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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 ## What is the value of x^2+y^2? tagged by: Vincen ##### This topic has 1 expert reply and 0 member replies ## What is the value of x^2+y^2? $$\text{what}\ \text{is}\ \text{the}\ \text{value}\ \text{of}\ x^2+y^2?$$ $$\left(1\right)\ \ x^2+y^2=2xy+1\ .$$ $$\left(2\right)\ \ x^2+y^2=4-2xy.$$ The OA is the option C. Experts, can you show me how to use each statement to get an answer here? Please. ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 Top Reply Vincen wrote: $$\text{what}\ \text{is}\ \text{the}\ \text{value}\ \text{of}\ x^2+y^2?$$ $$\left(1\right)\ \ x^2+y^2=2xy+1\ .$$ $$\left(2\right)\ \ x^2+y^2=4-2xy.$$ The OA is the option C. Experts, can you show me how to use each statement to get an answer here? Please. Statement 1: $$x^2 -2xy + y^2 = 1$$ $$(x-y)^2 = 1$$ Clearly not sufficient. Case 1: x = 3 and y = 2 --> x^2 + y^2 = 9 + 4 = 13 Case 2: x=5 and y = 4. --> x^2 + y^2 = 25 + 16 = 41 Statement 2: $$x^2 + 2xy + y^2 = 4$$$$(x + y)^2 = 4 Clearly not sufficient Case 1: x = 0 and y = 2 --> x^2 + y^2 = 0 + 4 = 4 Case 2: x=1 and y = 1. --> 1^2 + 1^2 = 1 + 1 = 2 Together, we can sum the equations x^2 + y^2 = 2xy + 1 and x^2 + y^2 = 4-2xy _____________________ 2x^2 + 2y^2 = 5 x^2 + y^2 = 5/2. A unique value. Sufficient. The answer is C _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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