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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 ## Is xy > 0? tagged by: Vincen ##### This topic has 2 expert replies and 0 member replies ## Is xy > 0? Is xy > 0? (1) x - y > -2 (2) x - 2y < -6 The OA is the option C. How can I get an answer here? I should prove that x and y have the same sign. How can I do that? Experts, may you help me? Thanks in advanced. ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15344 messages Followed by: 1864 members Upvotes: 13060 GMAT Score: 790 Top Reply Vincen wrote: Is xy > 0? (1) x - y > -2 (2) x - 2y < -6 Statement 1: x > y-2 If y=2 and x= 1, is 1*2 > 0? Yes. If y= -1 and x = 1, is 1*(-1) > 0? No. Since the answer can both Yes and No, insufficient. Statement 2: x < 2y-6 If y=1 and x = -10, is 1*(-10) > 0? No. If y = 10 and x = 1, is 1*10 > 0? Yes. Since the answer can be both No and Yes, insufficient. Statements 1 and 2 combined: Linking together the two statements, we get: y-2 < x < 2y-6 y-2 < 2y-6 y > 4. Since y > 4 and x > y-2, we know that x > 2. Thus, x and y are both positive. Sufficient. The correct answer is C. Another way to combine the two statements: Inequalities can be ADDED TOGETHER. One constraint: When we add the inequalities together, the <> must face the SAME DIRECTION in each inequality. Adding together x - y > -2 and -6 > x - 2y, we get: x - y + (-6) > -2 + x - 2y - y - 6 > -2 - 2y y > 4. Same result as in the solution above. _________________ 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. ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 Vincen wrote: Is xy > 0? (1) x - y > -2 (2) x - 2y < -6 The OA is the option C. How can I get an answer here? I should prove that x and y have the same sign. How can I do that? Experts, may you help me? Thanks in advanced. You pick numbers to quickly prove that each statement alone is not sufficient. When testing together, we can multiply the second inequality by -1 to make it -x + 2y > 6. Now we can add them x - y > -2 -x + 2y > 6 y > 4 So we know y is greater than 4. Now we can add this new inequality to the first one x - y > -2 y > 4 x > 2 If we know that x and y are both positive, then we know definitively that xy > 0. Together, the statements are 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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