• NEW! FREE Beat The GMAT Quizzes
Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
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 ## If (2x+y-z)^2 + (x-y)^2 + (z-3)^2 = -(3y-z)^2 , what is the tagged by: fskilnik@GMATH ##### This topic has 1 expert reply and 0 member replies ### GMAT/MBA Expert ## If (2x+y-z)^2 + (x-y)^2 + (z-3)^2 = -(3y-z)^2 , what is the ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult GMATH practice exercise (Quant Class 3) Answer: ______(A)__ _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 fskilnik@GMATH wrote: GMATH practice exercise (Quant Class 3) $$? = 3x + 2y + z$$ $${\left( {2x + y - z} \right)^2} + {\left( {x - y} \right)^2} + {\left( {z - 3} \right)^2} = - {\left( {3y - z} \right)^2}\,\,\,\,\,\left( * \right)$$ $$\left. \matrix{ {\left( {2x + y - z} \right)^2} + {\left( {x - y} \right)^2} + {\left( {z - 3} \right)^2}\,\,\, \ge 0\,\, \hfill \cr - {\left( {3y - z} \right)^2}\,\, \le 0 \hfill \cr} \right\}\,\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,{\left( {2x + y - z} \right)^2} + {\left( {x - y} \right)^2} + {\left( {z - 3} \right)^2} = 0\,\,\,\,\,\,\left[ { = - {{\left( {3y - z} \right)}^2}} \right]$$ $${\left( {2x + y - z} \right)^2} + {\left( {x - y} \right)^2} + {\left( {z - 3} \right)^2} = 0\,\,\,\,\,\,\, \Rightarrow \,\left\{ \matrix{ \,x - y = 0\,\,\,\,\, \Rightarrow \,\,\,\,\,x = y\,\,\, \hfill \cr \,z - 3 = 0\,\,\,\,\, \Rightarrow \,\,\,\,\,z = 3\,\,\,\, \hfill \cr \,2x + y - z = 0\,\,\,\,\mathop \Rightarrow \limits^{{\rm{both}}\,{\rm{above}}} \,\,\,\,\,3x - 3 = 0\, \hfill \cr} \right.\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,\left( {x,y,z} \right) = \left( {1,1,3} \right)$$ $$? = 3x + 2y + z = 3\left( 1 \right) + 2\left( 1 \right) + 3 = 8$$ The correct answer is (A). We follow the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br • 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 Study Smarter, Not Harder Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to \$200

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

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

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

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

### Top First Responders*

1 Ian Stewart 44 first replies
2 Jay@ManhattanReview 35 first replies
3 Brent@GMATPrepNow 34 first replies
4 Scott@TargetTestPrep 31 first replies
5 GMATGuruNY 18 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 Scott@TargetTestPrep

Target Test Prep

129 posts
2 Max@Math Revolution

Math Revolution

89 posts
3 Ian Stewart

GMATiX Teacher

53 posts
4 Brent@GMATPrepNow

GMAT Prep Now Teacher

50 posts
5 Jay@ManhattanReview

Manhattan Review

35 posts
See More Top Beat The GMAT Experts