forty percent of the lights that are supposed to be off are

[netigen]

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%

[VP_Jim]

Wow, *where* did you get this question?! This one is crazy. Here's my guess:

Let's say we have 100 lights total. Thus, 80 of them are on.

We are supposed to have 20 lights off (the ones that aren't on), but 40% of them are actually on. So, we have 8 lights that should be off that are on instead. Eight is 10% of 80, so the answer is 10% (D).

We can try to confirm this - we now need to have 8 lights that should be on be off instead, to replace the ones that should be off that are on. The question tells us that 10% of the lights that should be on are actually off. Since we are supposed to have 80 lights on, 10% of that is 8, so our answer checked out.

Whew!

[VP_Jim]

Addendum:

I was assuming that the proper TOTAL number of lights that are on, 80, is correct - just that they are a mix of lights that should be on and lights that should be off.

[netigen]

This is from MGMAT cat test.

OA is 10% you got it right

[AleksandrM]

Netigen,

I found this problem to be very simple.

What difficulty level do the MGMAT folks suggest this is? I know that they usually give you a range (e.g., 500-600 or 700-800, etc).

Thanks.

[VerbalAttack]

We are supposed to have 20 lights off (the ones that aren't on), but 40% of them are actually on. So, we have 8 lights that should be off that are on instead. Eight is 10% of 80, so the answer is 10% (D).

Hi Jim, could you elaborate this a bit..

How could you take 40% of 20 lights which are OFF, as number of lights which are ON but supposed to be OFF? :roll:

cheers

[durgesh79]

i did some algebra, lets assume total lights 100 and original number of lights supposed to be off and on are x and y.

0.4 x + 0.9 y = 80
x + y = 100

this gives us x = 20 and y = 80.

Now 0.4x = 8 which is 10% of 80.

[AleksandrM]

verbalattack,

since 40% of 10 is 8 and 10% of 80 is 8. This means that the 8 lights of the 10 that are supposed to be off are on. And the 8 lights of the 80 that are supposed to be on are off. As you may have noticed, nothing has really changed. The only thing that has changed = actual lights that are on or off. Therefore, since of the 80, 8 are supposed to be off but are on, then 8/80 = 10%

Hope this helps.

P.S. Maybe you could imagine a building in which there are 10 lights in the basement and 80 lights on the rest of the floors.

[canuckclint]

this was 700-800 rated on mgmat.

[canuckclint]

i did some algebra, lets assume total lights 100 and original number of lights supposed to be off and on are x and y.

0.4 x + 0.9 y = 80
x + y = 100

this gives us x = 20 and y = 80.

Now 0.4x = 8 which is 10% of 80.

Yes this is the recommended matrix way to solve:

soff son
off .10y
on .4x .9y 80
x y 100