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Manager  Joined: 04 Jan 2008
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Eighty percent of the lights at Hotel California are on at 8  [#permalink]

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Difficulty:   75% (hard)

Question Stats: 60% (02:41) correct 40% (03:05) wrong based on 344 sessions

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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%

Originally posted by dancinggeometry on 16 Sep 2008, 07:01.
Last edited by Bunuel on 28 Jul 2014, 06:42, edited 1 time in total.
Edited the question and added the OA.
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Re: Need help overlapping set question  [#permalink]

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

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Using Double matrix method:

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

Refer diagram below:
Attachments mat.png [ 5.64 KiB | Viewed 23712 times ]

##### General Discussion
Manager  Joined: 25 May 2011
Posts: 94
Re: Eighty percent of the lights at Hotel California are on at 8  [#permalink]

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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: Need help overlapping set question  [#permalink]

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Solved using Matrix method. Refer below:

Attachment: over.png [ 4.01 KiB | Viewed 21679 times ]

1. Let the total number of lights = 100

2. 80% of the lights are ON = 80

3. So, lights which are OFF = 100-80 = 20

4. Actual OFF = Suppose OFF = 20

5. 40% of "Suppose OFF" are "Actual ON" $$= \frac{40}{100}* 20 = 8$$

6. Percentage of the lights that are on are supposed to be off $$= \frac{8}{80} * 100 = 10%$$

Bunuel: Kindly update the OA

Also, in the problem, they have used words like "Eighty percent" (instead of 80%) etc.... is this normal in GMAT?
Manager  Joined: 25 May 2011
Posts: 94
Re: Eighty percent of the lights at Hotel California are on at 8  [#permalink]

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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]

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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%.
//E//
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Re: Need help overlapping set question  [#permalink]

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

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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: Need help overlapping set question  [#permalink]

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1
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]

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something like in the file attached
Attachments GMAT.xlsx [9.18 KiB]

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

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PareshGmat wrote:
Solved using Matrix method. Refer below:

Attachment:
over.png

1. Let the total number of lights = 100

2. 80% of the lights are ON = 80

3. So, lights which are OFF = 100-80 = 20

4. Actual OFF = Suppose OFF = 20

5. 40% of "Suppose OFF" are "Actual ON" $$= \frac{40}{100}* 20 = 8$$

6. Percentage of the lights that are on are supposed to be off $$= \frac{8}{80} * 100 = 10%$$

Bunuel: Kindly update the OA

Also, in the problem, they have used words like "Eighty percent" (instead of 80%) etc.... is this normal in GMAT?

Hey I am having a hard time on how you got step 4, I cannot see the wording in the problem that leads us to believe that those are equal

Thanks -- is this because 80% that are on means that actual = suppose to = 80%?
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Eighty percent of the lights at Hotel California are on at 8  [#permalink]

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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?

A. 22(2/9)%
B. 16(2/3)%
C. 11(1/9)%
D. 10%
E. 5%

We can let the total number of lights be 100 and let n = the number of lights supposed to be switched off. Thus, 100 - n = the number of lights supposed to be switched on.

From the information given in the problem, we see that 0.4n of the supposed turn-off lights are on and 0.9(100 - n) of the supposed turn-on lights are on. Since the total number of lights that are currently turned on is 0.8 x 100 = 80, we can create the equation:

0.4n + 0.9(100 - n) = 80

0.4n + 90 - 0.9n = 80

-0.5n = -10

n = 20

Since there are 20 supposed turn-off lights, but 0.4 x 20 = 8 of them are turned on, the percent of turn-on lights that are supposed to be turned off is 8/80 = 0.1 = 10%.

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Need help overlapping set question  [#permalink]

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

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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]

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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]

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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]

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VeritasPrepKarishma wrote:
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.

Hi Karishma,

I'm not sure if it is the terminology or something but I get confused with your explanation. This is because of the following:

you say 80 are ON. From the single variable equation, you get L = 80 = Number of lights supposed to be ON.

This means: The number of lights that are ON = Number of lights that are supposed to be ON.
If this is true then:
The number of lights that are OFF = Number of lights that are supposed to be OFF.

Is this possible from the given question? Please explain.
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Re: Eighty percent of the lights at Hotel California are on at 8  [#permalink]

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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?

A. 22(2/9)%
B. 16(2/3)%
C. 11(1/9)%
D. 10%
E. 5%

what a tricky wording...i did solve it with numbers as well...
suppose we have 100 lights.
80 should be on
20 should be off
from 20, 8 are on
from 80, 8 are not on
total on - 80.
8 that are one are supposed to be off. 8 from 80 is 10%
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Re: Eighty percent of the lights at Hotel California are on at 8  [#permalink]

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PareshGmat wrote:
Solved using Matrix method. Refer below:

Attachment:
over.png

1. Let the total number of lights = 100

2. 80% of the lights are ON = 80

3. So, lights which are OFF = 100-80 = 20

4. Actual OFF = Suppose OFF = 20

5. 40% of "Suppose OFF" are "Actual ON" $$= \frac{40}{100}* 20 = 8$$

6. Percentage of the lights that are on are supposed to be off $$= \frac{8}{80} * 100 = 10%$$

Bunuel: Kindly update the OA

Also, in the problem, they have used words like "Eighty percent" (instead of 80%) etc.... is this normal in GMAT?

Step 4 is not evident from question. Sure the values turn out to be same after solving an equation, but can we just draw step 4 as a conclusion? Re: Eighty percent of the lights at Hotel California are on at 8   [#permalink] 23 Jun 2017, 02:21

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