It is currently 11 Dec 2017, 02:40

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

A square garden is surrounded by a path of uniform width. If the path

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42536

Kudos [?]: 135189 [0], given: 12671

A square garden is surrounded by a path of uniform width. If the path [#permalink]

Show Tags

New post 29 Aug 2017, 02:07
Expert's post
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

43% (00:53) correct 57% (02:01) wrong based on 36 sessions

HideShow timer Statistics

A square garden is surrounded by a path of uniform width. If the path and the garden both have an area of x, then what is the width of the path in terms of x?


A. \(x \sqrt{2}\)

B. \(2 \sqrt{x} - \sqrt{2}\)

C. \(\frac{\sqrt{2}}{2} - \frac{x}{4}\)

D. \(x \sqrt{2} - \frac{x}{2}\)

E. \(\frac{\sqrt{2x}}{2} - \frac{\sqrt{x}}{2}\)
[Reveal] Spoiler: OA

_________________

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

Kudos [?]: 135189 [0], given: 12671

Director
Director
User avatar
G
Joined: 18 Aug 2016
Posts: 596

Kudos [?]: 177 [0], given: 136

GMAT 1: 630 Q47 V29
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
A square garden is surrounded by a path of uniform width. If the path [#permalink]

Show Tags

New post 29 Aug 2017, 02:38
Bunuel wrote:
A square garden is surrounded by a path of uniform width. If the path and the garden both have an area of x, then what is the width of the path in terms of x?


A. \(x \sqrt{2}\)

B. \(2 \sqrt{x} - \sqrt{2}\)

C. \(\frac{\sqrt{2}}{2} - \frac{x}{4}\)

D. \(x \sqrt{2} - \frac{x}{2}\)

E. \(\frac{\sqrt{2x}}{2} - \frac{\sqrt{x}}{2}\)


consider x as 4 then side of square will be 2
now side of square +path = \(2\sqrt{2}\)
width = \((2\sqrt{2} - 2)/2\) = \(\sqrt{2}-1\)
substituting 4 in place of x in options
E
_________________

We must try to achieve the best within us


Thanks
Luckisnoexcuse

Kudos [?]: 177 [0], given: 136

Intern
Intern
avatar
B
Joined: 15 Aug 2013
Posts: 26

Kudos [?]: [0], given: 167

Premium Member CAT Tests
Re: A square garden is surrounded by a path of uniform width. If the path [#permalink]

Show Tags

New post 30 Aug 2017, 11:01
Luckisnoexcuse wrote:
Bunuel wrote:
A square garden is surrounded by a path of uniform width. If the path and the garden both have an area of x, then what is the width of the path in terms of x?


A. \(x \sqrt{2}\)

B. \(2 \sqrt{x} - \sqrt{2}\)

C. \(\frac{\sqrt{2}}{2} - \frac{x}{4}\)

D. \(x \sqrt{2} - \frac{x}{2}\)

E. \(\frac{\sqrt{2x}}{2} - \frac{\sqrt{x}}{2}\)


consider x as 4 then side of square will be 2
now side of square +path = \(2\sqrt{2}\)
width = \((2\sqrt{2} - 2)/2\) = \(\sqrt{2}-1\)
substituting 4 in place of x in options
E


How now side of square +path = \(2\sqrt{2}\)???

Thanks

Kudos [?]: [0], given: 167

Intern
Intern
avatar
B
Joined: 11 Aug 2017
Posts: 9

Kudos [?]: 1 [0], given: 13

Re: A square garden is surrounded by a path of uniform width. If the path [#permalink]

Show Tags

New post 01 Sep 2017, 10:01
Bunuel wrote:
A square garden is surrounded by a path of uniform width. If the path and the garden both have an area of x, then what is the width of the path in terms of x?


A. \(x \sqrt{2}\)

B. \(2 \sqrt{x} - \sqrt{2}\)

C. \(\frac{\sqrt{2}}{2} - \frac{x}{4}\)

D. \(x \sqrt{2} - \frac{x}{2}\)

E. \(\frac{\sqrt{2x}}{2} - \frac{\sqrt{x}}{2}\)


E is the answer
the area of the garden is 2x
side of the garden is square root of 2x
the shaded area is a trapezoid, its area equal 1/4 the area of the path, and its height is the width of the path.
you can see in the picture attached
Attachments

FullSizeRender 7.jpg
FullSizeRender 7.jpg [ 1.09 MiB | Viewed 648 times ]

Kudos [?]: 1 [0], given: 13

Expert Post
Target Test Prep Representative
User avatar
S
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1771

Kudos [?]: 971 [0], given: 5

Re: A square garden is surrounded by a path of uniform width. If the path [#permalink]

Show Tags

New post 01 Sep 2017, 12:09
Bunuel wrote:
A square garden is surrounded by a path of uniform width. If the path and the garden both have an area of x, then what is the width of the path in terms of x?


A. \(x \sqrt{2}\)

B. \(2 \sqrt{x} - \sqrt{2}\)

C. \(\frac{\sqrt{2}}{2} - \frac{x}{4}\)

D. \(x \sqrt{2} - \frac{x}{2}\)

E. \(\frac{\sqrt{2x}}{2} - \frac{\sqrt{x}}{2}\)
\

Since the square garden has an area of x, its side length is √x. Since the square garden is surrounded by a path of uniform width, the shape of the path and garden combined is also a square. We can let the width of the path = n, and thus the side length of the square that is the path and garden combined is √x + 2n. Since the total area of the path and garden is x + x = 2x, we have:

(√x + 2n)^2 = 2x

Taking the square root of both sides, we have:

√x + 2n = √(2x)

2n = √(2x) - √x

n = √(2x)/2 - √x/2

Answer: E
_________________

Jeffery Miller
Head of GMAT Instruction

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

Kudos [?]: 971 [0], given: 5

Re: A square garden is surrounded by a path of uniform width. If the path   [#permalink] 01 Sep 2017, 12:09
Display posts from previous: Sort by

A square garden is surrounded by a path of uniform width. If the path

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


GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.