Problem Solving

One night a certain motel rented 3/4 of its rooms, including 2/3 of its air conditioned rooms. If 3/5 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%

Thank you for the help!

Say total number of rooms = 400

No. of rooms rented = 3/4 * 400 = 300 (not rented = 100)

No. of rooms with AC = 3/5 * 400 = 240

No. of rooms rented with AC = 2/3 * 240 = 160

No. of rooms Not rented with AC = 240 -160 = 80

Percent of rooms not rented with AC = 80/100 = 80%

Answer is E

Say there were 60 rooms. The we can arrive at the following table using given data.

---------------------------------------
| Rented | Not Rented |Total
---------------------------------------
AC | 24 | 12 | 36
---------------------------------------
No AC | 21 | 3 | 24
---------------------------------------
Total| 45 | 15 | 60
----------------------------------------

From table above, % of non rented ac rooms = 12/15 * 100 = 80%

IMO E

Call X total rooms => rented rooms = 3X/4 => not rented rooms = X/4
Then, we have AC rooms: 3X/5 => rented rooms with AC: (2/3)*(3X/5) = 2X/5
Thus, we have not rented rooms with AC: 3X/5 - 2X/5 = X/5
As a result, (X/5)/(X/4) = 0.8 = 80%
Answer: E

Hope it's useful

I understood everyone's solution! thanks!

total rooms = n
rented=3n/4
air conditioned rooms=x=3n/5
ac rooms rented = 2x/3=2n/5
ac rooms not rented = n/5
total non-rented rooms = n/4
thus% = 80
IMO E

its 80% the answer is E

Sum was easy but we got to try the GMAT language - what percent of the rooms that were not rented were air conditioned?

that is what is confusing....