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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 ## (x - 1)^2 = 400 -> ?? Positive square root quesiton ##### This topic has 4 expert replies and 0 member replies ## (x - 1)^2 = 400 -> ?? Positive square root quesiton If (x - 1)^2 = 400, which of the following could be the value of x-5? A. 15 B. 14 C. -24 D. -25 E. -26 The answer is C, -24. I can do this simply by taking the square root of each side and obtaining: x - 1 = +/- 20 x - 1 = 20 OR x - 1 = -20 Therefore, x=21, or x=-19 Then, (-19 - 5) = choice C, -24 However, I was under the impression that positive or even square roots on the GMAT are ALWAYS positive. So I got this one wrong b/c I took the square root of each side and obtained only one solution: (x - 1) = +20, therefore x = 21 Can someone explain to me why this OG problem is using +/- for an positive & even square root?? Thank you! ### GMAT/MBA Expert GMAT Instructor Joined 11 Apr 2010 Posted: 1179 messages Followed by: 88 members Upvotes: 447 Solution If the question had been (x-1) = (400)^(1/2) then we would have taken just the positive square root of 400 that is 20 but since the question is (x-1)^2 = 400, we have to take both positive and negative roots. _________________ Rahul Lakhani Quant Expert Gurome, Inc. https://www.GuroMe.com On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits 1-800-566-4043 (USA) +91-99201 32411 (India) ### GMAT/MBA Expert GMAT Instructor Joined 09 Apr 2015 Posted: 1461 messages Followed by: 18 members Upvotes: 39 MFaulkner wrote: If (x - 1)^2 = 400, which of the following could be the value of x-5? A. 15 B. 14 C. -24 D. -25 E. -26 Taking the square root of both sides, we have: (x - 1)^2 = 400 √(x - 1)^2 = √400 This gives us: |x - 1| = 20 This absolute value equation requires that we use two cases to determine all possible values of x. Case 1. When (x-1) is positive: x - 1 = 20 x = 21 Case 2. When (x-1) is negative: -(x - 1) = 20 -x + 1 = 20 -x =19 x = -19 Thus, (x - 5) can equal either 21 - 5 = 16 or -19 - 5 = -24. Answer: C ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10112 messages Followed by: 494 members Upvotes: 2867 GMAT Score: 800 Hi All, GMAT writers often provide little 'hints' in the wording of the question that can help you to avoid some of the work. Here, notice the phrase "...which of the following COULD be the value...." That's an interesting way to phrase a question - it's NOT asking "...what IS the value...." - it's asking "what COULD be the value...." This implies that there's MORE than 1 answer AND that the 'obvious' answer is not the one that's going to be listed. With (X-1)^2 = 400.... I know there are two solutions (because of the 'squared sign')... (X-1) COULD = 20 or -20 From the wording of the prompt though, it's likely that the "-20 option" is the one that we supposed to be going after, since that's the less obvious solution. X-1 = -20 X = -19 We're asked for a possible value of X-5, so in this case (X-5) = -24. Obviously, there's nothing wrong with being thorough and finding BOTH answers, but the question didn't ASK for that, so you have to be mindful about how much extra work you might be doing (and how much extra time you might be spending) on a given question, especially if you have a pacing problem. Final Answer: C GMAT assassins aren't born, they're made, Rich ### GMAT/MBA Expert GMAT Instructor Joined 04 Dec 2012 Posted: 2033 messages Followed by: 238 members Upvotes: 1443 MFaulkner wrote: However, I was under the impression that positive or even square roots on the GMAT are ALWAYS positive. So I got this one wrong b/c I took the square root of each side and obtained only one solution: (x - 1) = +20, therefore x = 21 Can someone explain to me why this OG problem is using +/- for an positive & even square root?? To answer your actual question here: When the GMAT given you a root *symbol*, as in √16, this represents just a positive number. This is understood to only have one value so that a question such as the following can have a single answer: https://www.beatthegmat.com/sqrt-80-t290557.html If you're given that x^2 = 16, then you perform the operation of square rooting both sides; this is when you get a positive & negative solution. _________________ 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! 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