fractions

Question

Can somebody please help me with the following problem:
Thanks in advance

A motel rented 2/3rd of all the rooms including 3/4th of its Air-conditioned rooms.
If 4/5th of all the rooms are air-conditioned, what percent of all rooms not
rented are air-conditioned rooms not rented?

Answers:
(A) 20% (B) 40% (C) 60%
(D) 80% (E) 100%

coolfish1103 · Answer

Rented 2/3 of the rooms, so 1/3 of the rooms are not rented.

2/3(3/4) = 1/2 of the rented rooms are a/ced,

2/3 - 1/2 = 1/6 of the rented rooms are not a/ced.

4/5 of the total rooms are a/ced... 4/5 - 1/2 = 3/10 of air conditioned rooms are not rented.
1/5 of the total rooms are not a/ced... 1/5 - 1/6 = 1/30 of the no a/ced rooms are not rented.

(3/10)/(1/3) = 9/10 = 90%

I don't see 90% as an option... did I do something wrong?

pmenon · Answer

i get C. I used numbers ... assume 60 total rooms. 40 are rented, and 20 are not.

Now, there will be 48 AC rooms in total, and 36 of them will be rented. So now we have of the 40 rooms, 36 AC and 4 non AC.

That leaves 12 AC rooms non rented, and 8 non-AC rooms not rented.

I believe the question is asking for what percent of non rented rooms are AC rooms. That would give me 12/20 or 60%

jcsekhar22 · Answer

I ma getting A as the answer

RyanDe680 · Answer

I think the easiest way to approach this is to use numbers that are factors of the denominators of the fractions.

I will say the hotel has 60 rooms total.

1. "A motel rented 2/3rd of all the rooms" - So 2/3 of all the rooms = 40 ( take 2/3 times 60) Therefore, are 20 rooms not rented.

2. "If 4/5th of all the rooms are air-conditioned" - So 4/5 of 60 rooms are air conditioned. 4/5 of 60 = 48 total rooms air conditioned.

3. "A motel rented 2/3rd of all the rooms including 3/4th of its Air-conditioned rooms" - So 3/4 of the airconditioned rooms are rented. There are 48 total air conditioned rooms, so 3/4 of 48 = 36 air-conditioned rooms are rented.

4. On to the question - "what percent of all rooms not rented are air-conditioned rooms not rented?" - Okay, well there are 20 rooms not rented. If there are 48 total air-conditioned rooms and 36 of them are rented, that leaves 12 of the air-conditioned rooms not rented. The question is asking how many not rented air-conditioned rooms there are.

This is solved by taking 12 (air-conditioned rooms not rented) / 20 (total rooms not rented) = 60%

C.

jcsekhar22 · Answer

You are right I interpreted the question wrong. I calculated for the % of the total rooms which is 20% instead of claulating the % of the not rented rooms. which is 60%

bkk145 · Answer

Make a table...

Say T= total rooms

__________Air___________________No Air__Total
Rent_____(3/4)*(4/5)T____________XXX___(2/3)T
Not Rent__(4/5)T - (3/4)*(4/5)T___ XXX____(1/3)T
Total_____(4/5)T

Ans =   /   =  /(1/3) = (1/5) / (1/3) = 3/5 = 60%

GMAT TIGER · Answer

rented all = 2/3
not-rented all = 1 - 2/3 = 1/3
rented a/c = 3/4 of 4/5 = 3/5
not-rented a/c = 4/5 - 3/5 = 1/5
the percent of all rooms not rented are air-conditioned rooms not rented = (1/5) / (1/30) = 60%

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