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) 3331%
(C) 35%
(D) 40%
(E) 80%

Could you do this by plugging in a number? I chose 65 as the total number of rooms..and created the double set table.

But then I didn't know what the 3/5 was referring to. Does it mean 3/5 of its total or 3/5 of the rooms that are currently being rented out?

Is the answer E ?

It is..but how did you arrive at E?

Say the total no of rooms = 'x'

to simplify consider there are 4 types of rooms

1) Rented 2) Not-rented 3) A/c 4) Non a/c.

T. Rented Rooms = 3/4 'x'

T. No of a/c rooms = 3/5 'x'

T. Rented A/c rooms = 2/3(3/5) 'x' = 2/5 'x'

Total Non rented rooms =Total rooms - T. rented rooms = 'x'- 3/4'x' = 1/4x

Total non rented ac rooms = Total No of a/c rooms - Total no of rented a/c rooms = 3/5'x' - 2/5'x' = 1/5'x'


what is asked is % rooms not rented that were a/c

1.e Total Non rented a/c rooms x/5
-------------------------------- = --------- = 80 %
Total No of Non rented rooms x/4


It will be easier if you can put everyuthing in a 2x 2 matrix form with rented and non rented rooms on one side and ac and non ac on the other and then work out .

I think the answer is 40% D)

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?


Let teh toatl numbe rof rooms be 60.

3/4*60 = 45
Out of the 3/4 ths reneted 2/3 are air conditioned Therefore 2/3*45 = 30 AC RENTED AND 15 NON AC RENTED

NON RENTED ROOMS = 60- 45 = 15

3/5 of its rooms were air-conditioned

3/5*60 = 36 AC

REMAINING AC ROOMS = 36-30 OUT OF 15
i.e 6 out 15

Therefore 6/15*100 = 40% that were not rented were air-conditioned

Whats the OA?

Priyanka is indeed correct. Got thrown off by the 2/3rdpart Did 2/3*45 which is a mistake

Rented = (3/4) X rooms

of which (2/3)(3/4)X = AC Rented
so 1/3 rooms are not AC and were rented

(3/5)X rooms were AC

so percent of the rooms that were not rented & were air-conditioned = (1/3) (3/4) X / [(3/5)X] = 5/12 = 41 % ~ 40%

so D

wow, 65 is a really weird number for the total. why 65? did you think there was a 13 somewhere in the problem?

it's probably easier to use 60, since that's divisible by 3, 4, and 5. as you'll see, it turns out that you're not dealing with thirds of the original number, so divisibility by 3 is irrelevant; however, it's certainly not reasonable to expect that degree of insight from a single glance at the denominators.
pick a number that's compatible with the denominators in the problem. since 65 isn't divisible by 4, that's a bad number to pick.

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if there are 60 rooms total, then the motel rented 45 rooms. this means that 15 of the rooms were not rented.
also, 3/5 of 60, or 36, rooms have aircon; the motel rented 2/3 of these, or 24, rooms. this means that 12 rooms with aircon weren't rented.
12 out of 15 = 80%.

you can put these data into the double-set matrix, which will almost certainly speed the calculations.

incorrect.

the problem says that 2/3 of the rooms with aircon were rented. it does NOT say that 2/3 of the rented rooms have aircon. these are two very different statements indeed.

for comparison, check out the following two statements:
(a) two-thirds of my friends are women;
(b) two-thirds of women are my friends.
these are obviously not identical statements.

you can't use the 2/3 figure until you first deduce the total number of rooms with aircon, which is (3/5)60, or 36. they're being mean by presenting those two statements in an order opposite to that in which you actually use them, but that's how they roll. you should get very much used to the idea of having to use statements in an order different from that in which they're presented.