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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 ## GMATPrep Problem ##### This topic has 3 expert replies and 12 member replies Goto page • 1, • 2 ## GMATPrep Problem If x<0, then Sqrt( -x|x| ) is (A) -x (B) -1 (C) 1 (D) x (A) sqrt(x) OA [spoiler]A[/spoiler] Junior | Next Rank: 30 Posts Joined 18 May 2010 Posted: 21 messages Isnt it D? Junior | Next Rank: 30 Posts Joined 23 Feb 2007 Posted: 15 messages Test Date: September 2010 Target GMAT Score: 720 GMAT Score: 610 Nope. My first response was D, but I was wrong Last edited by yankee.musk on Tue Jun 01, 2010 3:34 pm; edited 1 time in total Junior | Next Rank: 30 Posts Joined 18 May 2010 Posted: 21 messages k..i got it. During my calculations since x is a negative number i converted the -x to a +x...did not to that to my final result. Do you think that's right? Master | Next Rank: 500 Posts Joined 02 Oct 2009 Posted: 362 messages Followed by: 1 members Upvotes: 26 Sqrt( -x|x| ) => sqrt(-(-x)|-x|) ( as x has negative sign) => sqrt(x^2) =>-x ( x is less then 0) _________________ "Single Malt is better than Blended" Legendary Member Joined 28 Apr 2010 Posted: 1172 messages Followed by: 4 members Upvotes: 74 Test Date: ï£¿ Target GMAT Score: ï£¿ GMAT Score: ï£¿ Is this a legitimate GMAT question? I thought GMAT doesn't test questions like sqrt of a negative number. I guess to approach this question, I would convert sqrt to exponent: (-x|x|)^1/2 and then (-x^2)^(1/2) is equal to -x^(2/2), which is -x^1 = -x. Due to its ugliness, I don't think it is a GMAT question. ### GMAT/MBA Expert GMAT Instructor Joined 19 Oct 2009 Posted: 1302 messages Followed by: 162 members Upvotes: 539 GMAT Score: 800 When we apply the square root function, the result must be positive. So, we can eliminate negative answers. Choice B is clearly negative. But because x itself is negative, we can also automatically eliminate choice D (square root can't result in negative). Similarly, because we can't take the square root of a negative number, we can eliminate choice E. We don't know x's value, so we can eliminate choice C. The answer must be choice A! Because x is negative, "-x" must be positive. The "-" sign doesn't mean we were taking the square root of a negative or that the square root operation yielded a negative result. The "-" doesn't denote the sign of "x". It just tells you to multiply x by -1. If x<0, then square root of (x^2) is (-1)*x or -x. _________________ Kaplan Teacher in Toronto Free GMAT Practice Test under Proctored Conditions! - Find a practice test near you or live and online in Kaplan's Classroom Anywhere environment. Register today! Master | Next Rank: 500 Posts Joined 17 Mar 2010 Posted: 268 messages Upvotes: 17 Test Date: TBD Target GMAT Score: 750 Testluv wrote: If x<0, then square root of (x^2) is (-1)*x or -x. Can you please show, in detail ,how this works. i was working on following lines: for x<0 ,sq rt(x^2)=>sqrt (-1*x*x)=>x*sqrt(-1)...am stuck here.. _________________ My Blog: https://www.iwantutopia.blogspot.com/ Legendary Member Joined 28 Apr 2010 Posted: 1172 messages Followed by: 4 members Upvotes: 74 Test Date: ï£¿ Target GMAT Score: ï£¿ GMAT Score: ï£¿ Ya I completely ignored the x < 0... Legendary Member Joined 29 Dec 2009 Posted: 1460 messages Followed by: 7 members Upvotes: 135 this_time_i_will wrote: Testluv wrote: If x<0, then square root of (x^2) is (-1)*x or -x. Can you please show, in detail ,how this works. i was working on following lines: for x<0 ,sq rt(x^2)=>sqrt (-1*x*x)=>x*sqrt(-1)...am stuck here.. Sqrt(x^2)=x if x>0 or -x if x<0 if x<0,sqrt(x^2)=sqrt(-x*-x)=-x Hope this clarify Legendary Member Joined 28 Apr 2010 Posted: 1172 messages Followed by: 4 members Upvotes: 74 Test Date: ï£¿ Target GMAT Score: ï£¿ GMAT Score: ï£¿ Think of this way, what is sqrt of (x * x)? This question is essentially asking the same thing, except that x is a negative number, so -x is a positive number. Sqrt( -x|x| ) is essentially a positive x multiplies an absolute value of x, which is the same as x * x. Senior | Next Rank: 100 Posts Joined 26 Apr 2010 Posted: 84 messages Followed by: 1 members Upvotes: 6 Testluv wrote: When we apply the square root function, the result must be positive. So, we can eliminate negative answers. Choice B is clearly negative. But because x itself is negative, we can also automatically eliminate choice D (square root can't result in negative). Similarly, because we can't take the square root of a negative number, we can eliminate choice E. We don't know x's value, so we can eliminate choice C. The answer must be choice A! Because x is negative, "-x" must be positive. The "-" sign doesn't mean we were taking the square root of a negative or that the square root operation yielded a negative result. The "-" doesn't denote the sign of "x". It just tells you to multiply x by -1. If x<0, then square root of (x^2) is (-1)*x or -x. Hi! From your answer can we conclude : sqrt(x2)= IxI (for all real x) but i have a query here, for all x<0 or x>0 x2 is always positive (i.e. x2>0) so sqrt(x2) = x or -x (as a square of +ve or -ve number is always +ve, so sqrt (x2) in its result show both the number, as it ) x2 Legendary Member Joined 28 Apr 2010 Posted: 1172 messages Followed by: 4 members Upvotes: 74 Test Date: ï£¿ Target GMAT Score: ï£¿ GMAT Score: ï£¿ x square will always be a positive number is correct, but we're not squaring x in the question. Read the question carefully, it is Sqrt( -x|x| ), which is -x * |x|. -x * |x| is not the same as (-x)^2 or x^2. ### GMAT/MBA Expert GMAT Instructor Joined 19 Oct 2009 Posted: 1302 messages Followed by: 162 members Upvotes: 539 GMAT Score: 800 this_time_i_will wrote: Testluv wrote: If x<0, then square root of (x^2) is (-1)*x or -x. Can you please show, in detail ,how this works. i was working on following lines: for x<0 ,sq rt(x^2)=>sqrt (-1*x*x)=>x*sqrt(-1)...am stuck here.. |x| = sqrt(x^2) (this is how absolute value is defined) Both the absolute value and the square root functions must be positive. Therefore: If x>0, then both sqrt(x^2) and |x| are x; and if x<0, then both sqrt(x^2) and |x| are -x. (if x<0, then because absolute value and square root operations must result in positive, |x| and sqrt(x^2) have to be -x; they can't yield x because x is negative) ________________ In this question, confusion may arise from wanting/having to diagram "-x" when x itself is negative. (We can't let "-x" be x since "-x" is positive and x is negative). x is negative. But suppose there is a number, z. If z is positive and equal in absolute value to x, then z = -x or x = -z. The question asks for sqrt(-x*|x|) or sqrt[(-1)*(x)*|x|] Subbing "-z" into "x", the question becomes: what is sqrt[(-1)*(-z)*|-z|]? Because z is positive, clearly (-1)*(-z) is just z. Likewise |-z| is just z. Thus, we have: sqrt(z*z) which is just z which is equal to -x. _________________ Kaplan Teacher in Toronto Free GMAT Practice Test under Proctored Conditions! - Find a practice test near you or live and online in Kaplan's Classroom Anywhere environment. Register today! Senior | Next Rank: 100 Posts Joined 26 Apr 2010 Posted: 84 messages Followed by: 1 members Upvotes: 6 Testluv wrote: this_time_i_will wrote: Testluv wrote: If x<0, then square root of (x^2) is (-1)*x or -x. Can you please show, in detail ,how this works. i was working on following lines: for x<0 ,sq rt(x^2)=>sqrt (-1*x*x)=>x*sqrt(-1)...am stuck here.. |x| = sqrt(x^2) (this is how absolute value is defined) Both the absolute value and the square root functions must be positive. Therefore: If x>0, then both sqrt(x^2) and |x| are x; and if x<0, then both sqrt(x^2) and |x| are -x. (if x<0, then because absolute value and square root operations must result in positive, |x| and sqrt(x^2) have to be -x; they can't yield x because x is negative) ________________ In this question, confusion may arise from wanting/having to diagram "-x" when x itself is negative. (We can't let "-x" be x since "-x" is positive and x is negative). x is negative. But suppose there is a number, z. If z is positive and equal in absolute value to x, then z = -x or x = -z. The question asks for sqrt(-x*|x|) or sqrt[(-1)*(x)*|x|] Subbing "-z" into "x", the question becomes: what is sqrt[(-1)*(-z)*|-z|]? Because z is positive, clearly (-1)*(-z) is just z. Likewise |-z| is just z. Thus, we have: sqrt(z*z) which is just z which is equal to -x. thank you • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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