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Hotel California

This topic has 4 expert replies and 8 member replies

Hotel California

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Eighty percent of the lights at Hotel California are switched on at 8 p.m. one evening. However, forty percent of the lights that are supposed to be switched off are actually switched on, and ten percent of the lights that are supposed to be switched on are actually switched off. What percent of the lights that are switched on are supposed to be switched off?

1. 22(2/9)%
2. 16(2/3)%
3. 11(1/9)%
4. 10%
5. 5%

Source : MGMAT

OA later.

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sumanr84 wrote:
Eighty percent of the lights at Hotel California are switched on at 8 p.m. one evening. However, forty percent of the lights that are supposed to be switched off are actually switched on, and ten percent of the lights that are supposed to be switched on are actually switched off. What percent of the lights that are switched on are supposed to be switched off?

1. 22(2/9)%
2. 16(2/3)%
3. 11(1/9)%
4. 10%
5. 5%

Source : MGMAT

OA later.
Say hotel california has 1000 lights

800 are supposed to be on

Now 80 of the 200 which are supposed to be off are on

80 of the lights that are supposed to be on are off

80 of the lights which are supposed to be off are on

Total lights on =800

%of the lights which are supposed to be off are on = 80/800*100 =10%

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please help! getting an incorrect answer:

take x to be the total no. of lights

ten percent of lights that are spsd to be switched on are switched off means that 90% of 80% are switched on
forty percent of lights that are spsd to be off are on, which means than 40% of 20% are also switched on
--> (0.8)(0.9)x + (0.2)(0.4)x are switched on
--> 0.72x + 0.08x -> 0.8x are switched on

Which means that 80% of lights are switched on and hence no change is required. So, my answer comes to 0%
Sad Embarassed

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Ajith, How did you get the " 800 are supposed to be on " part? The question says 80% ARE ON AT 8pm ONE PARTICULAR EVENING. Its not supposed to be like that. Am I missing something?

I am getting 0% as well. Here is my approach:

Let total number of lights = 100
Let total Supposed ON = x
Then, Supposed OFF = 100-x

Now, The number supposed to be ON = (ON Currently) - 40% of (100-x) + 10% x
In other words,

x = 80 - 40/100 (100-x) + 10x

Solving for x, we get x = 80, which is of course the number on now. So no change is required..........

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The question is asking what percent of lights that are switched on are supposed to be switched off?

let total lights be = 100
so 80% or 80 are supposed to be switched on, and

40% of lights that are supposed to be switched off are on, hence 40% of remaining 20 which are supposed to be off are on. i.e. 8 lights which are supposed to be off are on.

also 10% of lights that are supposed to be on are off, hence 10% of 80 lights that are supposed to be on are off, i.e 8 lights are off.

consequently the total number of lights that are on is still 80. but the question is asking what percent of lights that are switched on are supposed to be switched off?

therefore, 8/80*100 = 10% ( ANSWER 4)

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The correct answer is D. ( 10 % )
Thanks kunal & ajith for making it simple.

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I am sorry, I still dont get it.
I would really appreciate it if someone can explain where we are getting "80 are supposed to be ON"? It doesn't say so anywhere in the question.
It says 80 lights are on. And that must be the wrong number because some lights that are supposed to be off are on and vica versa.

In other words, 80 are not supposed to be ON but are ON by mistake.
I must be missing something but just need to know where am I going wrong in my thought process.

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vibhusethi wrote:
I am sorry, I still dont get it.
I would really appreciate it if someone can explain where we are getting "80 are supposed to be ON"? It doesn't say so anywhere in the question.
It says 80 lights are on. And that must be the wrong number because some lights that are supposed to be off are on and vica versa.

In other words, 80 are not supposed to be ON but are ON by mistake.
I must be missing something but just need to know where am I going wrong in my thought process.
Let's complicate things then!

Eighty percent of the lights at Hotel California are switched on at 8 p.m. one evening. However, forty percent of the lights that are supposed to be switched off are actually switched on, and ten percent of the lights that are supposed to be switched on are actually switched off. What percent of the lights that are switched on are supposed to be switched off?

Let the total no of lights be, x

now 0.8x are on one evening

0.2x lights are supposed to be off

40% of it is on = 0.08x of lights which are supposed to be off are on

0.8x lights are supposed to be on

10% lights are supposed to be on are off = 0.8*.1x = 0.08x

The no of lights switched on which are supposed to be off = 0.08x
the no of lights supposed to be on = .8x

Now % = 0.08/0.8*100 =10%

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sumanr84 wrote:
Eighty percent of the lights at Hotel California are switched on at 8 p.m. one evening. However, forty percent of the lights that are supposed to be switched off are actually switched on, and ten percent of the lights that are supposed to be switched on are actually switched off. What percent of the lights that are switched on are supposed to be switched off?

1. 22(2/9)%
2. 16(2/3)%
3. 11(1/9)%
4. 10%
5. 5%

Source : MGMAT

OA later.
There is another thread on the same question at the link below... better if you check it for solution.

http://www.beatthegmat.com/lights-in-a-hotel-t34014.html#138417




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The crux of the problem lies in understanding the question line; "What percent of the lights that are switched on are supposed to be switched off?"

But at the same time the question also provided, "forty percent of the lights that are supposed to be switched off are actually switched on" - We know it is 0.08x.

I still didn't understood the question and those who understood it are lucky bunch.

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sumanr84 wrote:
Eighty percent of the lights at Hotel California are switched on at 8 p.m. one evening. However, forty percent of the lights that are supposed to be switched off are actually switched on, and ten percent of the lights that are supposed to be switched on are actually switched off. What percent of the lights that are switched on are supposed to be switched off?

A. 22(2/9)%
B. 16(2/3)%
C. 11(1/9)%
D. 10%
E. 5%
One option is to use the Double Matrix method.
Here, we have a population of lightbulbs, and the two characteristics of each bulb are:
- incandescent or fluorescent
- on or off

Since the questions asks us to find a certain PERCENT, let's say that there are 100 bulbs altogether.
So, we can set up our matrix as follows:


Eighty percent of ALL the bulbs are switched on at this moment
So, 80 bulbs are turned ON.
This also means that the remaining 20 bulbs are OFF.
Add this to our diagram to get:


Forty percent of the incandescent bulbs are switched on
This one is tough, because we don't know how many incandescent bulbs there are.
So, let's let x = the number of incandescent bulbs.
This means the remaining 100-x bulbs are fluorescent
Let's add this to our diagram first, and THEN tackle the given info:


Okay, if x = the number of incandescent bulbs, and 40% of those bulbs are switched on, then the number of incandescent bulbs that are on = 40% of x = 0.4x
Likewise, if 100-x = the number of fluorescent bulbs, and 90% of those bulbs are switched on, then the number of fluorescent bulbs that are on = 90% of 100-x = 0.9(100 - x)
Add this to our diagram to get:


When we examine the left-hand column, we can see that the sum of the boxes is 80.
In other words: 0.4x + 0.9(100 - x) = 80
Expand: 0.4x + 90 - 0.9x = 80
Simplify: -0.5x = -10
Solve: x = 20
So, there are 20 incandescent bulbs, and 40% of them are on. 40% of 20 = 8, so 8 of the incandescent bulbs are on:


We can see that, of the 80 bulbs that are on, 8 of them are incandescent.
8/80 = 1/10 = 10%

Answer: D

------------------------

NOTE: This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch this video: http://www.gmatprepnow.com/module/gmat-word-problems?id=919

Once you’re familiar with this technique, you can attempt these additional practice questions:

Easy Problem Solving questions
- http://www.beatthegmat.com/the-aam-aadmi-party-t272242.html
- http://www.beatthegmat.com/finance-majors-non-finance-majors-overlapping-set-question-t167425.html

Medium Problem Solving questions
- http://www.beatthegmat.com/probability-question-t273360.html
- http://www.beatthegmat.com/posted-speed-limit-t272374.html
- http://www.beatthegmat.com/motel-t271938.html
- http://www.beatthegmat.com/of-the-applicants-passes-a-certain-test-15-t270255.html
- http://www.beatthegmat.com/opening-night-and-late-patrons-t264869.html
- http://www.beatthegmat.com/ds-french-japanese-t222297.html
- http://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- http://www.beatthegmat.com/ratio-problem-t268339.html
- http://www.beatthegmat.com/overlapping-sets-question-t265223.html
- http://www.beatthegmat.com/fractions-t264254.html
- http://www.beatthegmat.com/overlapping-sets-t264092.html
- http://www.beatthegmat.com/mba/2011/05/09/random-double-matrix-question-2

Easy Data Sufficiency questions
- http://www.beatthegmat.com/for-what-percent-of-those-tested-for-a-certain-t270596.html
- http://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- http://www.beatthegmat.com/sets-matrix-ds-t271914.html
- http://www.beatthegmat.com/each-of-people-voted-once-in-an-election-x-t271375.html
- http://www.beatthegmat.com/a-manufacturer-t270331.html
- http://www.beatthegmat.com/in-costume-for-halloween-t269355.html
- http://www.beatthegmat.com/mba/2011/05/05/random-double-matrix-question-1

Difficult Data Sufficiency questions
- http://www.beatthegmat.com/double-set-matrix-question-t271423.html
- http://www.beatthegmat.com/sets-t269449.html
- http://www.beatthegmat.com/mba/2011/05/16/random-double-matrix-question-3

Cheers,
Brent

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We have two groups of lights: lights that should be on, and lights that should be off.

Overall, 80% of lights are on. Of lights that should be on, 90% are on (since 10% are off), and of lights that should be off, 40% are on. So we have a standard mixtures situation, which is always a weighted average situation; drawing these three 'averages' on a number line (I'm using a weighted average method here sometimes called 'alligation' that might not make much sense to anyone who has never seen it, but you can google that term to find a more detailed explanation) :

---40-----------------80---90----

the ratio of the distances to the middle must equal the ratio of the two groups. So the two types of lights are in a 40 to 10 ratio, or 4 to 1 ratio, and so 4/5 of them are supposed to be on (since 80 is closer to 90), and the rest, 1/5, are meant to be off.

So if we have 100 lights in total, 20 should be off, but actually 40% of those, or 8 of them, are on. Overall 80 lights are on, so 8/80 = 10% of those should have been off.

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sumanr84 wrote:
Eighty percent of the lights at Hotel California are switched on at 8 p.m. one evening. However, forty percent of the lights that are supposed to be switched off are actually switched on, and ten percent of the lights that are supposed to be switched on are actually switched off. What percent of the lights that are switched on are supposed to be switched off?

1. 22(2/9)%
2. 16(2/3)%
3. 11(1/9)%
4. 10%
5. 5%

Source : MGMAT

OA later.
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: 4/D

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