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# Eighty percent of the lights at Hotel California are

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

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10 Aug 2006, 09:37
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Eighty percent of the lights at Hotel California are supposed to be 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%
Manager
Joined: 26 Jun 2006
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10 Aug 2006, 09:55
I got lost in the wording a little bit, but then finally figured out what they are asking for.

It is (D), 10%

(Build 2x2 table and fill out the cells (that's an easy part) and then translate the question into what percent of what of what)
VP
Joined: 02 Jun 2006
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10 Aug 2006, 10:25
d)10%

Let total lights be 100

@ 8:00pm : 80 must be ON
@ 8:00pm : 20 must be OFF

10% of ON lights are OFF
=> 8 Lights are OFF (must be ON)
=>72Lights are ON (must be ON)

40% of OFF Lights are ON
=> 8 Lights are ON (must be OFF)
=>12Lights are OFF (must be OFF)

Total lights on = 80
Lights that must be OFF but are ON: 8

%tage = 10%

Senior Manager
Joined: 05 Mar 2006
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10 Aug 2006, 10:28
I'm getting stuck somewhere...

if 40% of the lights that are supposed to be OFF are ON

and the lights that are supposed to be off = 100-80 = 20%

then 40%(20%) of the lights that are supposed to be OFF are ON.

40%(20%) = 8%

What am I missing?
Manager
Joined: 12 May 2006
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10 Aug 2006, 10:35
D...

Lets say there are 100 lights

80 are supposed to be on
20 are supposed to be off

In the particular case 8 of the 20 are on (40%)

and 8 of the 80 are supposed to be off (10%)

All and all, there are 80 lights on, 8 of which are lights that were supposed to be turned off

8/80 = 1/10 = 10%[/b]
VP
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10 Aug 2006, 10:41
You are nearly there... 8% is 10% of 80% right?

agsfaltex wrote:
I'm getting stuck somewhere...

if 40% of the lights that are supposed to be OFF are ON

and the lights that are supposed to be off = 100-80 = 20%

then 40%(20%) of the lights that are supposed to be OFF are ON.

40%(20%) = 8%

What am I missing?
Senior Manager
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10 Aug 2006, 10:56
haas,

I see that you would divide by the total lights that are actually on, and to that you need that second sentance of 10% as well.

Thanks!
CEO
Joined: 20 Nov 2005
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Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
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10 Aug 2006, 11:43
Total = x
SOF = 0.8x
SON = 0.2x

AON = 0.8x + 0.2 * 0.4x (Supposed to be off but are on) - 0.8 * 0.1x (Supposed to be off but are on) = 0.8x
AOF = 0.2x

Percentage = 0.08x/0.8x = .1 i.e 10%
_________________

SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

SVP
Joined: 30 Mar 2006
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11 Aug 2006, 02:19
Let there be 100 lights

80 are supposed to be on
20 are supposed to be off

8 are off from the 80
8 are on from the 20.

hence total on = 80

Percent = 8/80 *100 = 10
11 Aug 2006, 02:19
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