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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: Difficulty level: 700, Source: GMATPrep tagged by: aishwaryav12 ##### This topic has 1 expert reply and 0 member replies ## DS: Difficulty level: 700, Source: GMATPrep Is sqrt ((x-3)^2) = 3-x? (1) x not equal to 3 (2) -x|x| > 0 Don't know how to go about this ... [B] How to arrive at the answer?[/spoiler] ### GMAT/MBA Expert GMAT Instructor Joined 04 Dec 2012 Posted: 2047 messages Followed by: 238 members Upvotes: 1443 The square root of a square is a coded way of saying absolute value. Whether the base is positive or negative, squaring will make it positive, and when given a root sign, we only take the positive root: So, we can rephrase the question this way: |x - 3| would equal (x - 3) if (x - 3) is greater than or equal to zero. It would equal 3 - x (in other words, -1(x - 3)) if x - 3 is negative. So the question becomes: x - 3 < 0 ? --> x < 3 ? (1) x not equal to 3 This does not answer our target question. x could still be greater than 3 (giving us a "no" answer to the question) or less than 3 (giving us a "yes" answer to the question). Insufficient. (2) -x|x| > 0 Since |x| is always positive (for any non-zero x), then the only way to get a positive product of -x and |x| is if -x is positive as well. If -x is positive, then x must be negative. Since our target question is "is x < 3 ?", then any negative value for x would give us a definitive "yes" answer to the question. The answer is B. _________________ 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. • 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 • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for 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 • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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