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If ( x – y – 2 )^2 + ( x + z + 3 )^2 = 0, then what is the value of y

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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If ( x – y – 2 )^2 + ( x + z + 3 )^2 = 0, then what is the value of y  [#permalink]

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01 Feb 2019, 02:52
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45% (medium)

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56% (02:00) correct 44% (02:23) wrong based on 41 sessions

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[GMAT math practice question]

If $$( x – y – 2 )^2 + ( x + z + 3 )^2 = 0$$, then what is the value of $$y + z$$?

$$A. 0$$
$$B. 3$$
$$C. -3$$
$$D. 5$$
$$E. -5$$

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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Director Joined: 09 Mar 2018 Posts: 997 Location: India Re: If ( x – y – 2 )^2 + ( x + z + 3 )^2 = 0, then what is the value of y [#permalink] Show Tags 01 Feb 2019, 03:13 MathRevolution wrote: [GMAT math practice question] If $$( x – y – 2 )^2 + ( x + z + 3 )^2 = 0$$, then what is the value of $$y + z$$? $$A. 0$$ $$B. 3$$ $$C. -3$$ $$D. 5$$ $$E. -5$$ If $$( x – y – 2 )^2 + ( x + z + 3 )^2 = 0$$ Both the expressions cannot be -ive, so we can think of plugging in some values for x, y and z x = 4 y = 2 & z = -7 will satisfy the expression y + z = -7 + 2 E _________________ If you notice any discrepancy in my reasoning, please let me know. Lets improve together. Quote which i can relate to. Many of life's failures happen with people who do not realize how close they were to success when they gave up. Senior Manager Joined: 04 Aug 2010 Posts: 474 Schools: Dartmouth College Re: If ( x – y – 2 )^2 + ( x + z + 3 )^2 = 0, then what is the value of y [#permalink] Show Tags 01 Feb 2019, 05:34 MathRevolution wrote: [GMAT math practice question] If $$( x – y – 2 )^2 + ( x + z + 3 )^2 = 0$$, then what is the value of $$y + z$$? $$A. 0$$ $$B. 3$$ $$C. -3$$ $$D. 5$$ $$E. -5$$ Let x=0. Plugging x=0 into $$( x – y – 2 )^2 + ( x + z + 3 )^2 = 0$$, we get: (-y-2)² + (z+3)² = 0 Since neither (-y-2)² nor (z+3)² can be negative, the resulting equation is valid only if -y-2=0 and z+3=0, with the result that y=-2 and z=-3. Thus, y+z = -2 + (-3) = -5 _________________ GMAT and GRE Tutor Over 1800 followers GMATGuruNY@gmail.com New York, NY If you find one of my posts helpful, please take a moment to click on the "Kudos" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. GMATH Teacher Status: GMATH founder Joined: 12 Oct 2010 Posts: 935 Re: If ( x – y – 2 )^2 + ( x + z + 3 )^2 = 0, then what is the value of y [#permalink] Show Tags 01 Feb 2019, 06:22 MathRevolution wrote: [GMAT math practice question] If $$( x – y – 2 )^2 + ( x + z + 3 )^2 = 0$$, then what is the value of $$y + z$$? $$A. 0$$ $$B. 3$$ $$C. -3$$ $$D. 5$$ $$E. -5$$ $${\left( {x - y - 2} \right)^2} + {\left( {x + z + 3} \right)^2} = 0\,\,\,\,\,\left( * \right)$$ $$? = y + z$$ $$\left. \matrix{ {\left( {x + z + 3} \right)^2} \ge 0 \hfill \cr {\left( {x - y - 2} \right)^2} \ge 0\,\,\, \hfill \cr} \right\}\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\left\{ \matrix{ \,x + z + 3 = 0 \hfill \cr \,x - y - 2 = 0 \hfill \cr} \right.\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( - \right)} \,\,\,\,\,\,\,z - \left( { - y} \right) + 3 - \left( { - 2} \right) = 0\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,? = - 5$$ The correct answer is therefore (E). We follow the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our high-level "quant" preparation starts here: https://gmath.net Senior Manager Joined: 27 Dec 2016 Posts: 310 Re: If ( x – y – 2 )^2 + ( x + z + 3 )^2 = 0, then what is the value of y [#permalink] Show Tags 01 Feb 2019, 19:54 1 60 seconds approach: We know something square + something square must equal 0 and the only to do this is if our equation becomes 0+0 = 0. To make each of the parentheses 0, let's number test the following numbers: x=4, y=2, z=-7. Our equation becomes 0+0=0. Y+Z = 2+(-7) = -5. Hence option E Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8001 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If ( x – y – 2 )^2 + ( x + z + 3 )^2 = 0, then what is the value of y [#permalink] Show Tags 04 Feb 2019, 05:42 => Since $$( x – y – 2 )^2 + ( x + z + 3 )^2 = 0$$, we must have $$x – y – 2 = 0$$ and $$x + z + 3 = 0.$$ So, $$x = y + 2$$ and $$x + z + 3 = ( y + 2 ) + z + 3 = y + z + 5 = 0.$$ Thus, $$y + z = -5.$$ Therefore, the answer is E. Answer: E _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: If ( x – y – 2 )^2 + ( x + z + 3 )^2 = 0, then what is the value of y   [#permalink] 04 Feb 2019, 05:42
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