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# Eighty percent of the lights at Hotel California are on at 8

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Manager
Joined: 28 Jul 2004
Posts: 136
Location: Melbourne
Schools: Yale SOM, Tuck, Ross, IESE, HEC, Johnson, Booth
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Eighty percent of the lights at Hotel California are on at 8 [#permalink]  08 Nov 2008, 23:02
Eighty percent of the lights at Hotel California are on at 8 p.m. a certain evening. However, forty percent of the lights that are supposed to be off are actually on and ten percent of the lights that are supposed to be on are actually off. What percent of the lights that are on are supposed to be off?

a) 22(2/9)%
b) 16(2/3)%
c) 11(1/9)%
d) 10%
e) 5%
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kris

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Joined: 31 Oct 2008
Posts: 32
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Kudos [?]: 5 [1] , given: 0

Re: Light bulbs ON/OFF [#permalink]  09 Nov 2008, 00:55
1
KUDOS
Oh snap, this one was pretty tricky (if for no other reason than the crazy Sphinxlike wording!) but I got D.

Let T=the total number of lights; F=the number of lights that should be oFF, and N the number of lights that should be oN.
$$0.8T=0.4F+0.9N$$
is the mathematical statement of that riddle. Conservation of light bulbs gives us
$$F+N=T$$
Substituting one expression into the other, I found
$$F=0.2T$$
Returning to the first equation,
$$0.8T=0.08T+0.9N$$
So the fraction that should be off is a 10% contribution to the total number on.

You can check out any time you'd like, but you can never leave...
Manager
Joined: 05 Jul 2008
Posts: 139
GMAT 1: Q V
GMAT 2: 740 Q51 V38
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Kudos [?]: 75 [0], given: 40

Re: Light bulbs ON/OFF [#permalink]  09 Nov 2008, 05:18
phdizzle wrote:
Oh snap, this one was pretty tricky (if for no other reason than the crazy Sphinxlike wording!) but I got D.

Let T=the total number of lights; F=the number of lights that should be oFF, and N the number of lights that should be oN.
$$0.8T=0.4F+0.9N$$
is the mathematical statement of that riddle. Conservation of light bulbs gives us
$$F+N=T$$
Substituting one expression into the other, I found
$$F=0.2T$$
Returning to the first equation,
$$0.8T=0.08T+0.9N$$
So the fraction that should be off is a 10% contribution to the total number on.

You can check out any time you'd like, but you can never leave...

Kudo,
I pick T= 100.
So I have
F+N= 100
0.4F + 0.9N= 80

F=20=>number of the lights that are on are supposed to be off is 20*0.4=8
Manager
Joined: 28 Jul 2004
Posts: 136
Location: Melbourne
Schools: Yale SOM, Tuck, Ross, IESE, HEC, Johnson, Booth
Followers: 1

Kudos [?]: 21 [0], given: 2

Re: Light bulbs ON/OFF [#permalink]  10 Nov 2008, 12:06
8 is the correct answer. Thanks a lot guys. I got confused by the wordings of the problem.
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kris

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Kudos [?]: 254 [0], given: 1

Re: Light bulbs ON/OFF [#permalink]  10 Nov 2008, 17:10
This is a good Q that one won't be able to solve easily using the grid. The simple reason is ON = ! OFF and OFF = !ON

The next tricky thing is to find out that 90% of the lights that are supposed to be on are on and come up with 0.4x+0.9y = 80. the total number of lights that are on are the lights are correctly on and wrongly on.

x+y =100 and we can then solve to get 8

Kudos to phdizzle. Not easy to solve in the heat of the exam.
Re: Light bulbs ON/OFF   [#permalink] 10 Nov 2008, 17:10
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