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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 ## DS arithmetic ##### This topic has 2 expert replies and 0 member replies ## DS arithmetic ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult If a>b>0, is b<2? 1) 1/a > 1/2 2) 1/a + 1/b = 1 OA:D ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15362 messages Followed by: 1866 members Upvotes: 13060 GMAT Score: 790 kyuhunl wrote: If a>b>0, is b<2? 1) 1/a > 1/2 2) 1/a + 1/b = 1 Statement 1: The inequality implies that a is POSITIVE, allowing us to cross-multiply: 1*2 > a*1 2 > a Since 2>a and a>b>0, we get: 2>a>b>0 Thus, b<2. SUFFICIENT. Statement 2: If b=2, we get: 1/a + 1/2 = 1 1/a = 1/2 a=2 Not possible, since the prompt requires that a>b. If b=3, we get: 1/a + 1/3 = 1 1/a = 2/3 3 = 2a 3/2 = a Not possible, since the prompt requires that a>b. The cases above illustrate that bâ‰¥2 is not viable. Thus, b<2. SUFFICIENT. The correct answer is D. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 kyuhunl wrote: If a>b>0, is b<2? 1) 1/a > 1/2 2) 1/a + 1/b = 1 $$a > b > 0\,\,\,\,\,\mathop \Rightarrow \limits^{:\,\,ab\,\, > \,\,0} \,\,\,\,\,\frac{1}{b} > \frac{1}{a}\,\,\,\,\left( * \right)$$ $$b\,\,\mathop < \limits^? \,\,2$$ $$\left( 1 \right)\,\,\,\frac{1}{a} > \frac{1}{2}\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,\frac{1}{b} > \frac{1}{2}\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( {**} \right)} \,\,\,\,b < 2\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{SUFF}}.$$ $$\left( {**} \right)\,\,\,\,\,\frac{1}{b} > \frac{1}{2}\,\,\,\,\mathop \Rightarrow \limits^{ \cdot \,\,2b\,\, > \,\,0} \,\,\,\,\,2 > b$$ $$\left( 2 \right)\,\,\,1 = \frac{1}{a} + \frac{1}{b}\,\,\mathop < \limits^{\left( * \right)} \,\,\,\frac{2}{b}\,\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( {***} \right)} \,\,\,\,\,\,b < 2\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{SUFF}}.$$ $$\left( {***} \right)\,\,1 < \frac{2}{b}\,\,\,\,\mathop \Rightarrow \limits^{ \cdot \,\,b\,\, > \,\,0} \,\,\,\,\,b < 2$$ We follow the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br • FREE GMAT Exam Know how you'd score today for$0

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