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

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Director
Joined: 12 Nov 2016
Posts: 691
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Re: Eighty percent of the lights at Hotel California are on at 8  [#permalink]

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24 Jun 2017, 03:25
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: 417
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, 09:50
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
Senior Manager
Joined: 29 Jun 2017
Posts: 417
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, 10:08
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 %
Manager
Joined: 31 Jul 2017
Posts: 197
Location: Tajikistan
Re: Eighty percent of the lights at Hotel California are on at 8  [#permalink]

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29 Aug 2018, 09:37
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 $$= \frac{8}{80} * 100 = 10%$$

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!
Manager
Joined: 31 Dec 2017
Posts: 88
Eighty percent of the lights at Hotel California are on at 8  [#permalink]

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07 Jun 2019, 02:54
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?
-------
Correct me if my logic is wrong
------
According to my simple thinking without calculation
Background: 80% light is on-->20% light is off.
Target question: % lights that are on are supposed to be off
Actual:
+40% off when it is supposed to be on-->this belongs to 20% light is off
+10% on when it is supposed to be off-->this belongs to 80% light is on
My answer is D (10%) since it perfectly matches my analysis.
-----
Since the question asks for % instead of actual number so I don't calculate or assume in actual numbers and go back to % as a conclusion.
If it has to be in actual numbers, it should be:
In 100 lights, there's 80 lights that are on, 20 lights that are off.
+40% off when it is supposed to be on-->this belongs to 20% light is off--->40% out of 20% category means 40% in 20 lights, and it equals to 8 lights.
+10% on when it is supposed to be off-->this belongs to 80% light is on--->10% in 80 lights, and it equals to 8 lights.
Percent of the lights that are on are supposed to be off-->(8/80)*100%= 10% (8 is extracted from 10% on when it is supposed to be off)
Intern
Joined: 03 Dec 2018
Posts: 9
Re: Eighty percent of the lights at Hotel California are on at 8  [#permalink]

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15 Jun 2019, 22:10
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?

Hello,, could you please explain why did you equate Actual OFF to Suppose OFF?
Thanks
Re: Eighty percent of the lights at Hotel California are on at 8   [#permalink] 15 Jun 2019, 22:10

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

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