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

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Senior Manager
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Joined: 29 Jun 2017
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WE: Engineering (Transportation)
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Re: Eighty percent of the lights at Hotel California are on at 8  [#permalink]

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New post 28 Aug 2017, 08:50
let a% be the lights to be switched on = a %
then lights to be switched off = (100-a) %

total percent of lights switched on is 80. which come on RHS

40% of lights supposed to be off ( 100-a)% are actually on = 0.4(100-a)
also 10% of lights supposed to be on are actually off , so 0.1(a) these are off , so remaining to be on = a - 0.1a

now total lights on = 80
0.4(100-a) + (a-.1a) = 80
a=80 should be on

% of lights supposed to be off are on = 0.4(100-a) / 80 x100
= 0.4x2x100/80
=10%

Ans is D
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Senior Manager
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Eighty percent of the lights at Hotel California are on at 8  [#permalink]

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New post 28 Aug 2017, 09:08
another method:
...........................................act on......................act off
supp on_______________________________________0.1(100-x)___________100-x
supp off_________________ 0.4x_________________0.6x__________________x
__________________________80___________________20___________________100

0.1(100-x) + 0.6x =20
x=20

% = 0.4x/80 *100 = 0.4x20/80 *100 = 10 %
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Re: Eighty percent of the lights at Hotel California are on at 8  [#permalink]

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New post 29 Aug 2018, 08:37
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 \(= \frac{8}{80} * 100 = 10%\)

Answer = D

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 dont understand how you got step 4, can you please clarify on it? thanks!
GMAT Club Bot
Re: Eighty percent of the lights at Hotel California are on at 8 &nbs [#permalink] 29 Aug 2018, 08:37

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