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Motel

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by deepoe » Thu May 21, 2009 1:21 pm
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, waht percent of the rooms were NOT rented were air-conditioned?

A. 20%
B. 33,3%
C. 35%
D. 40%
E. 80%

OA = E

I chose a total of 120 rooms.

3/4 rented = 90 rooms.

2/3 air conditioned = 60 rooms.


3/5 x 120 = 72 rooms air-conditioned

12/72 = 16.6%

What did I wrong?
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Source: — Problem Solving |

Re: Motel

by Svedankae » Thu May 21, 2009 1:34 pm
deepoe wrote:
2/3 air conditioned = 60 rooms.
this line is incorrect.

2/3 of all airconditioned rooms were rented, that is 2/3 of the airconditioned rooms are included in the 72. you are implying that 2/3 of the rented rooms are airconditioned, which is not stated in the question.

also on percent problems i would always recommend choosing n=100. it makes it way easier.
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by deepoe » Thu May 21, 2009 1:51 pm
3/4 x 100 = 75

3/5 x 100 = 60

2/3 x 100 = 40 rented

So 20 did not rented.

20 / 100 = .20 %

:(
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by ssmiles08 » Thu May 21, 2009 3:41 pm
I picked 60 as the total number of rooms

(3/4) * 60 = 45 rooms rented

60 - 45 = 15 rooms not rented

Total A.C rooms = (3/5) * 60 = 36 A.C rooms

A.C and rented rooms = (2/3)(3/5)(60) = (2/5)(60) = 24

A.C and not rented = 36 - 24 = 12

% (of A.C and not rented) / (not rented rooms) = 12/15 = 4/5 = 80%
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by getso » Fri May 22, 2009 9:17 pm
Could you please tell what is the answer for this..
Is it A 20% or E 80%

Thanks
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by dumb.doofus » Sat May 23, 2009 7:31 pm
Answer is 80% as ssmiles has shown above..

whenever fractions are given.. its mostly beneficial to choose the LCM of the denominators of those fractions as your starting number..

In this case, the LCM of 4,3 and 5 is 60
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