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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 straight highway connects two cities P and Q, and goes via ##### This topic has 2 expert replies and 0 member replies ### Top Member ## A straight highway connects two cities P and Q, and goes via ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult A straight highway connects two cities P and Q, and goes via two checkpoints M and N, in that order. A bus started from P and moved to M at an average speed of 30 mph. After crossing M, it increased its speed to 50 mph and moved towards N. When it reached N, it further increased its speed to 60 mph and continued to move at this speed till it reached Q. What is the average speed of the bus throughout the whole journey? Statement 1: The ratio of time the bus took to cover the distances PM, MN, and NQ respectively is 2:1:3 Statement 2: Out of the three distances, NQ is 3 times the distance PM and more than 3 times the distance MN OA A Source: e-GMAT ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15344 messages Followed by: 1864 members Upvotes: 13060 GMAT Score: 790 Top Reply BTGmoderatorDC wrote: A straight highway connects two cities P and Q, and goes via two checkpoints M and N, in that order. A bus started from P and moved to M at an average speed of 30 mph. After crossing M, it increased its speed to 50 mph and moved towards N. When it reached N, it further increased its speed to 60 mph and continued to move at this speed till it reached Q. What is the average speed of the bus throughout the whole journey? Statement 1: The ratio of time the bus took to cover the distances PM, MN, and NQ respectively is 2:1:3 Statement 2: Out of the three distances, NQ is 3 times the distance PM and more than 3 times the distance MN Statement 1: For every 2 hours spent at 30 mph and 1 hour spent at 50 mph, 3 hours are spent at 60 mph. Average speed per 6 hours = (2*30 + 1*50 + 3*60)/6 = 290/6. SUFFICIENT. Statement 2: Case 1: NQ = 180 miles, PM = 60 miles and MN = 50 miles Since NQ is traveled at 60 mph, the time for NQ =180/60 = 3 hours. Since PM is traveled at 30 mph, the time for PM = 60/30 = 2 hours. Since MN is traveled at 50 mph, the time for MN = 50/50 = 1 hour. Time ratio for PM, MN, and NQ = 2:1:3. Same time ratio as in Statement 1, implying that the average speed = 290/6. Case 2: NQ=180 miles, PM=60 miles and MN=10 miles Since NQ is traveled at 60 mph, the time for NQ =180/60 = 3 hours. Since PM is traveled at 30 mph, the time for PM = 60/30 = 2 hours. Since MN is traveled at 50 mph, the time for MN = 25/50 = 0.5 hour. Time ratio for PM, MN, and NQ = 2 : 0.5 : 3. Case 2 yields a different time ratio, with the result that the average speed â‰ 290/6. Since different average speeds are possible, INSUFFICIENT. The correct answer is A. _________________ 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: 1975 messages Followed by: 30 members Upvotes: 470 Top Reply BTGmoderatorDC wrote: A straight highway connects two cities P and Q, and goes via two checkpoints M and N, in that order. A bus started from P and moved to M at an average speed of 30 mph. After crossing M, it increased its speed to 50 mph and moved towards N. When it reached N, it further increased its speed to 60 mph and continued to move at this speed till it reached Q. What is the average speed of the bus throughout the whole journey? Statement 1: The ratio of time the bus took to cover the distances PM, MN, and NQ respectively is 2:1:3 Statement 2: Out of the three distances, NQ is 3 times the distance PM and more than 3 times the distance MN OA A Source: e-GMAT See the diagram depicting the highway. P -------30 mph---------M -------50 mph--------- N --------60 mph---------- Q Let's take each statement one by one. Statement 1: The ratio of time the bus took to cover the distances PM, MN, and NQ respectively is 2:1:3. Say, the time the bus took to cover the distances PM, MN, and NQ, respectively is 2x, x, and 3x. Thus, distance PM = 30 mph * 2x = 60x; distance MN = 50 mph * x = 50x; distance NQ = 60 mph * 3x = 180x Distance PQ = 60x + 50x = 180x = 290x miles Total time = 2x + x + 3x = 6x hours Average speed = 290x / 6x = 290/6 mph. Sufficient. Statement 2: Out of the three distances, NQ is 3 times the distance PM and more than 3 times the distance MN The phrase, "more than 3 times the distance MN," does not permit to fix the ratio of distances, making it not possible to find the average speed. Insufficient. The correct answer: A Hope this helps! -Jay _________________ Manhattan Review GMAT Prep Locations: GMAT Classes Manhattan | GMAT Prep Courses New Delhi | LSAT Prep Courses Hong Kong | Singapore SAT Prep Classes | and many more... 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