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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 the number of workers required to create w1 widgets at r1 ##### This topic has 1 expert reply and 0 member replies ### Top Member ## Is the number of workers required to create w1 widgets at r1 ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Is the number of workers required to create w1 widgets at r1 widgets per minute less than the number of workers required to create w2 widgets at r2 widgets per minute? (1) w1 is 20 less than w2. (2) r1 is 20 less than r2. OA E Source: Princeton Review ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 Top Reply Quote: During a certain production time, is the number of workers required to create w1 widgets at the rate of r1 widgets per minute per worker less than the number of workers required to create w2 widgets at the rate of r2 widgets per minute per worker? (1) w1 is 20 less than w2. (2) r1 is 20 less than r2. Excellent opportunity for UNITS CONTROL, one of the most powerful tools of our method! $$N \ge 1\,\,{\mathop{\rm int}} \,\,{\rm{workers}}\,\,\,\,\,\, \to \,\,\,\,\,{w_1}\,\,{\rm{widgets}}\,\,\,\left( {{{1\,\,{\rm{minute}}} \over {N \cdot {r_1}\,\,{\rm{widgets}}}}} \right)\,\,\,\,\, = \,\,\,\,{{{w_1}\,\,} \over {N \cdot {r_1}\,\,}}\,\,\,{\rm{minutes}}$$ $$M \ge 1\,\,{\mathop{\rm int}} \,\,{\rm{workers}}\,\,\,\,\,\, \to \,\,\,\,\,{w_2}\,\,{\rm{widgets}}\,\,\,\left( {{{1\,\,{\rm{minute}}} \over {M \cdot {r_2}\,\,{\rm{widgets}}}}} \right)\,\,\,\,\, = \,\,\,\,{{{w_2}\,\,} \over {M \cdot {r_2}\,\,}}\,\,\,{\rm{minutes}}$$ $${{{w_1}\,\,} \over {N \cdot {r_1}\,\,}} = {{{w_2}\,\,} \over {M \cdot {r_2}\,\,}}\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{{\rm{all}}\,\, \ne \,\,0} \,\,\,\,\,\,\,{N \over M} = {{{w_1} \cdot {r_2}} \over {{w_2} \cdot {r_1}}}$$ $$N\,\,\mathop < \limits^? \,\,M\,\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{M\, > \,0} \,\,\,\,\,\,\,{N \over M}\,\,\mathop < \limits^? \,\,1\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,{{{w_1} \cdot {r_2}} \over {{w_2} \cdot {r_1}}}\,\,\mathop < \limits^? \,\,1\,\,\,$$ LetÂ´s BIFURCATE both statement together at once, so that we are sure the correct answer is (E): $$\left( {1 + 2} \right)\,\,\,\left\{ \matrix{ \,{w_2} = {w_1} + 20 \hfill \cr \,\,{r_2} = {r_1} + 20 \hfill \cr} \right.\,\,\,\,\,$$ $$\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {{w_1},{w_2},{r_1},{r_2}} \right) = \left( {10,30,10,30} \right)\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr \,{\rm{Take}}\,\,\left( {{w_1},{w_2},{r_1},{r_2}} \right) = \left( {1,21,10,30} \right)\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr} \right.$$ 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 • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 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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