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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 ## Machines X and Y can work at their respective constant rates ##### This topic has 3 expert replies and 0 member replies ### Top Member ## Machines X and Y can work at their respective constant rates ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Machines X and Y can work at their respective constant rates to manufacture a certain production unit. If both are working alone, then the time taken by machine Y is what percentage more/less than that of machine X? (1) Machines X and Y, working together, complete a production order of the same size in two-thirds the time that machine Y, working alone, does. (2) Machine Y, working alone, fills a production order of twice the size in 6 hrs. OA A Source: e-GMAT ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15103 messages Followed by: 1859 members Upvotes: 13060 GMAT Score: 790 Top Reply BTGmoderatorDC wrote: Machines X and Y can work at their respective constant rates to manufacture a certain production unit. If both are working alone, then the time taken by machine Y is what percentage more/less than that of machine X? (1) Machines X and Y, working together, complete a production order of the same size in two-thirds the time that machine Y, working alone, does. (2) Machine Y, working alone, fills a production order of twice the size in 6 hrs. Statement 1: Time and rate have a RECIPROCAL relationship. Since X and Y together take 2/3 as long as Y alone, X and Y together work 3/2 as fast as Y alone. Thus, if Y's rate alone = 2 units per hour, then X and Y's combined rate = (3/2)(2) = 3 units per hour, implying that X's rate alone = 3-2 = 1 unit per hour. Since Y works twice as fast as X, Y's time will be 1/2 X's time. In other words: Y's time will be 50% less than X's time. SUFFICIENT. Statement 2: No information about X's rate or time. INSUFFICIENT. The correct answer is A. _________________ 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 GMAT Instructor Joined 09 Oct 2010 Posted: 1282 messages Followed by: 29 members Upvotes: 59 Top Reply BTGmoderatorDC wrote: Machines X and Y can work at their respective constant rates to manufacture a certain production unit. If both are working alone, then the time taken by machine Y is what percentage more/less than that of machine X? (1) Machines X and Y, working together, complete a production order of the same size in two-thirds the time that machine Y, working alone, does. (2) Machine Y, working alone, fills a production order of twice the size in 6 hrs. Source: e-GMAT $$?\,\,:\,\,{T_X}\,,\,\,{T_Y}\,\,{\rm{relationship}}\,\,\,\,\,\,\left( {? = {T_X}\mathop \to \limits^{\Delta \% } {T_Y} = {{{T_Y} - {T_X}} \over {{T_X}}} = {{{T_Y}} \over {{T_X}}} - 1} \right)$$ Important: the ratio of time taken (for any given job) is the inverse of the ratio of the work done (for any given time). $$\left( 1 \right)\,\,{{{T_{X \cup Y}}} \over {{T_Y}}} = {2 \over 3}\,\,\,\,\, \Rightarrow \,\,\,\,\,{{{W_{X \cup Y}}} \over {{W_Y}}} = {3 \over 2}\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\{ \matrix{ \,{W_{X \cup Y}} = 3k \hfill \cr \,{W_Y} = 2k \hfill \cr} \right.\,\,\,\,\, \Rightarrow \,\,\,{W_X} = k$$ $${{{W_Y}} \over {{W_X}}} = {2 \over 1}\,\,\,\,\, \Rightarrow \,\,\,\,{{{T_Y}} \over {{T_X}}} = {1 \over 2}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.$$ $$\left( 2 \right)\,\,{T_Y} = 3{\rm{h}}\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,{{\rm{T}}_{\rm{X}}} = 3{\rm{h}}\,\,\,\, \Rightarrow \Delta \% = 0 \hfill \cr \,{\rm{Take}}\,\,{{\rm{T}}_{\rm{X}}} = 4{\rm{h}}\,\,\,\, \Rightarrow \Delta \% \ne 0 \hfill \cr} \right.$$ 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: 1766 messages Followed by: 28 members Upvotes: 470 BTGmoderatorDC wrote: Machines X and Y can work at their respective constant rates to manufacture a certain production unit. If both are working alone, then the time taken by machine Y is what percentage more/less than that of machine X? (1) Machines X and Y, working together, complete a production order of the same size in two-thirds the time that machine Y, working alone, does. (2) Machine Y, working alone, fills a production order of twice the size in 6 hrs. OA A Source: e-GMAT Say the rate of Machine X is x hours per unit and that of Machine Y is y hours per unit. Let's take each statement one by one. (1) Machines X and Y, working together, complete a production order of the same size in two-thirds the time that machine Y, working alone, does. Part of work done by Machines X and Y, working together = 1/x + 1/y Part of work done by Machines Y, working alone = 1/y => 2/3(1/x + 1/y) = 1/y = x/y = 1/2. Time taken by machine Y is [(y - x)/x]*100% = [(2 - 1)/1]*100% = 100% more than that of machine X. Suffcient. (2) Machine Y, working alone, fills a production order of twice the size in 6 hrs. No information about Machine X is given. Insufficient. The correct answer: A Hope this helps! -Jay _________________ Manhattan Review GMAT Prep Locations: Manhattan Review India | Hyderabad GMAT Prep | Bangalore GMAT Courses | Kukatpally GMAT Prep | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! 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