sanjana wrote:One night a certain motel rented 4/3 of its rooms, including 3/2 of its air-conditioned rooms. If 5/3 of its rooms were air-conditioned, what percent of the rooms that were not rented were air-conditioned?
(A) 20%
(B) 33 1/3 %
(C) 35%
(D) 40%
(E) 80%

Can someone provide an explaination?

Are your fractions all upside down? Based on your post, the motel rented more than 100% of it's rooms.

Is it E?

The ratios seem weird. I assume they are inverted.

I assume total number of rooms = 100.
3/4 of its rooms are rented, so total of 75 rooms rented.
3/5 of the rooms are air-conditioned, so 60 rooms that have AC.
Out of those 60, 2/3 of them are used, so 40 air-conditioned rooms rented out.

So, you have 100 - 75 = 25 rooms that are not rented out. Out of those 25, there are 60 - 40 = 20 air-conditioned rooms that are not rented out.

20/25 = 80%. Choice E.

Stuart Kovinsky wrote: Are your fractions all upside down? Based on your post, the motel rented more than 100% of it's rooms.

Stuart, its called leverage.

pls check the question i think the question is trying to say that out of 60 rooms 80(4/3 of 80) are on rent thats impossible.

Sorry Stuart I actually turned the fractions upside down by mistake!

lets say we have 100 room :

Rented = 75
Not Rented = 25
total Air = 100 * 3/5 = 60
Rented Air = 60 * 2/3 = 40
Non-Rented Air = 20

Non-rented Air / Not Rented
20 / 25 = 80%

I believe answer choice E

Thanks for your help Guys!