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
