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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 ## In the xy coordinate plane, line L and line K intersect at tagged by: swerve ##### This topic has 2 expert replies and 0 member replies ### Top Member ## In the xy coordinate plane, line L and line K intersect at ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult In the xy coordinate plane, line L and line K intersect at the point (4,3). Is the product of their slopes negative? 1) The product of the x-intersects of lines L and K is positive. 2) The product of the y-intersects of lines L and K is negative. The OA is C Source: GMAT Prep ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 1984 messages Followed by: 30 members Upvotes: 470 swerve wrote: In the xy coordinate plane, line L and line K intersect at the point (4, 3). Is the product of their slopes negative? 1) The product of the x-intersects of lines L and K is positive. 2) The product of the y-intersects of lines L and K is negative. The OA is C Source: GMAT Prep Say the equations of line L and K are y = m1*x + c1; eqn of line L; y = m2*x + c2; eqn of line K Here, m1 and m2 are slopes of line L and line K; and c1 and c2 are y-intercepts of line L and line K. We have to determine whether m1*m2 < 0. Let's take each statement one by one. 1) The product of the x-intersects of lines L and K is positive. Let's transform the equations to get the x-intersects. We have y = m1*x + c1=> y - c1 = m1*x => y/m1 - c1/m1 = x => x-intercept of line L = -c1/m1 y = m2*x + c2=> y - c2 = m2*x => y/m2 - c2/m2 = x => x-intercept of line K = -c2/m2 Thus, (-c1/m1)*(-c2/m2) > 0 (c1*c2)/(m1*m2) > 0 Case 1: If c1*c2 > 0, we muat have m1*m2 > 0; the answer is No. Case 2: If c1*c2 < 0, we must have m1*m2 < 0; the answer is Yes. No unique answer. Insufficient. 2) The product of the y-intersects of lines L and K is negative. => c1*c2 < 0 It can't help determine whether m1*m2 < 0. Insufficient. (1) and (2) together Thus, Case 1 discussed in Statement 1 is invalid; or, only Case 2 is valid; thus, m1*m2 < 0. Sufficient. The correct answer: C Hope this helps! -Jay _________________ Manhattan Review GMAT Prep Locations: GMAT Classes Boston | GMAT Tutoring NYC | GRE Prep Dallas | TOEFL Prep Classes Seattle | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15362 messages Followed by: 1866 members Upvotes: 13060 GMAT Score: 790 swerve wrote: In the xy coordinate plane, line L and line K intersect at the point (4,3). Is the product of their slopes negative? 1) The product of the x-intersects of lines L and K is positive. 2) The product of the y-intersects of lines L and K is negative. Statement 1: The product of the x-intercepts of line L and K is positive. K has a negative x-intercept, L has a negative x-intercept, the product of the slopes is positive: K has a positive x-intercept, L has a positive x-intercept, the product of the slopes is negative: INSUFFICIENT. Statement 2: The product of the y-intercepts of line L and k is negative. K has a negative y-intercept, L has a positive y-intercept, the product of the slopes is negative: K has a negative y-intercept, L has a positive y-intercept, the product of the slopes is positive: INSUFFICIENT. Statements 1 and 2 combined: Statement 1 requires that both x-intercepts be negative or that both x-intercepts be positive (so that their product is positive). If both x-intercepts are negative, then both y-intercepts must be positive, violating statement 2: Thus, both x-intercepts must be positive. Statement 2 requires that one of the y-intercepts be positive, the other negative. A positive x-intercept and a positive y-intercept yields a negative slope. A positive x-intercept and a negative y-intercept yields a positive slope. See below: Thus, the product of the slopes must be negative. SUFFICIENT. The correct answer is C. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. • FREE GMAT Exam Know how you'd score today for$0

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