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%
incandescent
This topic has expert replies
-
- Legendary Member
- Posts: 510
- Joined: Thu Aug 07, 2014 2:24 am
- Thanked: 3 times
- Followed by:5 members
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Let total bulbs = 100.j_shreyans wrote: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%
Let x = incandescent bulbs.
Let 100-x = fluorescent bulbs.
40% of the incandescent bulbs switched on = .4x
10% of the fluorescent bulbs switched off = 90% switched on = .9(100-x).
Since .8*100 = 80 bulbs are switched on, we get:
.4x + .9(100-x) = 80.
4x + 900 - 9x = 800
-5x = -100
x = 20.
Thus, .4*20 = 8 of the incandescent bulbs are switched on.
Incandescent on/Total on = 8/80 = 10%.
The correct answer is D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Here's how Mitch's solution looks when we use the Double Matrix method.j_shreyans wrote: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%
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
Once you're familiar with this technique, you can attempt these additional practice questions:
Easy Problem Solving questions
- https://www.beatthegmat.com/the-aam-aadm ... 72242.html
- https://www.beatthegmat.com/finance-majo ... 67425.html
Medium Problem Solving questions
- https://www.beatthegmat.com/probability- ... 73360.html
- 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/ds-french-ja ... 22297.html
- https://www.beatthegmat.com/prblem-solving-t279424.html
Difficult Problem Solving questions
- 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.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://www.beatthegmat.com/double-set-m ... 71423.html
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3
Cheers,
Brent
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi j_shreyans,
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
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
- umasarath52
- Newbie | Next Rank: 10 Posts
- Posts: 6
- Joined: Fri Oct 10, 2014 11:01 pm
Let X = Incandescent Bulbs
Let Y = Fluorescent Bulbs
Total bulbs = x+y
40% of I bulbs are ON = 0.4x
90% of F bulbs are ON = 0.9y
Total number of bulbs ON = 0.4x+0.9y
Also given that 80% of all bulbs are ON = 0.8(x+y)
0.4x+0.9y = 0.8(x+y)
on solving
y = 4x
Percent of I bulbs ON = 0.4x/(0.8(x+y))
= 0.5 * (x/(x+y))
substituting y = 4x
= 0.5 * x/x+4x = 0.5 * 0.2 = 0.1 = 10%
Let Y = Fluorescent Bulbs
Total bulbs = x+y
40% of I bulbs are ON = 0.4x
90% of F bulbs are ON = 0.9y
Total number of bulbs ON = 0.4x+0.9y
Also given that 80% of all bulbs are ON = 0.8(x+y)
0.4x+0.9y = 0.8(x+y)
on solving
y = 4x
Percent of I bulbs ON = 0.4x/(0.8(x+y))
= 0.5 * (x/(x+y))
substituting y = 4x
= 0.5 * x/x+4x = 0.5 * 0.2 = 0.1 = 10%
-
- Master | Next Rank: 500 Posts
- Posts: 137
- Joined: Fri Nov 13, 2015 11:01 am
- Thanked: 1 times
- Followed by:2 members
I think it's also possible to solve this using two unknowns.
GMATGuruNY wrote:Let total bulbs = 100.j_shreyans wrote: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%
Let x = incandescent bulbs.
Let 100-x = fluorescent bulbs.
40% of the incandescent bulbs switched on = .4x
10% of the fluorescent bulbs switched off = 90% switched on = .9(100-x).
Since .8*100 = 80 bulbs are switched on, we get:
.4x + .9(100-x) = 80.
4x + 900 - 9x = 800
-5x = -100
x = 20.
Thus, .4*20 = 8 of the incandescent bulbs are switched on.
Incandescent on/Total on = 8/80 = 10%.
The correct answer is D.
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi Amrabdelnaby,
Yes, you can solve this question using 2 variables (If you read umasarath52's post - the one above yours - you'll see how).
GMAT assassins aren't born, they'r made,
Rich
Yes, you can solve this question using 2 variables (If you read umasarath52's post - the one above yours - you'll see how).
GMAT assassins aren't born, they'r made,
Rich