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speed

by jainrahul1985 » Sat Feb 26, 2011 7:33 am
It took the bus 4 hours to get from town A to town B. What was the average speed of the bus for the trip?

1. In the first 2 hours the bus covered 100 miles
2. The average speed of the bus for the first half of the distance was twice its speed for the second half

OA E
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Source: — Data Sufficiency |
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by Night reader » Sat Feb 26, 2011 8:23 am
given: T=4 (hours), D is a total distance, find average S (speed)-?
st(1) t(1)=2, D(part of the distance)=100, S(1)=100/2=50 since we don't have information about the total distance and the time or speed of bus for the second half of the distance - Not Sufficient;
st(2) S(2) speed for half of the distance=2*S(3) speed for the second half, BUT we don't what's the half of distance - Not Sufficient;
Combined: we have no reference points in st(1&2) Not Sufficient, hence E.
jainrahul1985 wrote:It took the bus 4 hours to get from town A to town B. What was the average speed of the bus for the trip?

1. In the first 2 hours the bus covered 100 miles
2. The average speed of the bus for the first half of the distance was twice its speed for the second half

OA E
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by Anurag@Gurome » Sat Feb 26, 2011 9:27 pm
Solution:
Average speed is = (Total distance)/(Total time taken to cover this distance).
Total time taken to cover this distance is 4 hours.
Let us first consider (1) alone.
In the first 2 hours, the bus covered 100 miles.
But we do not know the distance covered in next 2 hours.
Or (1) alone is not sufficient to answer the question.
We next consider (2) alone.
Let the total distance from A to B be d.
Let the average speed for the distance d/2 be s.
So, the time taken to cover this distance is d/2s.
Also, the speed for remaining d/2 distance is s/2.
So, the time taken to cover this distance is (d/2)/(s/2) = d/s.
Or total time taken is d/2s + d/s.
Or 3d/2s = 4.
Or d/s = 8/3.
Or average speed is d/4 = d/(3d/2s) = 2s/3.
But we do not know s or d.
Or (2) alone is not sufficient to answer the question.
We next combine both the statements together and check.
Even on combining, we do not come to know about s or d or anything else which tells us the average
speed.
Or both statements together are not sufficient to answer the question.

The correct answer is (E).
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