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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 ## Alice, Barbara, and Cynia work on identical tasks at differe ##### This topic has 3 expert replies and 0 member replies ### Top Member ## Alice, Barbara, and Cynia work on identical tasks at differe ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Alice, Barbara, and Cynia work on identical tasks at different constant rates. Alice, working alone, can complete the task in 21 hours. Is Alice's rate the slowest rate? (1) Barbara, working alone, can complete the task in 14 hours, and Barbara and Cynia working together can complete the task in approximately 86% of the time taken by Alice and Cynia working together to complete the task. (2) Barbara and Cynia can complete the task in approximately 71% of the time taken for Alice and Barbara to complete the task. OA A Source: Princeton Review ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 Top Reply BTGmoderatorDC wrote: Alice, Barbara, and Cynia work on identical tasks at different constant rates. Alice, working alone, can complete the task in 21 hours. Is Alice's rate the slowest rate? (1) Barbara, working alone, can complete the task in 14 hours, and Barbara and Cynia working together can complete the task in approximately 86% of the time taken by Alice and Cynia working together to complete the task. (2) Barbara and Cynia can complete the task in approximately 71% of the time taken for Alice and Barbara to complete the task. Source: Princeton Review Obs.: the term approximately invalidates the question because we know NOTHING about the approximation precision. (What should be considered "near" 86%, for instance?) We will consider equality in both cases, with the following (not problematic) aside: the numbers b and c (below) may be non-integers. LetÂ´s imagine the task is defined by 42 identical units of job (from now on simply "units"). Alice (A) can do 2 units/h (therefore in 21h she will do 2*21 = 42 units, i.e., the task). Barbara (B) can do (say) b units/h Cynia (C) can do (say) c units/h $$2\,\,\mathop < \limits^? \,\,\,\min \left( {b,c} \right)$$ $$\left( 1 \right)\,\,\left\{ \matrix{ b = 3 \hfill \cr \,{{{T_{B \cup C}}} \over {{T_{A \cup C}}}} = {{43} \over {50}}\,\,\,\,\,\mathop \Rightarrow \limits^{W = \,{\rm{work}}\,{\rm{rate}}} \,\,\,\,\,{{3 + c} \over {2 + c}} = {{{W_{B \cup C}}} \over {{W_{A \cup C}}}} = {{50} \over {43}} \hfill \cr} \right.$$ $${{3 + c} \over {2 + c}} = {{50} \over {43}}\,\,\,\, \Rightarrow \,\,\,\,c\,\,{\rm{unique}}\,\,\,\, \Rightarrow \,\,\,\,{\rm{SUFF}}.$$ $$\left( 2 \right)\,\,\,{{{T_{B \cup C}}} \over {{T_{A \cup B}}}} = {{71} \over {100}}\,\,\,\,\,\mathop \Rightarrow \limits^{W = \,{\rm{work}}\,{\rm{rate}}} \,\,\,\,\,{{b + c} \over {2 + b}} = {{100} \over {71}}$$ $$\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {b;c} \right) = \left( {1;{{300} \over {71}} - 1} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \hfill \cr \,{\rm{Take}}\,\,\left( {b;c} \right) = \left( {3;{{500} \over {71}} - 3} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \hfill \cr} \right.$$ 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 ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15257 messages Followed by: 1861 members Upvotes: 13060 GMAT Score: 790 Top Reply BTGmoderatorDC wrote: Alice, Barbara, and Cynia work on identical tasks at different constant rates. Alice, working alone, can complete the task in 21 hours. Is Alice's rate the slowest rate? (1) Barbara, working alone, can complete the task in 14 hours, and Barbara and Cynia working together can complete the task in approximately 86% of the time taken by Alice and Cynia working together to complete the task. (2) Barbara and Cynia can complete the task in approximately 71% of the time taken for Alice and Barbara to complete the task. TIME and RATE have a reciprocal relationship. Statement 1: The time ratio for Barbara and Alice = (14 hours)/(21 hours). The rate ratio for Barbara and Alice is equal to the reciprocal of the time ratio: (B's rate)/(A's rate) = 21/14 = 3/2. Let B = 3 units per hour and A = 2 units per hour. Barbara and Cynia working together can complete the task in approximately 86% of the time taken by Alice and Cynia working together to complete the task. The time ratio for B+C and A+C = 86/100 = 43/50. The rate ratio for B+C and A+C is equal to the reciprocal of the time ratio: (B+C)/(A+C) = 50/43. Plugging B=3 and A=2 into the equation above, we get: (3+C)/(2+C) = 50/43. Since we can solve for C, we can determine whether Alice has the lowest rate. SUFFICIENT. Statement 2: The time ratio for B+C and B+A= 71/100. The rate ratio for B+C and B+A is equal to the reciprocal of the time ratio: (B+C)/(B+A) = 100/71. Implication: B+C > B+A C>A. No way to determine whether Alice is slower than Barbara. INSUFFICIENT. The correct answer is A. Complete solution for Statement 1: (3+C)/(2+C) = 50/43 129 + 43C = 100 + 50C 29 = 7C C = 29/7 = 4 1/7. Since A=2, B=3 and C = 4 1/7, A's rate is the lowest. _________________ 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 22 Aug 2016 Posted: 1898 messages Followed by: 30 members Upvotes: 470 BTGmoderatorDC wrote: Alice, Barbara, and Cynia work on identical tasks at different constant rates. Alice, working alone, can complete the task in 21 hours. Is Alice's rate the slowest rate? (1) Barbara, working alone, can complete the task in 14 hours, and Barbara and Cynia working together can complete the task in approximately 86% of the time taken by Alice and Cynia working together to complete the task. (2) Barbara and Cynia can complete the task in approximately 71% of the time taken for Alice and Barbara to complete the task. OA A Source: Princeton Review We have to determine which one of the three Alice Barbara, and Cynia is the slowest. Let's take each statement one by one. (1) Barbara, working alone, can complete the task in 14 hours, and Barbara and Cynia working together can complete the task in approximately 86% of the time taken by Alice and Cynia working together to complete the task. Given Alice, working alone, can complete the task in 21 hours and Barbara, working alone, can complete the task in 14 hours, it is clear that Barbara is not the slowest. So, the answer is between Alice and Cynia. We know that Alice's rate = 1/21 and Barbara's rate = 1/14. At these values, Barbara's rate = [(1/21) / (1/14)]*100% = (14/21)*100% = (2/3)*100% = 66.66% of Alice's rate From the statement, we know that Barbara and Cynia working together can complete the task in approximately 86% of the time taken by Alice and Cynia working together to complete the task. When Barbara teams up with Cynia and Alice teams up with Cynia, Barbara and Cynia together Vs. Alice and Cynia (86% > 66.66%) is not as efficient as Barbara alone Vs. Alice alone (66.6%). Let's understand this better. Let's assume that the rates of Alice and Cynic are equal, then Barbara and Cynia working together SHOULD complete the task in 86% 66.66% of the time taken by Alice and Cynia working together. However,actuals not so, the actual figure is 86% > 66.67%. It implies that the rate of Cynia must be less than that of Alice. Thus, Cynia is the slowest. Sufficient. (2) Barbara and Cynia can complete the task in approximately 71% of the time taken for Alice and Barbara to complete the task. There are three variable rates of Alice, Barbara and Cynia and we know the rate of only Alice, thus, we cannot compare the values.Isufficient. The correct answer: A Hope this helps! -Jay _________________ Manhattan Review GMAT Prep Locations: New York | Hyderabad | Mexico City | Toronto | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. Last edited by Jay@ManhattanReview on Sat Oct 13, 2018 5:49 pm; edited 1 time in total • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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