Problem Solving

BTGmoderatorLU wrote:Source: Manhattan Prep

Each light bulb at Hotel California is either incandescent or fluorescent. At a certain moment, forty percent of the incandescent bulbs are switched on, and ninety percent of the fluorescent bulbs are switched on. If eighty percent of all the bulbs are switched on at this moment, what percent of the bulbs that are switched on are incandescent?

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

The OA is D

We can let the total number of lights to be 100. Thus, 0.8 x 100 = 80 lights are on and 100 - 80 = 20 lights are off.

If we let n = the number of incandescent lights and m = the number of fluorescent lights, we find that 0.4 x n = 0.4n of the incandescent lights and 0.9 x m = 0.9m of the fluorescent lights are on. Since the total number of lights that are on is 80, we have:

0.4n + 0.9m = 80

4n + 9m = 800

We also have n + m = 100. If we rewrite this as 4n + 4m = 400 and subtract from the equation above, we get:

5m = 400

m = 80

So, 80 of the lights are fluorescent and 100 - 80 = 20 of the lights are incandescent. Since 40% of the incandescent lights are on, there 20 x 0.4 = 8 turned on incandescent lights. Thus, 8/80 = 10% of the lights that are on are incandescent.

Answer: D