Overlapping sets - hotel california .. doubt with solution

[praveen_gmat]

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?

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

Answer is D

The solution I arrived at is



My doubt is:
when the question is asking What percent of the lights that are on are supposed to be off
then .. the we should be looking for:
Supposed to be off =
{ supposed to be off but actually ON}
+
{ supposed to be off and actually OFF}

Why are we taking 8/80 as the solution as 8 corresponds to the value that is only supposed to off but actually ON ?

Hope somebody can clarify my doubt ![/b]

[GmatMathPro]

My doubt is:
when the question is asking What percent of the lights that are on are supposed to be off
then .. the we should be looking for:
Supposed to be off =
{ supposed to be off but actually ON}
+
{ supposed to be off and actually OFF}

Why are we taking 8/80 as the solution as 8 corresponds to the value that is only supposed to off but actually ON ?

Hope somebody can clarify my doubt !

When the question asks "What percent of the lights that are on...", think of that phrase "of the lights that are on" as defining the set of lights that you are considering. Those 80 lights that are on are the only ones you care about. Sure there are other lights in the hotel, but this wording tells us to strictly focus on these 80. So now when you have to find what percent of these 80 lights are supposed to be off, we're only allowed to look at lights within this set of 80 lights. So you should look only at that column in your chart that is directly under "Actually ON". 8 of these lights that are actually on are supposed to be off, 8 out of 80 or 10% of the lights that are on are supposed to be off.

You can't include the 12 lights that are off that are supposed to be off in this calculation because they are not a part of the 80 lights you are supposed to be considering.

[GMATGuruNY]

Another approach is to use alligation. Check my solution here:

https://www.beatthegmat.com/percentages-t98432.html