BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

percentages !

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Community Manager
Posts: 1060
Joined: Fri May 13, 2011 6:46 am
Location: Utrecht, The Netherlands
Thanked: 318 times
Followed by:52 members

percentages !

by neelgandham » Fri Dec 02, 2011 4:00 am
Eighty percent of the lights at Hotel California are on at 8 p.m. a certain evening. However, forty percent of the lights that are supposed to be off are actually on and ten percent of the lights that are supposed to be on are actually off. What percent of the lights that are on are supposed to be off?
A)22(2/9)%
B)16(2/3)%
C)11(1/9)%
D)10%
E)5%

Source: A Friend
OA : After discussion
Anil Gandham
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pm
Location: Milpitas, CA
Thanked: 1854 times
Followed by:523 members
GMAT Score:770

by Anurag@Gurome » Fri Dec 02, 2011 4:02 am
neelgandham wrote:Eighty percent of the lights at Hotel California are on at 8 p.m. a certain evening. However, forty percent of the lights that are supposed to be off are actually on and ten percent of the lights that are supposed to be on are actually off. What percent of the lights that are on are supposed to be off?
A)22(2/9)%
B)16(2/3)%
C)11(1/9)%
D)10%
E)5%

Source: A Friend
OA : After discussion
Say, total number of lights in the hotel = 100
Also assume the number of lights that are supposed to be on = n.
Hence, number of lights that are supposed to be off = (100 - n)

Number of lights that are on = 80% of 100 = 80
Number of lights on that are supposed to be off = 40% of (100 - n) = 0.4(100 - n)
Number of lights off that are supposed to be on = 10% of n = 0.1n

Hence, total number of lights that are on = n - 0.1n + 0.4(100 - n) = 40 + 0.5n

Hence, (40 + 0.5n) = 80 => n = 80

Now, number of lights on that are supposed to be off = 0.4(100 - n) = 0.4(100 - 80) = 0.4*20 = 8

Hence, required percentage = (8/80)*100 = 10

The correct answer is D.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top
User avatar
Legendary Member
Posts: 588
Joined: Sun Oct 16, 2011 9:42 am
Location: New Delhi, India
Thanked: 130 times
Followed by:9 members
GMAT Score:720

by rijul007 » Fri Dec 02, 2011 4:14 am
Total no of lights = 100
No of lights on = 80
No of lights supposed to be off = x
No of lights that are supposed to be off but are on = 4x/10

80 = 4x/10 + 9(100-x)/10
800 = 900-5x
5x = 100
x = 20
No of lights that are supposed to be off but are on = 4*20/10 = 8
No of the lights that are on are supposed to be off = 8/80 *100 = 10

Option D
Top
User avatar
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

by GMATGuruNY » Fri Dec 02, 2011 6:42 am
neelgandham wrote:Eighty percent of the lights at Hotel California are on at 8 p.m. a certain evening. However, forty percent of the lights that are supposed to be off are actually on and ten percent of the lights that are supposed to be on are actually off. What percent of the lights that are on are supposed to be off?
A)22(2/9)%
B)16(2/3)%
C)11(1/9)%
D)10%
E)5%

Source: A Friend
OA : After discussion
This is a weighted average problem.

Let X = the lights that are supposed to be OFF.
Let Y = the lights that are supposed to be ON.
The total number of lights = X+Y = 100.

Percent of X that are actually on = 40.
Percent of Y that are actually on = 90. (Since 10% are off.)
Percent of X+Y that are actually on = 80.

X and Y are being combined to form a MIXTURE of X+Y.
To determine the ratio of X to Y in the mixture, we can use alligation, which dictates the following:

The proportion needed of each ingredient in the mixture is equal to the distance between the OTHER TWO PERCENTAGES.

Proportion needed of X = |90-80| = 10.
Proportion needed of Y = |40-80| = 40.
X:Y = 10:40 = 1:4.
Given 100 lights, since X:Y = 1:4 = 20:80, X=20 and Y=80.

Thus, the number of lights that are supposed to be OFF = 20.
Of these 20 lights, the number that are actually ON = .4(20) = 8.
Thus, (number of lights that are supposed to be OFF but are actually 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
Top
Post new topic Post Reply
• Page 1 of 1