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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 ## Lindsay can paint 1/x of a certain room in 20 minutes. What tagged by: swerve ##### This topic has 3 expert replies and 1 member reply ### Top Member ## Lindsay can paint 1/x of a certain room in 20 minutes. What ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Lindsay can paint 1/x of a certain room in 20 minutes. What fraction of the same room can Joseph paint in 20 minutes if the two of them can paint the room in an hour, working together at their respectives rates? A. 1/3x B. 3x/(x - 3) C. (x - 3) / 3x D. x / (x - 3) E. (x - 3) / x The OA is C. Source: GMAT Prep ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15186 messages Followed by: 1860 members Upvotes: 13060 GMAT Score: 790 Quote: Lindsay can paint 1/x of a certain room in 20 minutes. What fraction of the same room can Joseph paint in 20 minutes if the two of them can paint the room in an hour, working together at their respectives rates? A. 1/3x B. 3x/(x - 3) C. (x - 3) / 3x D. x / (x - 3) E. (x - 3) / x Let the room = 20 units. Let x = 4. Since Lindsay paints 1/x of the room in 20 minutes -- the equivalent of 1/3 hour -- Lindsay's rate = (1/4) * 20 = 5 units per 1/3 hour = 15 units per hour. Since Lindsay and Joseph paint the entire room in 1 hour, their combined rate = 20 units per hour. Thus, Joseph's rate = (combined rate) - (Lindsay's rate) = 20-15 = 5 units per hour. In 20 minutes -- the equivalent of 1/3 hour -- the amount of work produced by Joseph = r*t = 5 * (1/3) = 5/3 units. Thus, the fraction painted by Joseph = (5/3)/20 = 1/12. This is the target. Now plug x=4 into the answers to see which yields the target value of 1/12. Only C works: (x-3)/3x = (4-3)/(3*4) = 1/12. 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 Last edited by GMATGuruNY on Sun Sep 30, 2018 9:48 am; edited 1 time in total 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. ### Top Member Legendary Member Joined 02 Mar 2018 Posted: 908 messages Followed by: 1 members $$In\ 20\ \min utes\ lindsay\ can\ paint\ \frac{1}{x}$$ $$In\ 60\ \min utes\ \left(1hr\right)lindsay\ can\ paint\ =\frac{\left(\frac{1}{x}\cdot\ 60\right)}{20}$$ $$=\frac{\left(\frac{60}{x}\right)}{20}$$ $$=\frac{60}{x}\cdot\frac{1}{20\ }=\frac{3}{x}in\ 60\ \min utes\ \left(1hour\right)$$ $$If\ lindsay\ can\ paint\ \frac{3}{x}part\ of\ the\ room\ in\ 1\ hour,\ let\ the\ remaining\ part\ of\ the\ room\ be\ =y.$$ Bearing in mind that Joseph paints the remaining pat of the room . Therefore, Joseph can paint y in 60 minutes, $$\frac{3}{x\ }+y=x\ \left(total\ room\right)$$ $$y\ =\ x-\frac{3}{x}$$ $$If\ Joseph\ work\ for\ 60\ \min utes\ =\ x-\frac{\left(3\right)}{x},\ then,$$ $$20\ \min utes\ =\ \frac{\left(\left(\frac{x}{1}-\frac{3}{x}\right)\cdot\frac{20}{1}\right)}{60}$$ $$=\ \frac{\left(\frac{x}{1}-\frac{3}{x}\right)}{3}\ =\ \left(\frac{x}{1}-\frac{3}{x}\right)\cdot\frac{1}{3}$$ $$\frac{\left(x-3\right)}{3x}$$ Option C is CORRECT. ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12733 messages Followed by: 1246 members Upvotes: 5254 GMAT Score: 770 swerve wrote: Lindsay can paint 1/x of a certain room in 20 minutes. What fraction of the same room can Joseph paint in 20 minutes if the two of them can paint the room in an hour, working together at their respectives rates? A. 1/3x B. 3x/(x - 3) C. (x - 3) / 3x D. x / (x - 3) E. (x - 3) / x The OA is C. Source: GMAT Prep Given: Lindsay can paint 1/x of a certain room in 20 minutes So, in 1 HOUR, Lindsay can paint 3/x of the room Given: Lindsay and Joseph can paint the room in 1 HOUR. During that one hour, Lindsay can paint 3/x of the room. So, during that 1 HOUR, Joseph must paint the rest (whatever Lindsay did not paint) So, during the 1 HOUR, the fraction of the room that Joseph paints = 1 - 3/x = x/x - 3/x = (x-3)/x So, (x-3)/x = the fraction of the room that Joseph paints in one hour. Since 20 minutes = 1/3 of an hour, Joseph can paint (1/3)[(x-3)/x] of the room in 20 minutes. (1/3)[(x-3)/3x] = (x-3)/3x Answer: C Cheers, Brent _________________ Brent Hanneson – Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2204 messages Followed by: 17 members Upvotes: 43 swerve wrote: Lindsay can paint 1/x of a certain room in 20 minutes. What fraction of the same room can Joseph paint in 20 minutes if the two of them can paint the room in an hour, working together at their respectives rates? A. 1/3x B. 3x/(x - 3) C. (x - 3) / 3x D. x / (x - 3) E. (x - 3) / x We are given that Lindsay can paint 1/x of a room in 20 minutes; thus, she can paint 3/x of a room in 60 minutes (or in 1 hour). Thus, her hourly rate is 3/x room/hr. We are also given that when she works with Joseph, they can paint the entire room in 1 hour. If we let total work = 1 and j = the number of hours it takes Joseph to paint the room by himself, then Joseph’s rate = 1/j room/hr. We can create the following equation and isolate j: work of Lindsay + work of Joseph = 1 (3/x)(1) + (1/j)(1) = 1 3/x + 1/j = 1 Multiplying the entire equation by xj, we obtain: 3j + x = xj x = xj - 3j x = j(x - 3) x/(x - 3) = j Since j = x/(x - 3) and 1/j = Joseph’s rate, then Joseph’s rate, in terms of x, is (x - 3)/x. Since 20 minutes = 1/3 of an hour, and since work = rate x time, Joseph can complete: [(x - 3)/x](1/3) = (x - 3)/(3x) of the job in 20 minutes. Alternate Solution: Since Lindsay and Joseph, working together, can paint the entire room in 1 hour, then in 20 minutes, they can paint 1/3 of the room. If we let r be the fraction of the room that Joseph can paint in 20 minutes, then it must be true that: 1/x + r = 1/3 r = 1/3 - 1/x r = x/(3x) - 3/(3x) r = (x - 3)/(3x) Answer: C _________________ Scott Woodbury-Stewart Founder and CEO • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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