Hi Mo2men,

This question revolves around 'system' Algebra, but you'll likely have to play around with the question a bit to realize it.

We're told that there are 100 rooms in a hotel (so there's a LIMIT to how many rooms can be rented out at once). We're also told in November, an average of 80 rooms were rented each day. Since November has 30 days, that means a total of (80)(30) = 2400 room-days of rentals occurred in November. We're asked for the number of days in November that had ALL 100 rooms rented.

1) An average of 40 rooms were occupied on days that the rooms weren't all occupied.

With this Fact, we can create two 'groups' of numbers: X non-full days (at 40 rooms each) and Y full days (at 100 rooms each). With those variables, we can create the following equations:

X + Y = 30
40X + 100Y = 2400

This is a 'system' of equations, which we can solve and get the value of Y (so we CAN answer the question and there will be just one solution: X=10 and Y=20).
Fact 1 is SUFFICIENT

2) The sales of days that the rooms were all occupied is 5 times greater than the sales of days that the rooms were not all occupied.

This Fact is a little 'quirkier' to deal with, but you can use your work from Fact 1 and a bit of simple arithmetic to prove the solution without too much trouble.

From Fact 1, we know that 20 full days and 10 non-full days 'fits' the given prompt. Let's see how that information fits Fact 2:

20 full days = 20(100) = 2000 room-days of rentals

2000 is five times 400, so there would be 400 additional room-days of rentals. This matches the total (2400 total room-days in November), so this answer clearly fits what we're told. Is there any other way to add a number to 5 TIMES that number and get 2400?

X + 5X = 2400
6X = 2400
X = 400
Thus, 400 and 2000 is the ONLY way to get to 2400 here, so this is the only possible answer. There MUST be 20 full-days.
Fact 2 is SUFFICIENT

Final Answer:D

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