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One night a certain hotel rented 3/4 of its rooms. including [#permalink]

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28 Sep 2010, 00:01

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52% (02:55) correct
48% (01:38) wrong based on 296 sessions

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One night a certain hotel rented 3/4 of its rooms. including 2/3 of their air conditioned rooms. if 3/5 of its rooms were air conditioned, what percent of the rooms that were not rented were air conditioned?

One night a certain hotel rented 3/4 of its rooms. including 2/3 of their air conditioned rooms. if 3/5 of its rooms were air conditioned, what percent of the rooms that were not rented were air conditioned?

20 33 1/3 35 40 80

please explain the logic

Consider total # of rooms to be 100; As 3/5 of the rooms are air conditioned then # of rooms that are air conditioned is 3/5*100=60;

3/4 rooms were rented --> 1/4*100=25 were NOT rented; 2/3 of air conditioned rooms were rented --> 1/3*60=20 air conditioned room were NOT rented;

This can be easily solved using the matrix method as the % is asked i can choose a good # for total rooms..let me choose 60 as all the 3 fractions given have 3,4&5 in the denominator and 60 is divisible by all thease 3 #s.

Given: Total Rented=(60)3/4 = 45 Total AC rooms = (60)3/5 = 36 Total AC rooms rented = (36)2/3 = 24

Plug in:

Rented Not-rented | | AC 24 12 | 36 | | Non AC | ............................................................... 45 15 | 60

total rooms 60 total rented 60*3/4 =45 total conditioned 60*3/5 =36 total conditioned 36*2/3 24 1200/15=80% (rooms that were not rented were air conditioned

Let's consider T as the total number of rooms. If 2/3 of the air conditioned rooms were rented, than 1/3 of them were not rented. We know that the total number of air-conditioned rooms is 3/5, thus we can say that 1/5 of the total rooms in the hotel were air-conditioned and not rented (1/3 x 3/5 = 1/5). (a)

We know that 3/4 of the total rooms were rented, thus 1/4 were not rented. (b)

Using (a) and (b), we can calculate the ratio of air-conditioned rooms to the non-rented rooms: (1/5 x T) / (1/4 x T) = 4/5, and thus non air-conditioned rooms make 80% of the total non-rented rooms.

One night a certain hotel rented 3/4 of its rooms. including 2/3 of their air conditioned rooms. if 3/5 of its rooms were air conditioned, what percent of the rooms that were not rented were air conditioned?

20 33 1/3 35 40 80

please explain the logic

Can someone please explain where am i going wrong here?

Let total rooms be 60

Rented rooms = 3/4 * 60 = 45

Rented AC rooms = 2/3 * 45 = 30

Total AC rooms = 3/5* 60 = 36

% Rooms that are AC and not rented = [(36 - 30) /36] * 100 = 16 * (2/3)

I am not sure where is my mistake... Can someone please correct me ???

Re: One night a certain hotel rented 3/4 of its rooms. including [#permalink]

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11 Aug 2014, 19:42

Hello from the GMAT Club BumpBot!

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Re: One night a certain hotel rented 3/4 of its rooms. including [#permalink]

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11 Aug 2014, 21:14

Expert's post

siddhans wrote:

vanidhar wrote:

One night a certain hotel rented 3/4 of its rooms. including 2/3 of their air conditioned rooms. if 3/5 of its rooms were air conditioned, what percent of the rooms that were not rented were air conditioned?

20 33 1/3 35 40 80

please explain the logic

Can someone please explain where am i going wrong here?

Let total rooms be 60

Rented rooms = 3/4 * 60 = 45

Rented AC rooms = 2/3 * 45 = 30

Total AC rooms = 3/5* 60 = 36

% Rooms that are AC and not rented = [(36 - 30) /36] * 100 = 16 * (2/3)

I am not sure where is my mistake... Can someone please correct me ???

"including 2/3rd of their air conditioned rooms" implies that 2/3rd of their air conditioned rooms were a part of the rented rooms.

So if total air conditioned rooms = 36 (as found by you above), 2/3rd of these i.e. 24 of these were rented. So 12 AC rooms were rented.

Total number of rooms that were not rented = 60 - 45 = 15

So AC rooms form what percent of rooms not rented? 12/15 * 100 = 80% _________________

Re: One night a certain hotel rented 3/4 of its rooms. including [#permalink]

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22 Aug 2015, 23:25

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

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