Find all School-related info fast with the new School-Specific MBA Forum

It is currently 31 Jul 2014, 20:31

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Percent increase then percent decrease results in no effect

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Intern
Intern
avatar
Joined: 06 Jul 2012
Posts: 15
Followers: 0

Kudos [?]: 1 [0], given: 1

Percent increase then percent decrease results in no effect [#permalink] New post 29 Jul 2012, 21:24
What conditions must be met for the percent increase and subsequent percent decrease to result in no change?
Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4601
Location: Pune, India
Followers: 1043

Kudos [?]: 4563 [0], given: 162

Re: Percent increase then percent decrease results in no effect [#permalink] New post 29 Jul 2012, 21:36
Expert's post
arnivorous wrote:
What conditions must be met for the percent increase and subsequent percent decrease to result in no change?


The multiplication factor of increase should be inverse of the multiplication factor of decrease.

e.g. Say you have a number 100.

You increase it by 25%. The multiplication factor is 5/4 i.e. when you multiply 100 by 5/4, you get 100*5/4 = 125. This is 25% more than 100.
Now you want to decrease it by a certain % such that you get 100 back.
Basically, 100*5/4 * x = 100
So x = 4/5 (inverse of 5/4)
Hence, you decrease by 20% (the multiplication factor of 20% is 4/5)

or
Use this formula: cumulative % change = a + b + ab/100
You want the cumulative change to be 0.

a + b + ab/100 = 0
If you know that you are increasing by 25% and want to find the % by which you should decrease to get the same number,
25 + b + 25b/100 = 0
5b/4 = -25
b = -20

So you need to decrease (hence you get the -ve sign) by 20%.

Check out these posts for details of multiplication factors and the formula:
http://www.veritasprep.com/blog/2011/02 ... rcentages/
http://www.veritasprep.com/blog/2011/02 ... e-changes/
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Expert Post
Manhattan GMAT Instructor
User avatar
Joined: 22 Mar 2011
Posts: 341
Followers: 119

Kudos [?]: 203 [0], given: 10

Re: Percent increase then percent decrease results in no effect [#permalink] New post 29 Jul 2012, 21:43
Expert's post
If we want to make two changes and end up back where we started, the two numbers we need to multiply need to be one another's inverses. For instance, 100 * 3/2 * 2/3 = 100.

This is a little harder to see with percents, because we might write the above like this: 100 increased by 50% then decreased by 33 1/3% equals 100. That's why it can be easier to figure out what number or fraction we're actually multiplying by (e.g. 50% increase = multiply by 1.5; 33 1/3% decrease = multiply by .6666). We can use these formulas:

Increase by x%: Multiply by (100+x)/100

Decrease by x%: Multiply by (100-x)/100

After that, we can often convert to fractions or decimals and find an inverse from there.

Here's an example:

x increased by 60% then decreased by y% equals x. What is y?

x increased by 60% = x * 160/100 = x * 16/10 = x * 8/5

So what do we need to do to get back to x? Multiply by the inverse of 8/5 . . . 5/8.

x * 8/5 * 5/8 = x

So we know that reducing by y is the same as multiplying by 5/8.

5/8 = .625 = 62.5% If we multiplied by 62.5%, y must be the remaining 37.5%.

We can translate the original sentence and plug this in, just to be see how it works:

x increased by 60% then decreased by y% equals x.
x * 160/100 * (100-y)/100 = x
x * 160/100 * (100-37.5)/100 = x
x * 160/100 * 62.5/100 = x
x * 8/5 * 5/8 = x
x = x

It works!
_________________


Dmitry Farber | Manhattan GMAT Instructor | New York


Manhattan GMAT Discount | Manhattan GMAT Course Reviews | View Instructor Profile |
Manhattan GMAT Reviews

Re: Percent increase then percent decrease results in no effect   [#permalink] 29 Jul 2012, 21:43
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic x percent of y percent of z is decreased by y percent. What RyanP 3 13 Apr 2012, 14:56
1 Experts publish their posts in the topic x percent of y percent of z is decreased by y percent. What siddhans 6 23 Sep 2011, 00:05
Percent increase olivite 4 11 May 2011, 16:01
Percent Increase/decrease help!!! anuu 1 04 May 2011, 21:37
Experts publish their posts in the topic If the value of a piece of property decreases by 10 percent johngrg 6 08 Aug 2007, 06:22
Display posts from previous: Sort by

Percent increase then percent decrease results in no effect

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.