schrag2737 wrote:
Every night, the Biased News Network (BNN) features more guests from the Bow Tie Party than from the Ascot Party. If 11 members of each party are available to appear on BNN tonight, do more than 4 members of the Ascot party get to appear?
1. At least 462 different groups of the available Bow Tie Party members could be chosen to appear on BNN tonight.
2. At least 330 different groups of the available Ascot Party members could be chosen NOT to appear on BNN tonight.
I don't find it at all clear what the question means, since they aren't using language precisely. This is what I think the question is trying to say:
If b and a are integers between 0 and 11 (inclusive), and b > a, is a > 4? (that is, the network has already decided it will invite b people from the Bow party, and a from the Ascot party)
1. 11Cb
> 462 (i.e. the number of groups of b people you could choose from the 11 people is at least 462)
2. 11C(11-a)
> 330
It's annoying to calculate the values of 11Cn, but it turns out 11C5 = 462, and 11C6 = 462. All other values of 11Cb are smaller than 462. So Statement 1 tells us b = 5 or b = 6. We know a < b, but it's still possible that a = 5 and b = 6, so the answer to the question can be 'yes', but since a = 0 is also possible, we can get a 'no' answer, and Statement 1 is not sufficient.
For Statement 2, 11C4 and 11C7 both equal 330. So this Statement tells us 11 - a is 4, 5, 6 or 7, and a = 7, 6, 5 or 4. Since we don't know if a > 4, this is not sufficient, and even using both Statements, a can still be 4 or 5 if b = 6. So the answer is E.
I don't much care for the question - it's not well-worded, and the calculations aren't the type of thing you need to do on the GMAT.