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

Question

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%

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

PareshGmat · Accepted Answer

Using Double matrix method:

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

Refer diagram below:

KarishmaB · Answer

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.

Answer (D)

GMAT TIGER · Answer

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//

KASSALMD · Answer

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%

nverma · Answer

Is the Answer D.

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.

shahideh · Answer

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)

chawlavinu · Answer

I really didn't understand why did you pick the numbers 80 and 20?

shahideh · Answer

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 : )

PareshGmat · Answer

Solved using Matrix method. Refer below:

Attachment:

over.png [ 4.01 KiB | Viewed 48441 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 \(= \frac{8}{80} * 100 = 10%\)

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?

ScottTargetTestPrep · Answer

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%.

Answer: D

Kinshook · Answer

Given: 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.

Asked: What percent of the lights that are on are supposed to be off?

Actually on  Actually off  Total  
  Supposed to be on  .9(100%-x%)  .1(100%-x%)  100%-x%  
  Supposed to be off  .4x%  .6x%  x%  
  Total  80%  20%  100%

.9(100%-x%) + .4x% = 80%
90% -.5x% = 80%
x% = 20%

Actually on  Actually off  Total  
  Supposed to be on  72%  8%  80%  
  Supposed to be off  8%  12%  20%  
  Total  80%  20%  100%

The percent of the lights that are on are supposed to be off = 8%/80% = 10%

IMO D

MonishBhawale · Answer

simpler way to solve by algebra
x = lights the should be on , y= should be off

total = x+y
0.8(x+y) =0.9x+0.4y
x/y = 4/1
let x+y = 50
x= 40 , y=10
 80%50 =40
4/40*100 = 10

Mizan42 · Answer

On= x
Off= y

Now,

Actually on of x and y = (90% of x) + (40% of y)

ATQ,

90% of x + 40 % of y=80% of(x+y)

=> x =4y

Required percentage = {(2y/5)/4y}×100
= 10%

Posted from my mobile device

Purnank · Answer

Lets assume 100x are the lights that are supposed to be on and 100y are the lights that are supposed to be off.
Given 1. - Eighty percent of the lights at Hotel California are on at 8 p.m.
Means the lights which are on right now are 80% of 100x and 100y = 80x+80y - Eq1
Given 2. - 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.
Now out of the mixture of these two types the total of which are on = 40y (40% of 100y) + 90x (10% are off from 100x) - Eq2
Equating both,
40y+90x = 80x+80y
x=4y
Now,
Lets calculate What percent of the lights that are on are supposed to be off =  \frac{40y}{100x}*100 = \frac{40y}{4y} = 10% 
  Answer is D.

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=85317 --- Harsha GMAT-Club-Forum-o8hbur0u.png

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

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	Actually on	Actually off	Total
Supposed to be on	.9(100%-x%)	.1(100%-x%)	100%-x%
Supposed to be off	.4x%	.6x%	x%
Total	80%	20%	100%

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

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