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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 ## A curve is represented by the equation x^2 y^3 = k^3, where tagged by: BTGmoderatorLU ##### This topic has 2 expert replies and 0 member replies ### Top Member ## A curve is represented by the equation x^2 y^3 = k^3, where ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Source: e-GMAT A curve is represented by the equation x^2 y^3=k^3, where k < 0. At how many points does the line, y = -a, where a is an integer, intersects this curve? A. 0 B. 1 C. 2 D. 4 E. Cannot be determined The OA is E. ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1273 messages Followed by: 29 members Upvotes: 59 Top Reply BTGmoderatorLU wrote: Source: e-GMAT A curve is represented by the equation x^2 y^3=k^3, where k < 0. At how many points does the line, y = -a, where a is an integer, intersects this curve? A. 0 B. 1 C. 2 D. 4 E. Cannot be determined The correct answer is (E): $\left\{ \begin{gathered} \,{x^2}{y^3} = {k^3}\,\,\,\left( {k < 0} \right) \hfill \\ y = - a\,\,\,\left( {a\,\,\operatorname{int} } \right) \hfill \\ \end{gathered} \right.\,\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,{x^2}{\left( { - a} \right)^3} = {k^3}\,\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,{x^2} = - {\left( {\frac{k}{a}} \right)^3}\,\,\,\,\,,\,\,\,\,a \ne 0$ Take (for instance) : (a,k) = (1,-1) , then we have 2 points (x,y) = (x, -a) of intersection: (-1, -1) and (1, -1) (a,k) = (-1,-1) , then we have 0 points (x,y) = (x,-a) of intersection, because x^2 = -1 has no solutions (in the real numbers) This solution follows 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 ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 1756 messages Followed by: 28 members Upvotes: 470 BTGmoderatorLU wrote: Source: e-GMAT A curve is represented by the equation x^2 y^3=k^3, where k < 0. At how many points does the line, y = -a, where a is an integer, intersects this curve? A. 0 B. 1 C. 2 D. 4 E. Cannot be determined The OA is E. Let's plug-in y = - a in the equation x^2*y^3 = k^3 -x^2*a^3 = -|k^3|; we are given that k < 0 x^2*a^3 = |k^3| x^2 = |k^3| / a^3 There are three cases... 1. If a > 0 then x^2 = |k^3| / |a^3| => x = ±√(|k/a|^3. There are two points. 2. If a = 0 then x^2 = |k^3| / |0^3| is indeterminable. 3. If a ≤ 0 then x^2 = |k^3| / -|a^3| => x^2 = -[|k^3| / |a^3|]; squareroot of a negative number is not possible. Indeterminable. The correct answer: E Hope this helps! -Jay _________________ Manhattan Review GRE Prep Locations: GRE Classes Seattle | GMAT Prep Course Hong Kong | GRE Prep San Francisco | SAT Prep Classes NYC | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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