NEW HERE? LEARN MORE
closeclose
Last visit was: 23 Apr 2024, 19:20 It is currently 23 Apr 2024, 19:20
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

The price of a car was m dollars. It then depreciated by x%. Later, it

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92883
Own Kudos [?]: 618607 [3]
Given Kudos: 81563
Send PM
CAT Tests Forum Quiz Mode
The price of a car was m dollars. It then depreciated by x%. Later, it [#permalink] New post   10 Apr 2019, 23:42
3
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

73% (02:56) correct 27% (03:26) wrong based on 75 sessions
Hide Show timer Statistics
The price of a car was m dollars. It then depreciated by x%. Later, it appreciated by y% to n dollars. If there are no other changes in the price and if \(y = \frac{x}{1 - \frac{x}{100}}\), then which one of the following must n equal?

(A) 3m/4
(B) m
(C) 4m/3
(D) 3m/2
(E) 2m
ShowHide Answer
Official Answer
B
User avatar
B
Dare Devil
Manager
Manager
Joined: 01 May 2017
Posts: 59
Own Kudos [?]: 21 [1]
Given Kudos: 12
Location: India
Send PM
Re: The price of a car was m dollars. It then depreciated by x%. Later, it [#permalink] New post   11 Apr 2019, 01:38
1
Kudos
The price of a car was m dollars. It then depreciated by x%. Later, it appreciated by y% to n dollars. If there are no other changes in the price and if \(y=x/(1−x/100)\), then which one of the following must n equal?

(A) 3m/4
(B) m
(C) 4m/3
(D) 3m/2
(E) 2m

depreciated by x% implies, \(m*(1-x/100)\)
Appreciated by y% and final value id n
\(m*(1-x/100)*(1+y/100)\) = n
\(y = x/(1-x/100)\)

\(m*(1-x/100)(100+(x/(1-x/100))\) = n
m = n

Option B is correct
avatar
B
tinklepoo
Intern
Intern
Joined: 15 Aug 2018
Posts: 11
Own Kudos [?]: 9 [1]
Given Kudos: 59
Concentration: Organizational Behavior, Strategy
WE:Sales (Computer Software)
Send PM
The price of a car was m dollars. It then depreciated by x%. Later, it [#permalink] New post   13 Apr 2019, 10:16
1
Kudos
Bunuel wrote:
The price of a car was m dollars. It then depreciated by x%. Later, it appreciated by y% to n dollars. If there are no other changes in the price and if \(y = \frac{x}{1 - \frac{x}{100}}\), then which one of the following must n equal?

(A) 3m/4
(B) m
(C) 4m/3
(D) 3m/2
(E) 2m


Here's my approach :|

Setting up the problem algebraically:
\(m * ( 1- \frac{x}{100})*( 1+ \frac{y}{100}) = n\)

We know:
\(y= \frac {x}{1- \frac {x}{100}}\)

So we can substitute for \(y\):
\(m * ( 1- \frac{x}{100})*( 1+ \frac{\frac {x}{1- \frac {x}{100}}}{100}) = n\)

\(m * ( 1- \frac{x}{100})+ ( 1- \frac{x}{100})(\frac {x}{1- \frac {x}{100}}*\frac {1}{100}) = n\)

\(m * ( 1- \frac{x}{100})+ (x*\frac {1}{100}) = n\)

\(m * 1- \frac{x}{100}+ \frac {x}{100} = n\)

Some maths later:

\(m = n\)
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18753
Own Kudos [?]: 22041 [0]
Given Kudos: 283
Location: United States (CA)
Send PM
Re: The price of a car was m dollars. It then depreciated by x%. Later, it [#permalink] New post   13 Apr 2019, 19:11
Expert Reply
Bunuel wrote:
The price of a car was m dollars. It then depreciated by x%. Later, it appreciated by y% to n dollars. If there are no other changes in the price and if \(y = \frac{x}{1 - \frac{x}{100}}\), then which one of the following must n equal?

(A) 3m/4
(B) m
(C) 4m/3
(D) 3m/2
(E) 2m


Let’s simplify y first: Multiply x/(1 - x/100) by 100/100, and we have: y = 100x/(100 - x).

We can create the equation:

m * (1 - x/100) * ( 1 + y/100) = n

m * (100 - x)/100 * (1 + [100x/(100 - x)]/100) = n

m * (100 - x)/100 * (1 + x/(100 - x)) = n

m * (100 - x)/100 * (100 - x + x)/(100 - x) = n

m * (100 - x)/100 * 100/(100 - x) = n

m = n

Answer: B
GMAT Club Bot
gmatclubot
Re: The price of a car was m dollars. It then depreciated by x%. Later, it [#permalink]
13 Apr 2019, 19:11
Moderators:
Bunuel
Math Expert
92883 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions