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

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Board of Directors
Joined: 17 Jul 2014
Posts: 2722
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: Eighty percent of the lights at Hotel California are on at 8 [#permalink]

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25 Nov 2016, 07:45
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%
Intern
Joined: 11 Jun 2017
Posts: 1
Re: Eighty percent of the lights at Hotel California are on at 8 [#permalink]

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23 Jun 2017, 01:21
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?
Director
Joined: 12 Nov 2016
Posts: 791
Re: Eighty percent of the lights at Hotel California are on at 8 [#permalink]

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24 Jun 2017, 02:25
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%

This question is possibly just meant to disorient the test taker- anyways,

200 lights

200(.8) =160 normally on
200(.2) = 40 normally off

40(.6) = 24 actually off and 16 actually on
160(.9) = 144 actually on and 16 actually off

16/144 +16 = 10 % that should actually be off

Thus
"D"
Senior Manager
Joined: 29 Jun 2017
Posts: 439
GPA: 4
WE: Engineering (Transportation)
Re: Eighty percent of the lights at Hotel California are on at 8 [#permalink]

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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
Joined: 29 Jun 2017
Posts: 439
GPA: 4
WE: Engineering (Transportation)
Eighty percent of the lights at Hotel California are on at 8 [#permalink]

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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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Eighty percent of the lights at Hotel California are on at 8   [#permalink] 28 Aug 2017, 09:08

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