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A straight highway connects two cities P and Q, and goes via

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A straight highway connects two cities P and Q, and goes via

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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

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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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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
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