Walkabout wrote:
At what speed was a train traveling on a trip when it had completed half of the total distance of the trip?
(1) The trip was 460 miles long and took 4 hours to complete.
(2) The train traveled at an average rate of 115 miles per hour on the trip.
Target question: At what speed was a train traveling on a trip when it had completed half of the total distance of the trip? Statement 1: The trip was 460 miles long and took 4 hours to complete. IMPORTANT: there is nothing in this question to suggest that the train is traveling at a
CONSTANT speed. So, there's no way to determine the train's speed when it had competed half of the trip. To see what I mean, consider these two conflicting cases:
Case a: the train travels the first half (230 miles) of the trip at a constant speed 230 mph (for 1 hour), and then travels the second half (230 miles) at a constant speed 230/3 mph (for 3 hours). In this case,
the train was traveling at 230 mph when it had completed half of the total distance of the tripCase b: the train travels at a constant speed of 115 mph for the ENTIRE trip. In this case,
the train was traveling at 115 mph when it had completed half of the total distance of the tripSince we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The train traveled at an average rate of 115 miles per hour on the trip. NOTE: This statement
doesn't provide any new information.
That is, from statement 1, we can already determine that the trains average speed = (460 miles)/(4 hours) = 115 mph.
So, it's POSSIBLE to use the same counter-examples that we used for statement 1:
Case a: the train travels the first half (230 miles) of the trip at a constant speed 230 mph (for 1 hour), and then travels the second half (230 miles) at a constant speed 230/3 mph (for 3 hours). In this case,
the train was traveling at 230 mph when it had completed half of the total distance of the tripCase b: the train travels at a constant speed of 115 mph for the ENTIRE trip. In this case,
the train was traveling at 115 mph when it had completed half of the total distance of the tripSince we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined IMPORTANT: Notice that I was able to use the
same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED, which means the combined statements are still NOT SUFFICIENT
Answer: E
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