Problem Solving

80% of the lights in a hotel were on at 8.00 pm on some evening. If 40% of lights that were expected to be off, were in fact on, and 10% of lights that were expected to be on, were in fact off; what percent of the lights that are on, are the lights that were not expected to be on?
A. 10
B. 12
C. 100/9
D. 8
E. 18

I got D

But it takes me more than 2 mins

let take:

x is % of lights should be on
y is % of lights should be off

and of course x + y = 100

according to the question we have

40% lights should be off are on => 0.4y is the current % lights are on that should be off
10% lights should be on are off => 0.9x is the current % lights are on that should be on

we will get

0.9x + 0.4y = 80

Solve the equitation together we found [spoiler]y = 12[/spoiler]

What is the OA? How should this problem be solved?

I am getting 10

I used the same method as quocbao, but I disagree with him on the final result that y = 12, if you solve the two equations, then y comes out to be 20.

Then, as the question asks,
"what percent of the lights that are on, are the lights that were not expected to be on?"

Ans is : ((0.4 * 20 ) / 80) * 100

To save time, I did not go till the last step, i.e. the calculation part, after solving the equation, I noticed that the total number of lights which were earlier expected to be on are in fact on, thus, 40 % of lights which were expected to be off but are in fact on must equal the 10% of the lights which are off even though expected to be on.

But I do not think that when giving the exam, I would actually skip the calculation part. Hope I do!!!

Vemuri wrote:What is the OA? How should this problem be solved?

OA A

What does the matrix look like for this problem... I think it shud be 40% but it doesn't make sense.. How can they be asking for the information they have given.. Somehow I'm not getting the matrix right!!

Can instructors pls help??

Thanks
Shruti

KICKGMATASS123 wrote:What does the matrix look like for this problem... I think it shud be 40% but it doesn't make sense.. How can they be asking for the information they have given.. Somehow I'm not getting the matrix right!!

Can instructors pls help??

Thanks
Shruti

hope the attached helps.

sanju09 wrote:80% of the lights in a hotel were on at 8.00 pm on some evening. If 40% of lights that were expected to be off, were in fact on, and 10% of lights that were expected to be on, were in fact off; what percent of the lights that are on, are the lights that were not expected to be on?
A. 10
B. 12
C. 100/9
D. 8
E. 18

We can set up two equations with 2 unknowns to solve the system.

If 40% of the lights expected to be off were actually only, then 60% of the lights expected to be off were actually off.

If 90% of the lights expected to be on were actually on, then 10% of the lights expected to be on were actually off.

If we let the total number of lights = 100, we know that 80 are on and 20 are off.

Letting:

x = expected on
y = expected off

We then get:

.9x + .4y = 80

and

.1x + .6y = 20

and of course

x + y = 100

Now we can solve for x and y. Let's multiply the second equation by 10:

x + 6y = 200

x = 200 - 6y

Subbing into our 3rd equation:

(200 - 6y) + y = 100

200 - 5y = 100
100 = 5y
20 = y

Therefore, 20 lights were expected to be off and, since x + y = 100, 80 lights were expected to be on.

Back to the original question:

What percent of the lights that are on, are the lights that were not expected to be on?

% = part/whole * 100%

The whole = lights that are on = 80

The part = the lights that are on which weren't expected to be on = 40%(20) = 8

So, % = 8/80 * 100% = 1/10 * 100% = 10%... choose A.

Excellent Stuart!!

Could have been made shorter and easier. We really need only 2 equations, third one is a luxury only few can afford. The most confusing part of the question was to realize the number of lights that are on, and the lights that were not expected to be on, which Stuart explained very effectively.