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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 ## Challenge question: Is |1 - 4k| < k? tagged by: Brent@GMATPrepNow ##### This topic has 1 expert reply and 0 member replies ### GMAT/MBA Expert ## Challenge question: Is |1 - 4k| < k? ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Is |1 - 4k| < k? (1) k > 4xÂ³ (2) k < 2x - xÂ² - 2 Answer: B Difficulty level: 700+ Source: www.gmatprepnow.com _________________ Brent Hanneson â€“ 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 GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12827 messages Followed by: 1247 members Upvotes: 5254 GMAT Score: 770 Brent@GMATPrepNow wrote: Is |1 - 4k| < k? (1) k > 4xÂ³ (2) k < 2x - xÂ² - 2 Target question: Is |1 - 4k| < k? Statement 1: k > 4xÂ³ This pretty much tells is that k can have ANY value. For example, notice that, if x = -100, then 4xÂ³ = -4,000,000 So, for this value of x, k can be any number greater than -4,000,000 Let's TEST some values. There are several values of k that satisfy statement 1. Here are two: Case a: k = 0. Here, |1 - 4k| = |1 - 4(0)| = |1| = 1. In this case, the answer to the target question is NO, it is NOT the case that |1 - 4k| < k Case b: k = 0.25. Here, |1 - 4k| = |1 - 4(0.25)| = |0| = 0. In this case, the answer to the target question is YES, it IS the case that |1 - 4k| < k Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: k < 2x - xÂ² - 2 Rewrite as: k < -xÂ² + 2x - 1 - 1 Rewrite as: k < -(xÂ² - 2x + 1) - 1 Factor to get: k < -(x - 1)Â² - 1 Notice that (x - 1)Â² is always greater than or equal to zero So, -(x - 1)Â² is always LESS THAN or equal to zero So -(x - 1)Â² - 1 must be NEGATIVE So, statement 2 essentially tells us that k < some NEGATIVE number This means k must be NEGATIVE Since |1 - 4k| is always greater than or equal to zero, the answer to the target question is NO, it is NOT the case that |1 - 4k| < k Since we can answer the target question with certainty, statement 2 is SUFFICIENT Answer: B Cheers, Brent _________________ Brent Hanneson â€“ 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 GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! • 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 • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT 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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