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hotel california

by mirantdon » Fri Jun 03, 2011 8:33 am
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?
22(2/9)% 16(2/3)% 11(1/9)% 10% 5%
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by Frankenstein » Fri Jun 03, 2011 8:57 am
Hi,
Let the total number of lights be 100.
Let x be the number of lights supposed to be ON. So (100-x) is the number of lights supposed to be OFF
Based on the constraints number of lights ON = x - (0.1)x + 0.4(100-x)=0.5x+40
This is given as 80 = >0.5x+40 = 80 =>x=80.
Of these 0.4(100-x) are supposed to be OFF = 8
So, 8/80 = 10%

Hence D
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by Anurag@Gurome » Fri Jun 03, 2011 8:58 am
mirantdon wrote: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?
Say, total number of lights in the hotel = 100
Also assume the number of lights that are supposed to be on = n.
Hence, number of lights that are supposed to be off = (100 - n)

Number of lights that are on = 80% of 100 = 80
Number of lights on that are supposed to be off = 40% of (100 - n) = 0.4(100 - n)
Number of lights off that are supposed to be on = 10% of n = 0.1n

Hence, total number of lights that are on = n - 0.1n + 0.4(100 - n) = 40 + 0.5n

Hence, (40 + 0.5n) = 80 => n = 80

Now, number of lights on that are supposed to be off = 0.4(100 - n) = 0.4(100 - 80) = 0.4*20 = 8

Hence, required percentage = (8/80)*100 = 10

The correct answer is D.
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by Ozlemg » Fri Jun 03, 2011 10:19 am
Can this problem be solved by plug-in numbers?

thnx
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by cans » Fri Jun 03, 2011 10:29 am
let total be 100
lights on at 8pm = 80
let x lights supposed to be on and thus 100-x supposed to be off
.4*(100-x) + .9*x = 80
x=80
thus 80 lights supposed to be on and 20 supposed to be off.
No. of lights supposed to be off = .4*(100-x) = 8
thus percentage = 8/80 = 10%
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by gmat1978 » Sat Jun 04, 2011 8:40 am
Can anyone please point out if anything is wrong in the following approach -

Let's say total number of lights = 100.
80% of lights are on in the evening = 80.
20% of the lights are off in the evening = 20.
Lights that are supposed to be off but are on = 40% of 20 = 8.
The percentage of lights that are on are supposed to be off = lights supposed to be off / lights that are on = 8/80 * 100 = 10%

Thanks
Anurag@Gurome wrote:
mirantdon wrote: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?
Say, total number of lights in the hotel = 100
Also assume the number of lights that are supposed to be on = n.
Hence, number of lights that are supposed to be off = (100 - n)

Number of lights that are on = 80% of 100 = 80
Number of lights on that are supposed to be off = 40% of (100 - n) = 0.4(100 - n)
Number of lights off that are supposed to be on = 10% of n = 0.1n

Hence, total number of lights that are on = n - 0.1n + 0.4(100 - n) = 40 + 0.5n

Hence, (40 + 0.5n) = 80 => n = 80

Now, number of lights on that are supposed to be off = 0.4(100 - n) = 0.4(100 - 80) = 0.4*20 = 8

Hence, required percentage = (8/80)*100 = 10

The correct answer is D.
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by Frankenstein » Sat Jun 04, 2011 9:10 am
gmat1978 wrote:Can anyone please point out if anything is wrong in the following approach -

Let's say total number of lights = 100.
80% of lights are on in the evening = 80.
20% of the lights are off in the evening = 20.
Lights that are supposed to be off but are on = 40% of 20 = 8.
The percentage of lights that are on are supposed to be off = lights supposed to be off / lights that are on = 8/80 * 100 = 10%

Thanks
Hi,
40% of lights that are supposed to be off are on. You have considered 40% of lights that are actually off now. It is just a coincidence that answers matched.
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