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# Need help overlapping set question

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Need help overlapping set question [#permalink]  16 May 2010, 10:55
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50% (03:34) correct 50% (02:46) wrong based on 0 sessions
Eighty percent of the lights at Hotel California are on at 8pm a certain evening. However, forty percent of the lights that are supposed to 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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Re: Need help overlapping set question [#permalink]  16 May 2010, 14:03
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valaparla wrote:
Eighty percent of the lights at Hotel California are on at 8pm a certain evening. However, forty percent of the lights that are supposed to 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%

let me try..

Let the light which are supposed to be OFF = SO
Let the light which are supposed to be ON = SN
Let the light which are ACTUALLY OFF = AO
Let the light which are ACTUALLY ON = AN

Let the total no. of lights be 100,
So ACTUALLY ON lights = 80
And ACTUALLY OFF lights = 20

Also given >> forty percent of the lights that are supposed to off are actually on >>> (40/100)*SO are ACTUALLY ON
it means >>> (60/100)*SO are ACTUALLY OFF

Also given >> ten percent of the lights that are supposed to be on are actually off >>> (10/100)*SN are ACTUALLY OFF
it means >>> (90/100)*SN are ACTUALLY ON

So, Total ACTUALLY ON lights = (40/100)*SO + (90/100)*SN = 80
and Total ACTUALLY OFF lights = (60/100)*SO + (10/100)*SN = 80

From here we get SO = 20

we need to find: What percent of the lights that are on are supposed to be off >>> So light ACTUALLY ON are 80 and light which are ACTUALLY ON, which are supposed to be OFF = (40/100)*SO = 8.

So (8/80)*100 = 10%

OA plz.
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Re: Need help overlapping set question [#permalink]  10 Aug 2010, 01:36
I can confirm it's 10%, D.
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Re: Need help overlapping set question [#permalink]  10 Aug 2010, 09:56
Let

off = # supposed to be off
on = # supposed to be on

Then from the information given we have:

.4*off + (1-.1)*on = .8*(off + on)

We are trying to find the number that should be off (but are on) as a portion of everything that is on, e.g.:

\frac{.4*off}{.8*(off+on)}

Solving the first equation for on, we get

on = 4*off

Substituting this into the second equation, we can eliminate the dependence on the variable off and we solve the fraction to be 1/10 (d).
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Re: Need help overlapping set question [#permalink]  10 Aug 2010, 16:39
something like in the file attached
Attachments

GMAT.xlsx [9.18 KiB]

Re: Need help overlapping set question   [#permalink] 10 Aug 2010, 16:39
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