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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 ## what is the area of the un-grazed, un-shaded region? tagged by: AAPL ##### This topic has 1 expert reply and 0 member replies ### Top Member ## what is the area of the un-grazed, un-shaded region? Zoom here, https://postimg.cc/image/3sluthknf/ Two goats are each tied at corners A and B of a fenced rectangular field of area 50. The goat's tethers allow them to graze within circular regions of radius 5, centered at A and B, respectively. The two grazing areas meet at point G, but do not overlap. If the goats graze the entire shaded area within their respective reach by the end of the day, what is the area of the un-grazed, un-shaded regiion? $$A.\ 50-25\pi$$ $$B.\ 25\left(2-\frac{\pi}{2}\right)$$ $$C.\ 25\left(2-\frac{\pi}{4}\right)$$ $$D.\ 12.5\pi$$ $$E.\ 25\pi$$ The OA is B. I know that I just need determine the area of the two semicircular regions and it will be $$2\cdot\left(\frac{1}{4}\pi\cdot r^2\right)=\frac{1}{2}\pi\cdot r^2=\frac{25}{2}\pi$$ Then the area of the un-shaded region will be, $$50-\frac{25}{2}\pi\ =\ 25\left(2-\frac{\pi}{2}\right)$$ But, is there a strategic approach to this PS question? Can any experts help me, please? Thanks! ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Quote: Two goats are each tied at corners A and B of a fenced rectangular field of area 50. The goat's tethers allow them to graze within circular regions of radius 5, centered at A and B, respectively. The two grazing areas meet at point G, but do not overlap. If the goats graze the entire shaded area within their respective reach by the end of the day, what is the area of the un-grazed, un-shaded regiion? $$A.\ 50-25\pi$$ $$B.\ 25\left(2-\frac{\pi}{2}\right)$$ $$C.\ 25\left(2-\frac{\pi}{4}\right)$$ $$D.\ 12.5\pi$$ $$E.\ 25\pi$$ The OA is B. Hi AAPL, Let's take a look at your question. In the rectangle ABCD, Let BC =AD = x Then BG = AG = x because these are the radii of the circular area. Hence we can write the dimensions of the rectangular area as: Width = BC = x Length = AB = x + x = 2x The area equation can be written as: $$Area\ =\ Length\ \times\ Width$$ $$Area\ =\ \left(2x\right)\times\ \left(x\right)$$ $$50\ =\ 2x^2$$ $$x^2=25$$ $$x=5$$ Therefore, $$Width=5$$ $$Length=10$$ Now we will use the width of the rectangle as the radius of the circular area to find the area of shaded region. We can see that the shaded area consists of two quarter circle which makes a total of half the circle. So we can find its are as half the area of a circle. $$\text{Area of shaded region}=\ \frac{1}{2}\pi r^2$$ $$\text{Area of shaded region}=\ \frac{1}{2}\pi\left(5\right)^2$$ $$\text{Area of shaded region}=\ \frac{25}{2}\pi$$ Now we can find the area of the region that is not shaded by subtracting the above area from the total area of the rectangle. $$\text{Area of un-shaded region}=50-\ \frac{25}{2}\pi$$ $$\text{Area of unshaded region}=25\left(2-\ \frac{\pi}{2}\right)$$ Therefore, Option B is correct. Hope it helps. I am available if you'd like any follow up. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now. • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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