VJesus12 wrote: ↑

Sun Feb 14, 2021 1:57 pm

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%

Answer: D

Source: e-GMAT

Here's a step-by-step solution using the Double Matrix method.
Here, we have a population of lightbulbs, and the two characteristics of each bulb are:
- incandescent or fluorescent
- on or off

Since the questions asks us to find a certain PERCENT, let's say that there are 100 bulbs altogether.
So, we can set up our matrix as follows:


Eighty percent of ALL the bulbs are switched on at this moment
So, 80 bulbs are turned ON.
This also means that the remaining 20 bulbs are OFF.
Add this to our diagram to get:


Forty percent of the incandescent bulbs are switched on
This one is tough, because we don't know how many incandescent bulbs there are.
So, let's let x = the number of incandescent bulbs.
This means the remaining 100-x bulbs are fluorescent
Let's add this to our diagram first, and THEN tackle the given info:


Okay, if x = the number of incandescent bulbs, and 40% of those bulbs are switched on, then the number of incandescent bulbs that are on = 40% of x = 0.4x
Likewise, if 100-x = the number of fluorescent bulbs, and 90% of those bulbs are switched on, then the number of fluorescent bulbs that are on = 90% of 100-x = 0.9(100 - x)
Add this to our diagram to get:


When we examine the left-hand column, we can see that the sum of the boxes is 80.
In other words: 0.4x + 0.9(100 - x) = 80
Expand: 0.4x + 90 - 0.9x = 80
Simplify: -0.5x = -10
Solve: x = 20
So, there are 20 incandescent bulbs, and 40% of them are on. 40% of 20 = 8, so 8 of the incandescent bulbs are on:


We can see that, of the 80 bulbs that are on, 8 of them are incandescent.
8/80 = 1/10 = 10%

Answer: D