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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 ## Two positive numbers differ by 12 and their reciprocals tagged by: swerve ##### This topic has 2 expert replies and 0 member replies ### Top Member ## Two positive numbers differ by 12 and their reciprocals ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Two positive numbers differ by $$12$$ and their reciprocals differ by $$\frac{4}{5}$$. What is their product? A. $$\frac{2}{15}$$ B. $$\frac{48}{5}$$ C. $$15$$ D. $$42$$ E. $$60$$ The OA is C Source: Manhattan Prep ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12975 messages Followed by: 1249 members Upvotes: 5254 GMAT Score: 770 swerve wrote: Two positive numbers differ by $$12$$ and their reciprocals differ by $$\frac{4}{5}$$. What is their product? A. $$\frac{2}{15}$$ B. $$\frac{48}{5}$$ C. $$15$$ D. $$42$$ E. $$60$$ The OA is C Source: Manhattan Prep Two positive numbers differ by 12 Let x = the smaller number So x + 12 = the larger number NOTE: our goal is to find the value of x(x + 12) Their reciprocals differ by 4/5 We get: 1/x - 1/(x+12) = 4/5 Multiply both sides by x to get: 1 - x/(x + 12) = 4x/5 Multiply both sides by 5 to get: 5 - 5x/(x + 12) = 4x Multiply both sides by (x + 12) to get: 5(x + 12) - 5x = 4x(x +12) Expand left side to get: 5x + 60 - 5x = 4x(x +12) Simplify left side to get: 60 = 4x(x +12) Divide both sides by 4 to get: 15 = x(x +12) Answer: C Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2791 messages Followed by: 18 members Upvotes: 43 swerve wrote: Two positive numbers differ by $$12$$ and their reciprocals differ by $$\frac{4}{5}$$. What is their product? A. $$\frac{2}{15}$$ B. $$\frac{48}{5}$$ C. $$15$$ D. $$42$$ E. $$60$$ The OA is C Source: Manhattan Prep We can create the equations: x - y = 12 and 1/y - 1/x = 4/5 (notice that x > y, so 1/y > 1/x) Letâ€™s multiply the second equation by xy, and we have: x - y = (4/5)xy Since x - y = 12, we have: 12 = (4/5)xy Multiplying both sides by 5/4, we have: 15 = xy Answer: C _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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