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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 ## If x is positive, which of the following tagged by: VJesus12 ##### This topic has 1 expert reply and 0 member replies ### Top Member ## If x is positive, which of the following If x is positive, which of the following could be correct ordering of $$\frac{1}{x},\ 2x\ ,\ \ \ \ and\ \ x^2\ ?$$ $$(I)\ \ \ \ x^2<2x<\frac{1}{x}$$ $$(II)\ \ \ x^2<\frac{1}{x}<2x$$ (III) 2x (A) none (B) I only (C) III only (D) I and II (E) I, II and III The OA is the option D. How can I know the correct answer? Experts, I need your help here. ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Hello Vjesus12. First of all, I want to comment that the third option is not displayed. The third option is: $$(III)\ \ \ 2x Let's try with x=1/2. Then$$\frac{1}{x}=\frac{1}{\frac{1}{2}}=2\ \ \ \ \ \ \ \ \ 2x=2\cdot\frac{1}{2}=1\ \ \ \ \ \ \ \ \ \ x^2=\left(\frac{1}{2}\right)^2=\frac{1}{4}.$$Therefore, the option (I) is possible. If x=8/9 then$$\frac{1}{x}=\frac{1}{\frac{8}{9}}=\frac{9}{8}=1.125\ \ \ \ \ \ \ \ \ 2x=2\cdot\frac{8}{9}=\frac{16}{9}=1.777\ \ \ \ \ \ \ \ \ \ x^2=\left(\frac{8}{9}\right)^2=\frac{64}{81}=0.79.$$Therefore, the option can be possible too. When x is between 1 and 2, the order is 1/x < x^2 < 2x and when x is greater than 2, the order is 1/x < 2x < x^2, but these two options are no in the list. So, the option (III) can not be possible. So, the correct answer is D=(I) and (II). I hope this explanation may help you. Feel free to ask me again if you have any doubt. Regards. _________________ 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. • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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