


Combining facts you'll have to do some math to prove the possibilities. Since there is a range (from Fact 2), we have to TEST some possibilities (using the info from Fact 1) to see what falls within the range:

If
L = 6
M = 3
The odds of getting 3 mixers is 3/9 x 2/8 x 1/7 = 1/84 which is NOT possible, given the info in Fact 2

If
L = 8
M = 4
The odds of getting 3 mixers is 4/12 x 3/11 x 2/10 = 1/55 which IS POSSIBLE

At this point, notice how the odds are INCREASING? What do you think will happen when we raise the numbers?

If
L = 10
M = 5
The odds of getting 3 mixers is 5/15 x 4/14 x 3/13 = 2/91 which is about 1/45, which is NOT POSSIBLE

There's ONLY ONE ANSWER that fits both Facts:
L = 8
M = 4

Final Answer: C

GMAT assassins aren't born, they're made,
Rich