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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 Autom ##### This topic has 1 expert reply and 1 member reply ### Top Member ## Automobile A is traveling at two-thirds the speed that Autom ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult 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 Source: Princeton Review ### Top Member Legendary Member Joined 02 Mar 2018 Posted: 1039 messages Followed by: 2 members $$A=\frac{2}{3}of\ B$$ How fast is Automobile A travelling Statement 1 If both automobiles increased their speed by 10 miles per hour, Automobile A would be travelling at three - quarter the speed that automobile B will be travelling. $$A+10=\frac{3}{4}of\ \left(B+10\right)$$ From question $$A=\frac{2}{3}B$$ $$\frac{2}{3}B+10=\frac{3}{4}B+\frac{80}{4}$$ $$\frac{2}{3}B-\frac{3}{4}B=\frac{30}{4}-10$$ $$\frac{8B-9B}{12}=\frac{30-40}{4}$$ $$-\frac{B}{12}=-\frac{10}{4}$$ $$-\frac{4B}{4}=-\frac{120}{4}$$ $$b=30$$ $$Since\ A=\frac{2}{3}of\ B$$ statement 1 is INSUFFICIENT. $$\frac{2}{3}\cdot30=20$$ Statement 2 If both automobile reduce their speed by 10 mph Automobile A will be travelling a 1/2 the speed of that B would be travelling. Therefore, $$A-10==\frac{1}{2}\left(B-10\right)where\ A=\frac{2}{3}B$$ $$\frac{2}{3}B-10=\frac{1}{2}B-5$$ $$\frac{2}{3}B-\frac{1}{2}B=-5+10$$ $$\frac{4B-3B}{6}=5$$ $$b=6\cdot5=30mph$$ $$where\ A=\frac{2}{3}of\ B$$ $$where\ A=\frac{2}{3}of\ 30$$ $$where\ A=20mph$$ Statement 2 is also SUFFICIENT. $$Answer\ is\ Option\ D$$ Both statement alone are SUFFICIENT. ### GMAT/MBA Expert GMAT Instructor Joined 02 Jun 2008 Posted: 2424 messages Followed by: 349 members Upvotes: 1090 GMAT Score: 780 Each Statement gives the same type of relationship between the two speeds, so the answer will be C, D or E. If we let a and b be the two speeds of the cars, we know that a = 2b/3. Using Statement 1 alone, you might be able to see by inspection that the speeds are 20 and 30. Or we can use algebra: a + 10 = (3/4)(b + 10) = (3b/4) + 7.5 Substituting for a, we have (2b/3) + 10 = (3b/4) + 7.5 which is an equation we can clearly solve for b, and thus we can find a. Statement 2 will produce a similar equation, so the answer is D. _________________ If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com • 5 Day FREE Trial Study Smarter, Not Harder 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 • Free Practice Test & Review How would you score if you took the GMAT 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 • Magoosh Study with Magoosh GMAT prep 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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