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

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Eighty percent of the lights at Hotel California are on at 8 [#permalink] New post 16 Sep 2008, 06:01
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Question Stats:

59% (02:24) correct 41% (01:53) wrong based on 42 sessions
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%
[Reveal] Spoiler: OA

Last edited by Bunuel on 28 Jul 2014, 05:42, edited 1 time in total.
Edited the question and added the OA.
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Re: Eighty percent of the lights at Hotel California are on at 8 [#permalink] New post 16 Sep 2008, 08:13
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dancinggeometry 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?

22(2/9)%
16(2/3)%
11(1/9)%
10%
5%


this kind of the wording is always confusing for me.

a= number of lights supposed to be on
b= number of lights supposed to be off
total = a+b
no of lights that are on = 0.8(a+yb

Light that are supposed to be on but are actually off = 10% of a
Light that are supposed to be on are on = 90% of a

Light that aare supposed to be but are on = 40% of b
Light that aare supposed to be off are off = 60% of b

0.9a + 0.4b = 0.8 (a+b)
a = 4b

Suppose total Lights = 100
so, a = 80 and b = 20

No of lights that are on are on but are supposed to be off = 40% of b = 0.4 (20) = 5

So, the % of lights that are on are supposed to be off = 5/100 = 5%.
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Re: Eighty percent of the lights at Hotel California are on at 8 [#permalink] New post 16 Sep 2008, 12:35
Let x be the total no. of lights and y be the no. of lights off.
Therefore, (x-y) is the total no. of "on" lights.
Since 40% of lights that should be off are on, 60% of lights that are supposed to be off are actually off. However, 10% of lights that are supposed to be on are off.
Therefore, 60*y/100 + 10*(x-y)/100 = 20*x/100. Solving this gives us x= 5*y. Therefore the no. of lights on are (x-y) = 5y-y = 4y.
Therefore, % of "on" lights that should have been off = {(40y/100) /4y}*100 = 10%
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Re: Eighty percent of the lights at Hotel California are on at 8 [#permalink] New post 22 Sep 2011, 14:47
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KASSALMD wrote:
Let x be the total no. of lights and y be the no. of lights off.
Therefore, (x-y) is the total no. of "on" lights.
Since 40% of lights that should be off are on, 60% of lights that are supposed to be off are actually off. However, 10% of lights that are supposed to be on are off.
Therefore, 60*y/100 + 10*(x-y)/100 = 20*x/100. Solving this gives us x= 5*y. Therefore the no. of lights on are (x-y) = 5y-y = 4y.
Therefore, % of "on" lights that should have been off = {(40y/100) /4y}*100 = 10%



Agree with you. My approach:

just pick a number (e. 100) for lights.
80 lights are supposed to be on, but 0.1 (that is 8 lights) are off.
20 lights are supposed to be off, but 0.4 (that is 8 lights) are on.

Totally, 80 - 8 + 8=80 lights are on
and the percentage of lights which are on (and not supposed to be on) is 10% (8 out of 80)
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Re: Eighty percent of the lights at Hotel California are on at 8 [#permalink] New post 22 Sep 2011, 15:44
All this is under the assumption that there are no lights which are neither supposed to be on or off.
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Re: Eighty percent of the lights at Hotel California are on at 8 [#permalink] New post 22 Sep 2011, 17:55
shahideh wrote:
KASSALMD wrote:
Let x be the total no. of lights and y be the no. of lights off.
Therefore, (x-y) is the total no. of "on" lights.
Since 40% of lights that should be off are on, 60% of lights that are supposed to be off are actually off. However, 10% of lights that are supposed to be on are off.
Therefore, 60*y/100 + 10*(x-y)/100 = 20*x/100. Solving this gives us x= 5*y. Therefore the no. of lights on are (x-y) = 5y-y = 4y.
Therefore, % of "on" lights that should have been off = {(40y/100) /4y}*100 = 10%



Agree with you. My approach:

just pick a number (e. 100) for lights.
80 lights are supposed to be on, but 0.1 (that is 8 lights) are off.
20 lights are supposed to be off, but 0.4 (that is 8 lights) are on.

Totally, 80 - 8 + 8=80 lights are on
and the percentage of lights which are on (and not supposed to be on) is 10% (8 out of 80)


I really didn't understand why did you pick the numbers 80 and 20?
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Re: Eighty percent of the lights at Hotel California are on at 8 [#permalink] New post 23 Sep 2011, 03:29
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Quote:
I really didn't understand why did you pick the numbers 80 and 20?


when you encounter with a question related to "percentage", it's easier for you to just intellectually pick a number that covers the percentages of the question, and then solve the problem with that number. This approach makes the question tangible.

So, for this question, I pick the number 100 for lights. that is, i suppose the total lights are 100. According to the question, 80% of lights are on at a certain time. So:
80% * 100=80
That is in my approach, 80 lights are on, and 20 other lights, (100-80=20) are off.

In continue, the question says: forty percent of the lights that are supposed to be off are actually on
40% * 20 = 8
That is, 20 lights are supposed to be off, but 8 of them are on now.


again in continue, the question says: ten percent of the lights that are supposed to be on are actually off
10% * 80 = 8
that is, 80 lights are supposed to be on, but 8 lights of them are off now.

so the total number of lights which are on is: 80 + 8 - 8 = 80

To calculate the percentage: (8/80)*100=10

let me know if my explanation is clear : )
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Re: Eighty percent of the lights at Hotel California are on at 8 [#permalink] New post 03 Nov 2011, 01:27
shahideh wrote:
Quote:
I really didn't understand why did you pick the numbers 80 and 20?


when you encounter with a question related to "percentage", it's easier for you to just intellectually pick a number that covers the percentages of the question, and then solve the problem with that number. This approach makes the question tangible.

So, for this question, I pick the number 100 for lights. that is, i suppose the total lights are 100. According to the question, 80% of lights are on at a certain time. So:
80% * 100=80
That is in my approach, 80 lights are on, and 20 other lights, (100-80=20) are off.

In continue, the question says: forty percent of the lights that are supposed to be off are actually on
40% * 20 = 8
That is, 20 lights are supposed to be off, but 8 of them are on now.


again in continue, the question says: ten percent of the lights that are supposed to be on are actually off
10% * 80 = 8
that is, 80 lights are supposed to be on, but 8 lights of them are off now.

so the total number of lights which are on is: 80 + 8 - 8 = 80

To calculate the percentage: (8/80)*100=10

let me know if my explanation is clear : )



So clear
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Re: Eighty percent of the lights at Hotel California are on at 8 [#permalink] New post 03 Nov 2011, 06:37
My answer is also 10%
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Re: Eighty percent of the lights at Hotel California are on at 8 [#permalink] New post 28 Jul 2014, 05:32
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Re: Eighty percent of the lights at Hotel California are on at 8 [#permalink] New post 30 Jul 2014, 00:01
Using Double matrix method:

Answer = \frac{8}{80} * 100 = 10%

Refer diagram below:
Attachments

mat.png
mat.png [ 5.64 KiB | Viewed 356 times ]


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Re: Eighty percent of the lights at Hotel California are on at 8   [#permalink] 30 Jul 2014, 00:01
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