good old plugging in numbers--ETS paper test

[wawatan]

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%

please explain why answer choice d is wrong.

OA is E

[netigen]

Rooms not rented = 1/4
Total AC rooms = 3/5
AC rooms rented = 2/3 x 3/5 = 2/5
AC room not rented = 3/5 - 2/5 = 1/5

so out of 1/4 not rented rooms 1/5 are AC
so % = 1/5 x 4/1 x 100 = 80%

[mim3]

Rooms not rented = 1/4
Total AC rooms = 3/5
AC rooms rented = 2/3 x 3/5 = 2/5
AC room not rented = 3/5 - 2/5 = 1/5

so out of 1/4 not rented rooms 1/5 are AC
so % = 1/5 x 4/1 x 100 = 80%

Alternatively, the "smart" numbers method...

60= total number of rooms (common denominator of 3,4,5). Based on that:

3/4 of the rooms rented- 45
1/4 not rented- 15

3/5 have AC- 36
2/5 don't- 24

2/3 of AC rooms rented- 24
1/3 not rented- 12

ac rooms not rented/rooms not rented= 12/15= 4/5= 80%