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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 ## The perimeter of a polygon with sides of integer... tagged by: AAPL ##### This topic has 1 expert reply and 0 member replies ### Top Member ## The perimeter of a polygon with sides of integer... The perimeter of a polygon with sides of integer length is 45. If the smallest side of the polygon is 5 and the longest side of the polygon is 10, then the number of sides could be any number from? A. 5 to 7 B. 5 to 8 C. 5 to 9 D. 6 to 8 E. 6 to 9 The OA is B. I don't have clear this PS question. I know that the perimeter is the sum of all the sides of the polygon, then $$P=45=5+10+x_3+x_4+...+x_n$$ But, I don't know how can I get the x values to determine the number of sides. I appreciate if any expert explain it for me. Thank you so much. ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Top Reply Quote: The perimeter of a polygon with sides of integer length is 45. If the smallest side of the polygon is 5 and the longest side of the polygon is 10, then the number of sides could be any number from? A. 5 to 7 B. 5 to 8 C. 5 to 9 D. 6 to 8 E. 6 to 9 The OA is B. I don't have clear this PS question. I know that the perimeter is the sum of all the sides of the polygon, then $$P=45=5+10+x_3+x_4+...+x_n$$ But, I don't know how can I get the x values to determine the number of sides. I appreciate if any expert explain it for me. Thank you so much. Hi AAPL, Let's take a look at your question. The perimeter of the polygon is 45 and 2 sides, the smallest and longest are 5 and 10. Therefore the sum of the rest of the sides will be 45 - 10 - 5 = 30 Also, length of the remaining sides will be between the smallest and the longest side, i.e. between 5 and 10 inclusive. Using the smallest length, the side lengths of the polygon could be 5 + 5 + 5 + 5 + 5 + 5 = 30 So the total sides of the polygon with all the remaining sides equal to 5 will be: 6 +2 = 8 sides Using the longest length, the side lengths of the polygon could be 10 + 10 + 10 = 30 So the total sides of the polygon with all the remaining sides equal to 10 will be: 3 + 2 = 5 sides Which shows that minimum number of sides of polygon is 5 and maximum number of sides could be 8. 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 • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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