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

00:00

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Difficulty:

5% (low)

Question Stats:

50% (02:14) correct
50% (01:36) wrong based on 14 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?

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// _________________

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%

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)

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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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

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