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%

One option is to use 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 = [spoiler]10%[/spoiler]

Answer: D

------------------------

NOTE: This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch our free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

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Cheers,
Brent

Hi jain2016,

This question is essentially a 'Weighted Average' question with a couple of extra steps.

We're told that 40% of the Incandescent bulbs and 90% of the Fluorescent bulbs are switched on; we're also told that 80% of the TOTAL bulbs are switched on.

N = # of Incandescent bulbs
F = # of Fluorescent bulbs

(.4N + .9F)/(N + F) = .8

.4N + .9F = .8N + .8F
.1F = .4N
F = 4N

This means that for every 1 incandescent bulb, there are 4 fluorescent bulbs. This ratio is important - you can use it to TEST VALUES or do the remaining algebra.

We're THEN asked what percent of the bulbs that are SWITCHED ON are INCANDESCENT.

TESTing VALUES can help to make this math easier, but it's not necessary. We already know that 40% of the incandescent and 90% of the fluorescent bulbs are turned on.....

(.4)(1) + .9(4) = .4 + 3.6 = 4

So, for every 4 bulbs that are turned on, 0.4 of them are incandescent.

.4/4.0 = 1/10 = 10%

Final Answer: D

GMAT assassins aren't born, they're made,
Rich