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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 ## Pat, Kate and Marck charged a total of 162 hours of... tagged by: AAPL ##### This topic has 3 expert replies and 0 member replies ### Top Member ## Pat, Kate and Marck charged a total of 162 hours of... Pat, Kate, and Marck charged a total of 162 hours of a certain project. If Pat charged twice as much time to the project as Kate and 1/3 as much times as Marck. How many more hours did Marck charge to the project than Kate? A. 18 B. 36 C. 72 D. 90 E. 108 The OA is D. I think that it can be solved as follow, If Pat, Kate, and Marck charged o total of 162 hours, it can be written as $$P+K+M=162\ \ (1)$$ Pat charged twice as much time as Kate, it can be written as $$P=2K\ \ (2)$$ Pat charged 1/3 as much times as Mark, that's mean $$P=\frac{1}{3}M\ \ (3)$$ We have 3 equations and 3 incognitas, solving it we get, $$From\ \left(2\right)\ \Rightarrow K=\frac{P}{2}\$$ $$From\ \left(3\right)\ \Rightarrow M=3P\$$ Then, substituting them into (1), we get $$P+\frac{P}{2}+3P=162\ \Rightarrow P=36$$ Hence $$K=18,\ \ M=108$$ Finally $$M-K=108-18=90$$ Is there another strategic approach to solve this PS question? Can any experts help, please? ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 13046 messages Followed by: 1253 members Upvotes: 5254 GMAT Score: 770 Top Reply AAPL wrote: Pat, Kate, and Marck charged a total of 162 hours of a certain project. If Pat charged twice as much time to the project as Kate and 1/3 as much times as Marck. How many more hours did Marck charge to the project than Kate? A. 18 B. 36 C. 72 D. 90 E. 108 We can also solve the question using one variable We can see that Kate charged the fewest hours, so... Let x =the number of hours Kate charged Pat charged twice as much time to the project as Kate So, 2x = the number of hours Pat charged Pat charged 1/3 as much times as Mark In other words, Mark charged THREE TIMES as much time as Pat So, 3(2x ) = the number of hours Mark charged In other words, 6x = the number of hours Mark charged Pat, Kate and Mark charged a total of 162 hours to a certain project. We can write: x + 2x + 6x = 162 Simplify: 9x = 162 Solve: x = 18 So, Kate charged 18 hours When we plug x = 18 into 6x, we see that Mark charged 108 hours How many more hours did Mark charge to the project than Kate? Answer = 108 - 18 = 90 = D 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 May 2010 Posted: 15387 messages Followed by: 1872 members Upvotes: 13060 GMAT Score: 790 AAPL wrote: Pat, Kate, and Marck charged a total of 162 hours of a certain project. If Pat charged twice as much time to the project as Kate and 1/3 as much times as Marck. How many more hours did Marck charge to the project than Kate? A. 18 B. 36 C. 72 D. 90 E. 108 Test the SMALLEST POSSIBLE CASE. Let M = 6. Since Pat charged 1/3 as much as Mark, P = (1/3)(6) = 2. Since Pat charged twice as much as Kate, Kate's amount is 1/2 Pat's amount: K = (1/2)(2) = 1. Smallest possible total = 6+2+1 = 9. Since (actual total)/(smallest possible total) = 162/9 = 18, the values for M, P and K must each be increased by a factor of 18: M = 6*18 = 108, P = 2*18 = 36, K = 1*18 = 18, T = M+P+K = 108+36+18 = 162. Thus: M-K = 108-18 = 90. The correct answer is D. _________________ 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 Apr 2015 Posted: 1465 messages Followed by: 19 members Upvotes: 39 AAPL wrote: Pat, Kate, and Marck charged a total of 162 hours of a certain project. If Pat charged twice as much time to the project as Kate and 1/3 as much times as Marck. How many more hours did Marck charge to the project than Kate? A. 18 B. 36 C. 72 D. 90 E. 108 We can let P, K, and M = the amount time spent on the project by Pat, Kate, and Marck, respectively, and create the equations: P + K + M = 162 and P = 2K P/2 = K and P = (M)(1/3) 3P = M Substituting, we have: P + P/2 + 3P = 162 Multiplying by 2, we have: 2P + P + 6P = 324 9P = 324 P = 36, so M = 108 and K = 18. M - K = 108 - 18 = 90. Answer: D _________________ Jeffrey Miller Head of GMAT Instruction jeff@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. 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