BTGModeratorVI wrote: ↑

Sat Mar 14, 2020 7:08 am

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: Manhattan 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

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 this video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you’re familiar with this technique, you can attempt these additional practice questions:

Easy Problem Solving questions
- https://www.beatthegmat.com/finance-majo ... 67425.html

Medium Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/920
- https://www.beatthegmat.com/posted-speed ... 72374.html
- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appli ... 70255.html
- https://www.beatthegmat.com/opening-nigh ... 64869.html
- https://www.beatthegmat.com/at-least-100 ... 74669.html
- https://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/946
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping- ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2

Easy Data Sufficiency questions
- https://www.gmatprepnow.com/module/gmat- ... /video/943
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume-f ... 69355.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-1

Difficult Data Sufficiency questions
- https://youtu.be/dsCeqF9Kbk8
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://youtu.be/dOZ9KM1m5Hs
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent

BTGModeratorVI wrote: ↑

Sat Mar 14, 2020 7:08 am

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: Manhattan GMAT

We can let the total number of lights 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