GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 19 Sep 2018, 19:49

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.

Close

Request Expert Reply

Confirm Cancel

The length of a rectangle is decreased by 15% and its width is increas

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49251
The length of a rectangle is decreased by 15% and its width is increas  [#permalink]

Show Tags

New post 17 Jan 2016, 10:10
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

83% (00:53) correct 18% (01:55) wrong based on 120 sessions

HideShow timer Statistics

The length of a rectangle is decreased by 15% and its width is increased by 40%. Does the area of the rectangle decrease or increase and by what percent?

A. Decreases by 19%
B. Decreases by 25%
C. Increases by 6%
D. Increases by 19%
E. Increases by 25%

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
User avatar
Joined: 19 Dec 2015
Posts: 111
Location: United States
GMAT 1: 720 Q50 V38
GPA: 3.8
WE: Information Technology (Computer Software)
The length of a rectangle is decreased by 15% and its width is increas  [#permalink]

Show Tags

New post 17 Jan 2016, 10:41
Let the length of the rectangle be 100x, and width be 100y. Area = 100x * 100y = 10000xy
Now after the change Length = 85x, and width = 140 y. Area = 11900xy
% Change = (11900xy - 10000xy)/(10000xy) = 19 % Increase. Hence D.
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12415
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: The length of a rectangle is decreased by 15% and its width is increas  [#permalink]

Show Tags

New post 18 Jan 2016, 23:35
Hi All,

This question can be solved in a variety of different ways, including various algebraic approaches and TESTing VALUES. Here's how you can use fractions to your advantage and save some time.

We're told that the length of a rectangle is decreased by 15% and its width is increased by 40%. We're asked if the area of the rectangle decreases or increases and by what percent.

The original area of the rectangle can be written as...

(L)(W) = Area

The two changes can be written as:
15% decrease = 8.5/10
40% increase = 14/10

After the changes occur, we have...

(8.5/10)(L)(14/10)(W) =
(8.5/10)(14/10)(L)(W) =
(8.5)(14)/100 x (L)(W) =
119/100 x (L)(W)

119/100 = a 19% increase

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Intern
Intern
avatar
B
Joined: 11 Dec 2016
Posts: 33
Re: The length of a rectangle is decreased by 15% and its width is increas  [#permalink]

Show Tags

New post 13 May 2017, 09:07
1
We can also solve this by using the formula

a+b+(a*b)/100
=(-15)+(40)+(-15*40)/100
=25-6
=19%
which is positive so it represents a 19% increase.
D is the answer
Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 1977
Premium Member CAT Tests
The length of a rectangle is decreased by 15% and its width is increas  [#permalink]

Show Tags

New post 13 May 2017, 12:59
1
asfandabid wrote:
We can also solve this by using the formula

a+b+(a*b)/100
=(-15)+(40)+(-15*40)/100
=25-6
=19%
which is positive so it represents a 19% increase.
D is the answer

asfandabid, this shortcut looks handy. Clearly it's a percent change formula, but its elements and operations in the numerator aren't clear to me.

(Yes, I see that you've taken Change 1 of a side, added Change 2 of another side, then added the product of the two. Why? I'm having a hard time wrapping my mind around the idea that you would account separately for each one-dimensional change, add them, then account for a two-dimensional change, and add that on. And are you assuming original values of 100 per side?)

Please explain the formula? Perhaps you could write out the elements in the numerator and explain why the operators work as they do? Thanks in advance.
_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"

Manager
Manager
User avatar
B
Joined: 02 Aug 2013
Posts: 65
Location: India
Concentration: Technology, Leadership
WE: Programming (Consulting)
GMAT ToolKit User
Re: The length of a rectangle is decreased by 15% and its width is increas  [#permalink]

Show Tags

New post 16 May 2017, 00:40
Let the original length be 20 ; and width = 10
original area = 20 * 10 = 200

New length = .85 * 20 = 17
New width = 1.40 * 10 = 14

new area = 17 * 14 = 238

% increase =\(\frac{38}{200} * 100\) = 19%

Ans: D
Senior Manager
Senior Manager
User avatar
P
Joined: 07 Jul 2012
Posts: 369
Location: India
Concentration: Finance, Accounting
GPA: 3.5
Premium Member
Re: The length of a rectangle is decreased by 15% and its width is increas  [#permalink]

Show Tags

New post 16 May 2017, 02:29
Let original length= L; original width= W
New length= 0.85L; New width= 1.4W

Original Area= LW
New Area= 0.85L*1.4W= 1.19LW

Change in Area= 1.19LW-LW= 0.19LW
Percentage increase= \(\frac{0.19LW}{LW}\)*100= 19%

Answer: D.

Kudos please if you like my explanation!
_________________

Kindly hit kudos if my post helps!

Intern
Intern
avatar
Joined: 18 Aug 2010
Posts: 1
Re: The length of a rectangle is decreased by 15% and its width is increas  [#permalink]

Show Tags

New post 16 May 2017, 03:28
Simplest Way:-
New Length : 0.85L (L= Original length)
New Width : 1.4W (L= Original width)
Therefore New Area= 0.85*1.4*L*W=1.19LW implies 19%Increase.

Sent from my HM NOTE 1S using GMAT Club Forum mobile app
Board of Directors
User avatar
P
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4020
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member
Re: The length of a rectangle is decreased by 15% and its width is increas  [#permalink]

Show Tags

New post 16 May 2017, 11:19
1
Bunuel wrote:
The length of a rectangle is decreased by 15% and its width is increased by 40%. Does the area of the rectangle decrease or increase and by what percent?

A. Decreases by 19%
B. Decreases by 25%
C. Increases by 6%
D. Increases by 19%
E. Increases by 25%


\(-15 + 40 +\frac{(-15)(40)}{100}\)

\(= 25 - 6\)

\(= 19\)

Thus, there will be an increase in area by (D) 19%
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Manager
Manager
User avatar
B
Joined: 02 Aug 2013
Posts: 65
Location: India
Concentration: Technology, Leadership
WE: Programming (Consulting)
GMAT ToolKit User
The length of a rectangle is decreased by 15% and its width is increas  [#permalink]

Show Tags

New post 16 May 2017, 20:05
Abhishek009 wrote:
Bunuel wrote:
The length of a rectangle is decreased by 15% and its width is increased by 40%. Does the area of the rectangle decrease or increase and by what percent?

A. Decreases by 19%
B. Decreases by 25%
C. Increases by 6%
D. Increases by 19%
E. Increases by 25%


\(-15 + 40 +\frac{(-15)(40)}{100}\)

\(= 25 - 6\)

\(= 19\)

Thus, there will be an increase in area by (D) 19%



Hi Abhishek,

Please explain above approach. Is this approach applicable for all % increase or % decrease problems ?

How will you identify that 19 is increase or decrease % ?

thanks
Abhijeet
Target Test Prep Representative
User avatar
G
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3518
Location: United States (CA)
Re: The length of a rectangle is decreased by 15% and its width is increas  [#permalink]

Show Tags

New post 19 May 2017, 06:19
Bunuel wrote:
The length of a rectangle is decreased by 15% and its width is increased by 40%. Does the area of the rectangle decrease or increase and by what percent?

A. Decreases by 19%
B. Decreases by 25%
C. Increases by 6%
D. Increases by 19%
E. Increases by 25%


We can let the original length of the rectangle = x and the original width of the rectangle = y. Thus, the original area is xy.

When the length decreases by 15%, the new length is 0.85x, and when the width increases by 40%, the new width is 1.4y. Thus, the new area is (0.85x)(1.4y) = 1.19xy.

We can use the percent change formula: (New Value - Old Value)/Old Value x 100%. Thus, the area changes by (1.19xy - xy)/xy = 0.19xy/xy = 0.19 = 19%. This value is positive, indicating an increase.

Answer: D
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8095
Premium Member
Re: The length of a rectangle is decreased by 15% and its width is increas  [#permalink]

Show Tags

New post 13 Jun 2018, 03:36
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: The length of a rectangle is decreased by 15% and its width is increas &nbs [#permalink] 13 Jun 2018, 03:36
Display posts from previous: Sort by

The length of a rectangle is decreased by 15% and its width is increas

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


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

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.