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

It is currently 23 Oct 2014, 02:36

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

If the side length of a square is reduced by p percent, what

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
User avatar
Joined: 18 Jul 2013
Posts: 63
Location: Italy
GMAT 1: 600 Q42 V31
Followers: 0

Kudos [?]: 18 [0], given: 111

CAT Tests
If the side length of a square is reduced by p percent, what [#permalink] New post 03 Aug 2014, 12:44
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

59% (02:27) correct 41% (00:46) wrong based on 54 sessions
If the side length of a square is reduced by p percent, what is the resulting percent reduction in the area of the square?

(A) \frac{p^2}{100}%
(B) [1-\frac{p^2}{100}]^2%
(C) [2p-\frac{p^2}{100}]%
(D) \frac{(100-p)^2}{100} %
(E) \frac{p^2-2p}{100}%
[Reveal] Spoiler: OA
1 KUDOS received
Manager
Manager
User avatar
Joined: 22 Feb 2009
Posts: 229
Followers: 5

Kudos [?]: 46 [1] , given: 138

GMAT ToolKit User CAT Tests
Re: If the side length of a square is reduced by p percent, what [#permalink] New post 03 Aug 2014, 13:48
1
This post received
KUDOS
oss198 wrote:
If the side length of a square is reduced by p percent, what is the resulting percent reduction in the area of the square?

(A) \frac{p^2}{100}%
(B) [1-\frac{p^2}{100}]^2%
(C) [2p-\frac{p^2}{100}]%
(D) \frac{(100-p)^2}{100} %
(E) \frac{p^2-2p}{100}%



I set the side length of a square is 1 ( just to simplify the calculation). Set x = p/100 ( since p is in percent, for instance, p = 50% , x = 0.5) Area = 1^2 = 1

New side length = 1*( 1-x) = 1-x , Area after the reduction = (1-x)^2

the resulting percent reduction = (1- (1-x)^2)/1 *100% = [1- ( 1- 2x+ x^2)] * 100% =( 2x - x^2 ) *100%

replace p for x: [2p-\frac{p^2}{100}]%

C is the answer
_________________

.........................................................................
+1 Kudos please, if you like my post

Manager
Manager
User avatar
Joined: 21 Jul 2014
Posts: 70
Followers: 2

Kudos [?]: 42 [0], given: 6

GMAT ToolKit User
Re: If the side length of a square is reduced by p percent, what [#permalink] New post 03 Aug 2014, 14:10
oss198 wrote:
If the side length of a square is reduced by p percent, what is the resulting percent reduction in the area of the square?

(A) \frac{p^2}{100}%
(B) [1-\frac{p^2}{100}]^2%
(C) [2p-\frac{p^2}{100}]%
(D) \frac{(100-p)^2}{100} %
(E) \frac{p^2-2p}{100}%


Two ways to solve this problem. My preferred option here is to determine the pattern (I always like to do that over memorizing complex formulas or rules).

I drew 3 squares with sides of 10, 9 and 8. The areas are 100, 81, 64.

Based on that, I was able to easily figure out the answer choice C fits that mold just by plugging in. It all took less than 90 seconds.

The second way to do this is algebraically.

Side of a square = s^2.
Side reduced by p% = s(1-(p/100))
Area after side reduced by p% = (s(1-(p/100)))^2
Difference = ((s^2) - (s(1-(p/100)))^2)/(s^2)

Simplify (and it's not easy to simplify this thing!), and you end up with answer choice C.
_________________

Lighthouse Prep

Learn more about Polaris, (FREE Official Guide companion app) and free 20-Minute GMAT Drills at www.lighthouseprep.us, Facebook, Google+, and Twitter.

VP
VP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1086
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 6

Kudos [?]: 304 [0], given: 170

Re: If the side length of a square is reduced by p percent, what [#permalink] New post 04 Aug 2014, 00:05
Lets say side = x;

Original Area = x^2 ........ (1)

Reduction = p% = \frac{xp}{100}

New side dimension = x - \frac{xp}{100}

New Area = x^2(1-\frac{p}{100})^2

= x^2 (1 - \frac{2p}{100} + \frac{p^2}{100^2}).............. (2)

Reduction = (1) - (2)

x^2 (1 - 1 + \frac{2p}{100} - \frac{p^2}{100^2})

Percentage reduction

= \frac{x^2 (1 - 1 + \frac{2p}{100} - \frac{p^2}{100^2})}{x^2} * 100

= 2p - \frac{p^2}{100}

Answer = C
_________________

Kindly press "+1 Kudos" to appreciate :)

Manager
Manager
User avatar
Joined: 10 Mar 2013
Posts: 212
Followers: 0

Kudos [?]: 15 [0], given: 1909

Re: If the side length of a square is reduced by p percent, what [#permalink] New post 10 Aug 2014, 11:25
The most effective way to solve this problem is to use smart numbers.
Ex: s=10, p=50
A = 100
A_reduced = 25
% reduction = (100-25)/100*100% = 75%
Only C gives the correct answer of 75.
Re: If the side length of a square is reduced by p percent, what   [#permalink] 10 Aug 2014, 11:25
    Similar topics Author Replies Last post
Similar
Topics:
Given that the length of the side of a square is L and that sdrandom1 2 14 Jul 2009, 12:11
Is the quadrilateral a square? 1) The lengths of 4 sides are apollo168 3 19 Aug 2006, 02:14
Suppose the number of squares with sides of length 4 units kevincan 15 03 Aug 2006, 01:24
The side length of a square is a decimal, the nearest getzgetzu 4 06 May 2006, 04:15
Is the quadrilateral a square? 1) The lengths of 4 sides are pb_india 8 25 Feb 2005, 06:30
Display posts from previous: Sort by

If the side length of a square is reduced by p percent, what

  Question banks Downloads My Bookmarks Reviews Important topics  


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®.