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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 ## Is it true that x > 0? ##### This topic has 2 expert replies and 0 member replies ### Top Member ## Is it true that x > 0? ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Is it true that x > 0? (1) x^2 = 2x (2) x^3 = 3x OA C Source: GMAT Prep ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12975 messages Followed by: 1249 members Upvotes: 5254 GMAT Score: 770 Top Reply BTGmoderatorDC wrote: Is it true that x > 0? (1) xÂ² = 2x (2) xÂ³ = 3x Target question: Is it true that x > 0? Statement 1: xÂ² = 2x Rewrite as: xÂ² - 2x = 0 Factor: x(x - 2) = 0 So, EITHER x = 0 OR x = 2 Let's examine each possible case Case a: If x = 0, then the answer to the target question is NO, it is not true that x > 0 Case b: If x = 2, then the answer to the target question is YES, it is true that x > 0 Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: xÂ³ = 3x Rewrite as: xÂ³ - 3x = 0 Factor: x(xÂ² - 3) = 0 Factor again: x(x - âˆš3)(x + âˆš3) = 0 So, x = 0, OR x = âˆš3 OR x = -âˆš3 Let's examine each possible case Case a: If x = 0, then the answer to the target question is NO, it is not true that x > 0 Case b: If x = âˆš3, then the answer to the target question is YES, it is true that x > 0 Case c: If x = -âˆš3,, then the answer to the target question is NO, it is not true that x > 0 Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT Statements 1 and 2 combined Statement 1 tells us that x = 0 OR x = 2 Statement 2 tells us that x = 0, OR x = âˆš3 OR x = -âˆš3 The only x-value that satisfies BOTH statements is x = 0 So, the answer to the target question is NO, it is not true that x > 0 Since we can answer the target question with certainty, the combined statements are SUFFICIENT Answer: C Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15344 messages Followed by: 1864 members Upvotes: 13060 GMAT Score: 790 Top Reply BTGmoderatorDC wrote: Is it true that x > 0? (1) x^2 = 2x (2) x^3 = 3x Statement 1: Case 1: x=0 In this case, the answer to the question stem is NO. Case 2: xâ‰ 0, allowing us to divide both sides by x xÂ²/x = 2x/x x = 2 In this case, the answer to the question stem is YES. INSUFFICIENT. Statement 2: Case 1: x=0 In this case, the answer to the question stem is NO. Case 2: xâ‰ 0, allowing us to divide both sides by x xÂ³/x = 3x/x xÂ² = 3 x = Â±âˆš3 If x=âˆš3, the answer to the question stem is YES. INSUFFICIENT. Statements combined: Only x=0 satisfies both statements. Thus, the answer to the question stem is NO. SUFFICIENT. The correct answer is C. _________________ 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. • Award-winning private GMAT tutoring Register now and save up to$200

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