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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 x > 0 ? tagged by: VJesus12 ##### This topic has 2 expert replies and 0 member replies ## Is x > 0 ? ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Is x > 0 ? (1) x < x^2 (2) x < x^3 The OA is the option E. Why is not sufficient any of the statements? Could anyone explain to me how to prove this? I'd be thankful for your help. ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10109 messages Followed by: 494 members Upvotes: 2867 GMAT Score: 800 Top Reply Hi VJesus12, We're asked if X is greater than 0. This is a YES/NO question and can be approached in a couple of different ways, including by using Number Properties. 1) X < X^2 For X^2 to be greater than X, there are 2 possibilities: 1) X is ANY negative number... at which point the answer to the question is NO. 2) X is a positive number GREATER than 1... at which point the answer to the question is YES. Fact 1 is INSUFFICIENT 2) X < X^3 For X^3 to be greater than X, there are 2 possibilities: 1) X is a negative fraction... at which point the answer to the question is NO. 2) X is a positive number GREATER than 1... at which point the answer to the question is YES. Fact 2 is INSUFFICIENT Combined, we have some examples that 'fit' BOTH Facts: 1) X is a negative fraction... at which point the answer to the question is NO. 2) X is a positive number GREATER than 1... at which point the answer to the question is YES. Combined, INSUFFICIENT Final Answer:E GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12740 messages Followed by: 1247 members Upvotes: 5254 GMAT Score: 770 VJesus12 wrote: Is x > 0 ? (1) x < x² (2) x < x³ Target question: Is x > 0 ? Let's go straight to... Statements 1 and 2 combined Statement 1 tells us that x < x² Statement 2 tells us that x < x³ There are several values of x that satisfy BOTH statements. Here are two: Case a: x = 2. Notice that 2 < 2² AND 2 < 2³. In this case, the answer to the target question is YES, x IS greater than 0 Case b: x = -1/2. Notice that (-1/2) < (-1/2)² AND (-1/2) < (-1/2)³. In this case, the answer to the target question is NO, x is NOT greater than 0 Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT Answer: E Cheers, Brent _________________ Brent Hanneson – Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months! • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep 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 • Award-winning private GMAT tutoring Register now and save up to$200

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