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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]  09 Sep 2008, 07:40
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%

My approach gets me --

Let T be the total number of light-bulbs,
x = number that are supposed off
y = number that are supposed on.

Then, y -0.1y +0.4x = 0.8T
Also, x+y = T

Therefore, x = T/5 ...and 0.4x = 40% * (T/5) = 0.08T = 8%...what am I missing?
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Re: Problem solving - light bulbs [#permalink]  09 Sep 2008, 08:08
gmatkudi 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%

My approach gets me --

Let T be the total number of light-bulbs,
x = number that are supposed off
y = number that are supposed on.

Then, y -0.1y +0.4x = 0.8T
Also, x+y = T

Therefore, x = T/5 ...and 0.4x = 40% * (T/5) = 0.08T = 8%...what am I missing?

Say total 100 bulbs.

80 bulbs are on.

EDIT: sorry I forgot to add below calculations.
x=bulbs that are supposed to be off
y=bulbs that are supposed to be on

0.8(x+y) = 0.4x+0.9y
y=4x
x=20 y=80

40% of bulbs that suppose to be off actually on = 40/100 *20 =8

percent = 8/80 *100=10%
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Re: Problem solving - light bulbs [#permalink]  09 Sep 2008, 08:31
Ahh...dumb attack. thank you!
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Re: Problem solving - light bulbs [#permalink]  09 Sep 2008, 08:42
let the total no. of bulbs that are on be x........[B]

so total no. of bulbs = 5x/4
so bulbs actually off=5x/4 - x
but given that actual bulbs that are off are 60% of the total no. of bulbs that were to be off.
so total bulbs to be off = 10/6(5x/4-x).
and it says out of total bulbs off, the no. of bulbs on are 40%
so 0.4 *10/6*(5x/4 - x)..........[A] which is the total no. of bulbs that are on and which are to be off
dividing A/B, we get
.16666 or 16.66%.

whats the OA?
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Re: Problem solving - light bulbs [#permalink]  09 Sep 2008, 09:34
gmatkudi 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%

My approach gets me --

Let T be the total number of light-bulbs,
x = number that are supposed off
y = number that are supposed on.

Then, y -0.1y +0.4x = 0.8T
Also, x+y = T

Therefore, x = T/5 ...and 0.4x = 40% * (T/5) = 0.08T = 8%...what am I missing? :(

You have got 0.4x that will be the fraction of total bulbs that are off. However, the question is asking the percentage of bulbs that are on and should be off. This will be 0.4x/0.8T.

I approached the question as below.

if f is the number of bulbs that should be off and n that should be on then.
0.4f + 0.9n = 0.8(f+n) => n = 4f.

Now, required percentage = 0.4f/(0.8f + 0.8n) = 1/10 = 10%.
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Re: Problem solving - light bulbs [#permalink]  09 Sep 2008, 09:51
scthakur wrote:
gmatkudi 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%

My approach gets me --

Let T be the total number of light-bulbs,
x = number that are supposed off
y = number that are supposed on.

Then, y -0.1y +0.4x = 0.8T
Also, x+y = T

Therefore, x = T/5 ...and 0.4x = 40% * (T/5) = 0.08T = 8%...what am I missing? :(

You have got 0.4x that will be the fraction of total bulbs that are off. However, the question is asking the percentage of bulbs that are on and should be off. This will be 0.4x/0.8T.

I approached the question as below.

if f is the number of bulbs that should be off and n that should be on then.
0.4f + 0.9n = 0.8(f+n) => n = 4f.

Now, required percentage = 0.4f/(0.8f + 0.8n) = 1/10 = 10%.

good approach...donno where im going wrong.
Manager
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Re: Problem solving - light bulbs [#permalink]  09 Sep 2008, 10:37
Quote:
Say total 100 bulbs.

80 bulbs are on.

40% of bulbs that suppose to be off actually on = 40/100 *20 =8

percent = 8/80 *100=10%

I dont think that you could take 20 as the number of bulbs that are supposed to be off but are on.
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Re: Problem solving - light bulbs [#permalink]  09 Sep 2008, 15:18
I agree with the last post. That 20% bulbs are off does not mean that they are SUPPOSED to be off. The answer I am getting is 10% but with a different method.
Let x = total no. of bulbs.
Let N = On bulbs and Let F = off bulbs.
N = 80x/100 and F = 20x/100
Since 40% bulbs that should be F(off) are N(on), 60% bulbs that should be F are ACTUALLY, F. In addition, 10% bulbs that should be N are F.
Therefore, we get the equation for Off bulbs as follows:
60F/100 + 10N/100 = 20x/100
We know that x= N + F.
Hence, 60F + 10(x-F)/100 = 20X/100.
On solving, F/x = 1/5 This means, for every 100 bulbs, 80 are on.
Also 40% of F are actually N i.e., 40/100 * 1/5 = 8%
Therefore 8 out of 100 bulbs should be off but are on. The questioner wants to know what % of N is 8. We know that for every 100 bulbs, N = 80. Therefore, 8/80 = 10%.
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Re: Problem solving - light bulbs [#permalink]  09 Sep 2008, 20:59
KASSALMD wrote:
I agree with the last post. That 20% bulbs are off does not mean that they are SUPPOSED to be off. The answer I am getting is 10% but with a different method.
Let x = total no. of bulbs.
Let N = On bulbs and Let F = off bulbs.
N = 80x/100 and F = 20x/100
Since 40% bulbs that should be F(off) are N(on), 60% bulbs that should be F are ACTUALLY, F. In addition, 10% bulbs that should be N are F.
Therefore, we get the equation for Off bulbs as follows:
60F/100 + 10N/100 = 20x/100
We know that x= N + F.
Hence, 60F + 10(x-F)/100 = 20X/100.
On solving, F/x = 1/5 This means, for every 100 bulbs, 80 are on.
Also 40% of F are actually N i.e., 40/100 * 1/5 = 8%
Therefore 8 out of 100 bulbs should be off but are on. The questioner wants to know what % of N is 8. We know that for every 100 bulbs, N = 80. Therefore, 8/80 = 10%.

GMBA85 and KASSALMD

Thanks for pointing out. I forgot to add the calculations. I edited the post now.
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Re: Problem solving - light bulbs [#permalink]  09 Sep 2008, 21:22
KASSALMD wrote:
I agree with the last post. That 20% bulbs are off does not mean that they are SUPPOSED to be off. The answer I am getting is 10% but with a different method.
Let x = total no. of bulbs.
Let N = On bulbs and Let F = off bulbs.
N = 80x/100 and F = 20x/100
Since 40% bulbs that should be F(off) are N(on), 60% bulbs that should be F are ACTUALLY, F. In addition, 10% bulbs that should be N are F.
Therefore, we get the equation for Off bulbs as follows:
60F/100 + 10N/100 = 20x/100
We know that x= N + F.
Hence, 60F + 10(x-F)/100 = 20X/100.
On solving, F/x = 1/5 This means, for every 100 bulbs, 80 are on.
Also 40% of F are actually N i.e., 40/100 * 1/5 = 8%
Therefore 8 out of 100 bulbs should be off but are on. The questioner wants to know what % of N is 8. We know that for every 100 bulbs, N = 80. Therefore, 8/80 = 10%.

v well explained! good job!
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Re: Problem solving - light bulbs [#permalink]  09 Sep 2008, 22:00
Let's say total = 100

ON = 80

Supposedly Off = X

Supposedly On = 100-X

$$40%X + 90%(100-X) = 80$$

X = 20

$$40%X = 8$$

$$(8/80)*100 = 10%.$$
Re: Problem solving - light bulbs   [#permalink] 09 Sep 2008, 22:00
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