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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 ## Inequality tagged by: ceilidh.erickson ##### This topic has 1 expert reply and 1 member reply ## Inequality If 'a' not equal to 0, is 1/a> a/(b^4+3)? 1. a^2=b^2 2. a^2=b^4 Please help. _________________ Thanks, Bharat. Legendary Member Joined 14 Aug 2012 Posted: 1556 messages Followed by: 34 members Upvotes: 448 Target GMAT Score: 750 GMAT Score: 650 pareekbharat86 wrote: If 'a' not equal to 0, is 1/a> a/(b^4+3)? 1. a^2=b^2 2. a^2=b^4 Please help. To find: 1/a > a/(b^4 + 3) Statement 1: a^2=b^2 ==> either a = b or a = -b If a = b, then 1/b > b/(b^4 + 3) b^4 + 3 > b^2 If a = -b 1/-b > -b/(b^4+3) b/(b^4 + 3) > 1/b b^2 > b^4 + 3 INSUFFICIENT Statement 2: a = b^2 or -a = b^2 if a = b^2 1/a > a/(b^4 + 3) 1/b^2 > b^2/(b^4 + 3) b^4 + 3 > b^4 3 > 0 YES if -a = b^2 -a/(b^4+3) > 1/-a b^2/(b^4+3) > 1/b^2 b^4 > b^4 + 3 0 > 3 NO Combining... a = b or a = -b a = b^2 or -a = b^2 We cannot deduce anything {E}???? _________________ R A H U L ### GMAT/MBA Expert GMAT Instructor Joined 04 Dec 2012 Posted: 2047 messages Followed by: 238 members Upvotes: 1443 Quote: If 'a' not equal to 0, is 1/a> a/(b^4+3)? 1. a^2=b^2 2. a^2=b^4 There is no obvious way to rephrase this question. We don't want to cross-multiply, since we don't know whether a or b^4 + 3 is negative. So, all we can do is consider the statements. 1) As Rahul said, we want to translate this question as a=b or a=-b. In other words, |a|=|b|. We can quickly test numbers to prove insufficiency: If a=2 and b=2, then: (1/2) > 2/(16 + 3) yes If a=-2 and b=2, then: (1/-2) > -2/(16 + 3) no Insufficient 2) If a^2=b^4, then |a|=b^2 Again, test values: If a=4 and b=2, then: 1/4 > 4/(16 + 3) yes If a=-4 and b=2, then: 1/-4 > -4/(16 + 3) no Insufficient 1&2) Together, the statements tell us something very significant. The statements both have to be true, and thus can't contradict each other. If a^2=b^2 and a^2=b^4, then a^2 has to be equal to 1 or 0. The question stem tells us that a can't be 0, so a^2 has to be 1. Thus, a=1 or a=-1, and b=1 or b=-1. Test values again: If a=1 and b=1, then: 1/1 > 1/(1 +3) yes If a=-1 and b=1, then: 1/-1 > -1/(1 + 3) no Insufficient The answer is E.[/i] _________________ Ceilidh Erickson Manhattan Prep GMAT & GRE instructor EdM in Mind, Brain, and Education Harvard Graduate School of Education Manhattan Prep instructors all have 99th+ percentile scores and expert teaching experience. Sign up for a FREE TRIAL, and learn why we have the highest ratings in the GMAT industry! Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week. • Award-winning private GMAT tutoring Register now and save up to$200

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