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

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!

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.

This is from MGMAT cat test.

OA is 10% you got it right

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.

VP_Jim wrote: 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

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.

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.

this was 700-800 rated on mgmat.

durgesh79 wrote: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