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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 ## Automobile A is traveling at two-thirds the speed that tagged by: AAPL ##### This topic has 2 expert replies and 0 member replies ### Top Member ## Automobile A is traveling at two-thirds the speed that ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Princeton Review Automobile A is traveling at two-thirds the speed that Automobile B is traveling. How fast is Automobile A traveling? 1) If both automobiles increased their speed by 10 miles per hour, Automobile A would be traveling at three-quarters the speed that Automobile B would be traveling. 2) If both automobiles decreased their speed by 10 miles per hour, Automobile A would be traveling at half the speed that Automobile B would be traveling. OA D ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12827 messages Followed by: 1247 members Upvotes: 5254 GMAT Score: 770 AAPL wrote: Princeton Review Automobile A is traveling at two-thirds the speed that Automobile B is traveling. How fast is Automobile A traveling? 1) If both automobiles increased their speed by 10 miles per hour, Automobile A would be traveling at three-quarters the speed that Automobile B would be traveling. 2) If both automobiles decreased their speed by 10 miles per hour, Automobile A would be traveling at half the speed that Automobile B would be traveling. OA D Given: Automobile A is traveling at two-thirds the speed that Automobile B is traveling. Let A = Car A's speed Let B = Car B's speed So, we can write: A = (2/3)B Target question: What is the value of A? Statement 1: If both automobiles increased their speed by 10 miles per hour, Automobile A would be traveling at three-quarters the speed that Automobile B would be traveling. Car A's new speed = A + 10 Car B's new speed = B + 10 So, we can write: A + 10 = (3/4)(B + 10) We already know that: A = (2/3)B IMPORTANT: Since we have a system of 2 different linear equations with 2 variables, we COULD solve the system for A and B (but we'd never waste valuable time on test day doing so) So, we COULD answer the target question with certainty. Statement 1 is SUFFICIENT Statement 2: If both automobiles decreased their speed by 10 miles per hour, Automobile A would be traveling at half the speed that Automobile B would be traveling Car A's new speed = A - 10 Car B's new speed = B - 10 So, we can write: A - 10 = (1/2)(B - 10) We already know that: A = (2/3)B Once again, we have a system of 2 different linear equations with 2 variables, which we COULD solve for A and B. Statement 2 is SUFFICIENT Answer: D Cheers, Brent _________________ Brent Hanneson â€“ 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 GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 AAPL wrote: Princeton Review Automobile A is traveling at two-thirds the speed that Automobile B is traveling. How fast is Automobile A traveling? 1) If both automobiles increased their speed by 10 miles per hour, Automobile A would be traveling at three-quarters the speed that Automobile B would be traveling. 2) If both automobiles decreased their speed by 10 miles per hour, Automobile A would be traveling at half the speed that Automobile B would be traveling. Excellent opportunity for the k technique, one of our powerful tools when dealing with ratios! $$A = {2 \over 3}B\,\,\,\,\,\mathop \Rightarrow \limits^{B\,\, \ne \,\,0} \,\,\,\,\,{A \over B} = {2 \over 3}\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\{ \matrix{ \,A = 2k \hfill \cr \,B = 3k \hfill \cr} \right.\,\,\,\,\,\left( {k > 0} \right)\,\,\,\,\,\,\,\,\,\left[ {\,k\,\,{\rm{in}}\,\,{\rm{mph}}\,} \right]$$ $$? = A\,\,\,\,\, \Leftrightarrow \,\,\,\,\boxed{\,? = k\,}$$ $$\left( 1 \right)\,\,\,2k + 10 = {3 \over 4}\left( {3k + 10} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,k\,\,\,{\rm{unique}}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{SUFF}}.$$ $$\left( 2 \right)\,\,\,2k - 10 = {1 \over 2}\left( {3k - 10} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,k\,\,\,{\rm{unique}}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{SUFF}}.$$ 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 • 1 Hour Free BEAT THE GMAT EXCLUSIVE 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 • FREE GMAT Exam Know how you'd score today for$0

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