tricky PS when using numbers

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ildude02: Master | Next Rank: 500 Posts; Posts: 320; Joined: Sun Jan 13, 2008 10:00 pm; Thanked: 10 times

by ildude02 » Thu Jul 10, 2008 1:26 pm

One night a certain motel renetd 3/4 of its rooms, including 2/3 of its AC rooms. If 3/5 of its rooms were AC, what % of the rooms that were not renetd were AC?

1. 20
2. 33 1/3
3 35
4 40
5 80

If I tried picking numbers and solving it, I went wrong with it. But I was able to solve it drawing a grid. I would like to see someone solve this with the help of picking numbers. I wanted to see where I went wrong with my numbers approach.

Last edited by ildude02 on Thu Jul 10, 2008 2:23 pm, edited 2 times in total.

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Source: Beat The GMAT — Problem Solving | Thu Jul 10, 2008 1:26 pm

lion147: Senior | Next Rank: 100 Posts; Posts: 66; Joined: Sun Jul 06, 2008 9:14 am; Location: Florida; Thanked: 7 times; GMAT Score:710

by lion147 » Thu Jul 10, 2008 1:57 pm

Might there be something wrong with this question?

I ask because I picked a number of rooms - 100 - and got this:

100 rooms total
3/4 * 100 = 75 rented rooms
3/5 * 100 = 60 rooms with a/c
2/5 * 60 = 24 rented rooms with a/c

So, 25 total rooms were not rented, but 36 a/c rooms were not rented either.

Maybe I went wrong somewhere?

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ildude02: Master | Next Rank: 500 Posts; Posts: 320; Joined: Sun Jan 13, 2008 10:00 pm; Thanked: 10 times

by ildude02 » Thu Jul 10, 2008 2:04 pm

Sorry, I updated the question . It should be 2/3 of it's air conditioned rooms.

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lion147: Senior | Next Rank: 100 Posts; Posts: 66; Joined: Sun Jul 06, 2008 9:14 am; Location: Florida; Thanked: 7 times; GMAT Score:710

by lion147 » Thu Jul 10, 2008 2:13 pm

ildude02 wrote:Sorry, I updated the question . It should be 2/3 of it's air conditioned rooms.

ah, OK, so now the rented rooms with a/c is (2/3)*60 = 40, and 60-40=20 rooms with a/c were not rented, therefore the answer to the question is:

( a/c rooms not rented / total rooms not rented ) * 100 =
(20/25)*100 = 80

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ildude02: Master | Next Rank: 500 Posts; Posts: 320; Joined: Sun Jan 13, 2008 10:00 pm; Thanked: 10 times

by ildude02 » Thu Jul 10, 2008 2:22 pm

The mistake I made was, I calculated "2/3 of rented rooms" for AC rented rooms. Somehow, "2/3 of it's airconditioned rooms" got me thinking it's "2/3 of the rented rooms that are AC". That's where I went wrong and came up with 40% instead of 80%.

Thanks for your response.

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