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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## A square garden is surrounded by a path of uniform width. If tagged by: swerve ##### This topic has 2 expert replies and 0 member replies ### Top Member ## A square garden is surrounded by a path of uniform width. If ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult 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? $$\text{A. } x\sqrt{2}$$ $$\text{B. } 2\sqrt{x}-\sqrt{2}$$ $$\text{C. } \frac{\sqrt{2}}{2}-\frac{x}{4}$$ $$\text{D. } x\sqrt{2}-\frac{x}{2}$$ $$\text{E. } \frac{\sqrt{2x}}{2}-\frac{\sqrt{x}}{2}$$ The OA is E Source: Magoosh ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 1893 messages Followed by: 30 members Upvotes: 470 swerve 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? $$\text{A. } x\sqrt{2}$$ $$\text{B. } 2\sqrt{x}-\sqrt{2}$$ $$\text{C. } \frac{\sqrt{2}}{2}-\frac{x}{4}$$ $$\text{D. } x\sqrt{2}-\frac{x}{2}$$ $$\text{E. } \frac{\sqrt{2x}}{2}-\frac{\sqrt{x}}{2}$$ The OA is E Source: Magoosh Say the length of the width = w Area of the path = Area of the path incl. garden - Area of the garden x = Area of the path incl. garden - x Area of the path incl. garden = 2x Area of the path incl. garden = (length of the garden + 2*width of the path)^2 Length of the garden = Square root of the area of the garden = Square root of x Length of the garden = âˆšx Thus, the area of the path incl. garden = (âˆšx + 2w)^2 => 2x = (âˆšx + 2w)^2 âˆš2.âˆšx = âˆšx + 2w 2w = âˆš2.âˆšx - âˆšx => w = âˆš2x/2 - âˆšx/2 The correct answer: E Hope this helps! -Jay _________________ Manhattan Review Locations: Manhattan Review Kukatpally | GMAT Prep Jayanagar | GRE Prep Tarnaka | Madhapur GRE Coaching | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2424 messages Followed by: 18 members Upvotes: 43 swerve 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? $$\text{A. } x\sqrt{2}$$ $$\text{B. } 2\sqrt{x}-\sqrt{2}$$ $$\text{C. } \frac{\sqrt{2}}{2}-\frac{x}{4}$$ $$\text{D. } x\sqrt{2}-\frac{x}{2}$$ $$\text{E. } \frac{\sqrt{2x}}{2}-\frac{\sqrt{x}}{2}$$ The OA is E Source: Magoosh Since the square garden has an area of x, its side length is âˆšx. 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 âˆšx + 2n. Since the total area of the path and garden is x + x = 2x, we have: (âˆšx + 2n)^2 = 2x Taking the square root of both sides, we have: âˆšx + 2n = âˆš(2x) 2n = âˆš(2x) - âˆšx n = âˆš(2x)/2 - âˆšx/2 Answer: E _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews • FREE GMAT Exam Know how you'd score today for$0

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