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 ≠290/6.
Since different average speeds are possible, INSUFFICIENT.
The correct answer is
A.
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