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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 ## A driver paid n dollars for auto insurance for the year tagged by: swerve ##### This topic has 5 expert replies and 0 member replies ### Top Member ## A driver paid n dollars for auto insurance for the year ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult A driver paid n dollars for auto insurance for the year 1997. This annual premium was raised by p percent for the year 1998; for each of the years 1999 and 2000, the premium was decreased by 1/6 from the previous year’s figure. If the driver’s insurance premium for the year 2000 was again n dollars, what is the value of p? $$A.\ 12$$ $$B.\ 33\ \frac{1}{3}$$ $$C.\ 36$$ $$D.\ 44$$ $$E.\ 50$$ The OA is D. Source: Manhattan Prep ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 1770 messages Followed by: 28 members Upvotes: 470 swerve wrote: A driver paid n dollars for auto insurance for the year 1997. This annual premium was raised by p percent for the year 1998; for each of the years 1999 and 2000, the premium was decreased by 1/6 from the previous year’s figure. If the driver’s insurance premium for the year 2000 was again n dollars, what is the value of p? $$A.\ 12$$ $$B.\ 33\ \frac{1}{3}$$ $$C.\ 36$$ $$D.\ 44$$ $$E.\ 50$$ The OA is D. Source: Manhattan Prep > 1997: Premium = n > 1998: Premium = n(1 + p%) > 1999: Premium = n(1 + p%) - n(1 + p%)/6 = 5n/6 * (1 + p%) > 2000: Premium = 5n/6 * (1 + p%) - 5n/36 * (1 + p%) = 25n/36 * (1 + p%) => 25n/36 * (1 + p%) = n 25/36 * (1 + p%) = 1 1 + p% = 36/25 p% = 36/25 - 1 p% = 11/25 p = 11/25 * 100 = 44 The correct answer: D Hope this helps! -Jay _________________ Manhattan Review GRE Prep Locations: GRE Classes Los Angeles | GMAT Prep Course Singapore | GRE Prep Orlando | SAT Prep Courses Toronto | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12663 messages Followed by: 1246 members Upvotes: 5254 GMAT Score: 770 swerve wrote: A driver paid n dollars for auto insurance for the year 1997. This annual premium was raised by p percent for the year 1998; for each of the years 1999 and 2000, the premium was decreased by 1/6 from the previous year’s figure. If the driver’s insurance premium for the year 2000 was again n dollars, what is the value of p? $$A.\ 12$$ $$B.\ 33\ \frac{1}{3}$$ $$C.\ 36$$ $$D.\ 44$$ $$E.\ 50$$ First recognize that INCREASING a value by p percent is the same as multiplying by (100 + p)/100 For example, increasing a value by 7% is the same as multiplying by (100 + 7)/100 [i.e. 1.07] Likewise, increasing a value by 25% is the same as multiplying by (100 + 25)/100 [i.e. 1.25] Also, recognize that DECREASING a value by 1/6 is the same as multiplying by 5/6 Okay, let's begin: Premium for 1997: n Premium for 1998: [(100 + p)/100]n Premium for 1999: (5/6)[(100 + p)/100]n Premium for 2000: (5/6)(5/6)[(100 + p)/100]n We're told that the premium for 2000 is n. So, we can write: (5/6)(5/6)[(100 + p)/100]n = n Divide both sides by n to get: (5/6)(5/6)[(100 + p)/100] = 1 Simplify: (25/36)[(100 + p)/100] = 1 Simplify: (25)(100 + p)/(36)(100) = 1 Simplify: (100 + p)/(36)(4) = 1 So we know that 100 + p = (36)(4) Simplify: 100 + p = 144 So, p = 44 Answer: D 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 09 Oct 2010 Posted: 1297 messages Followed by: 29 members Upvotes: 59 swerve wrote: A driver paid n dollars for auto insurance for the year 1997. This annual premium was raised by p percent for the year 1998; for each of the years 1999 and 2000, the premium was decreased by 1/6 from the previous year’s figure. If the driver’s insurance premium for the year 2000 was again n dollars, what is the value of p? $$A.\ 12 \,\,\,\,\,\,\,\, B.\ 33\ \frac{1}{3} \,\,\,\,\,\,\,\, C.\ 36 \,\,\,\,\,\,\,\, D.\ 44 \,\,\,\,\,\,\,\, E.\ 50$$ $? = p$ $97:\,\,n\,\,\,\,\,\, \to \,\,\,\,\,\,98:\,\,\,\left( {1 + \frac{p}{{100}}} \right)\,\,n\,\,\,\, \to \,\,\,\,99:\,\,\,\frac{5}{6}\,\,\,\left( {1 + \frac{p}{{100}}} \right)\,\,n\,\,\,\,\, \to \,\,00:\,\,\,{\left( {\frac{5}{6}} \right)^{\,2}}\,\left( {1 + \frac{p}{{100}}} \right)\,\,n$ ${\left( {\frac{5}{6}} \right)^{\,2}}\,\left( {1 + \frac{p}{{100}}} \right)\,\,n = n\,\,\,\,\, \Rightarrow \,\,\,\,\,\,1 + \frac{p}{{100}} = {\left( {\frac{6}{5}} \right)^{\,2}}\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = p = 100\left( {\frac{{36}}{{25}} - \frac{{1 \cdot \boxed{25}}}{{\boxed{25}}}} \right) = 4 \cdot 11 = 44$ 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 Apr 2015 Posted: 2012 messages Followed by: 15 members Upvotes: 43 swerve wrote: A driver paid n dollars for auto insurance for the year 1997. This annual premium was raised by p percent for the year 1998; for each of the years 1999 and 2000, the premium was decreased by 1/6 from the previous year’s figure. If the driver’s insurance premium for the year 2000 was again n dollars, what is the value of p? $$A.\ 12$$ $$B.\ 33\ \frac{1}{3}$$ $$C.\ 36$$ $$D.\ 44$$ $$E.\ 50$$ We can create the equation: n x (100 + p)/100 x 5/6 x 5/6 = n (100 + p)/100 x 25/36 = 1 (100 + p)/100 = 36/25 25(100 + p) = 100 x 36 100 + p = 4 x 36 100 + p = 144 p = 44 Answer: D _________________ Scott Woodbury-Stewart Founder and CEO ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10074 messages Followed by: 494 members Upvotes: 2867 GMAT Score: 800 Hi All, We're told that a driver paid N dollars for auto insurance for the year 1997. This annual premium was raised by P percent for the year 1998, then for EACH of the years 1999 and 2000, the premium was decreased by 1/6 from the previous year’s figure, leaving the driver’s insurance premium for the year 2000 at N dollars. We're asked for the value of P. This question can be solved with a mix of TESTing VALUES and TESTing THE ANSWERS. When TESTing THE ANSWERS, it's typically best to start with either Answer B or Answer D. Since Answer D is the 'nicer' of the two options, we'll start there. Answer D: 44 IF... P=44 and N=100, then.... Insurance in 1997 =$100
Insurance in 1998 = $100 + (44% of$100) = $100 +$44 = $144 Insurance in 1999 =$144 - (1/6)($144) =$144 - $24 =$120
Insurance in 2000 = $120 - (1/6)($120) = $120 -$20 = $100 The value of N is the SAME in 1997 and 2000, so this MUST be the answer. Final Answer: D GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep 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 • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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