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

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Difficulty:

65% (hard)

Question Stats:

64% (02:41) correct
36% (02:13) wrong based on 76 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?

Re: Eighty percent of the lights at Hotel California are on at 8 [#permalink]
16 Sep 2008, 08:13

1

This post received KUDOS

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%. //E// _________________

Re: Eighty percent of the lights at Hotel California are on at 8 [#permalink]
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%

Need help overlapping set question [#permalink]
16 May 2010, 09:55

1

This post was BOOKMARKED

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?

Re: Need help overlapping set question [#permalink]
16 May 2010, 13:03

1

This post received KUDOS

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%

Is the Answer D.

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.

Re: Eighty percent of the lights at Hotel California are on at 8 [#permalink]
22 Sep 2011, 14:47

1

This post received KUDOS

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)

Re: Eighty percent of the lights at Hotel California are on at 8 [#permalink]
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? _________________

If you find my posts useful, Appreciate me with the kudos!! +1

Re: Eighty percent of the lights at Hotel California are on at 8 [#permalink]
23 Sep 2011, 03:29

3

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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

Re: Eighty percent of the lights at Hotel California are on at 8 [#permalink]
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

Re: Eighty percent of the lights at Hotel California are on at 8 [#permalink]
28 Jul 2014, 05:32

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Re: Need help overlapping set question [#permalink]
09 Sep 2014, 18:29

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Re: Need help overlapping set question [#permalink]
09 Sep 2014, 21:17

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Expert's post

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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%

You can do it using algebra to get an equation with a single variable:

Say, total 100 lights. 80 are ON.

Say L are supposed to be on and 100-L are supposed to be off.

Lights that are on = 40% of (100 - L) + 90% of L = 80 L = 80 = Number of lights supposed to be on. 20 = Number of lights supposed to be off. 40% of these are on so should be switched off. 40% of 20 = 8

Of the lights that are on, 8/80 = 10% should be switched off.

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