Question: A train traveled from Station A to Station B at an average speed of 80 kilometers per hour and then from Station B to Station C at an average speed of 60 kilometers per hour. If the train did not stop at Station B, what was the average speed at which the train traveled from Station A to C?
- The distance that the train traveled from Station A to Station B was 4 times the distance that train traveled from Station B to Station C
- The amount of time it took to the train travel from Station A to Station B is 3 times that amount of time that it took the train to travel from Station B to Station C
- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- EACH statement ALONE is sufficient.
- Statements (1) and (2) TOGETHER are NOT sufficient.
Answer:
Solution with Explanation:
Approach Solution (1):
Average speed = \(\frac{Total distance}{Total time}\)
(1) A --- B --- C
Let BC = x, therefore AC = 4x, and AB = 3x
Thus average speed = \(\frac{4x}{\frac{3x}{80}+\frac{x}{60}}\)
We can easily calculate the value of average speed from the above exp.
Hence sufficient
(2) A --- B ---- C
Let distance between AB = x and BC = y
\(\frac{x}{80}=\frac{4y}{60}\)
We can substitute the value of x in terms of y in the above expression to find out the average speed
Hence sufficient
Correct Option: D
Approach Solution (2):
We are given the average speed from Station A to Station B and the average speed from Station B to Station C.
A couple of things we can take away right away:
- The average speed must be between 60 kilometers and 80 kilometers
- Since we are provided the average speed of both parts, we only need a ratio of each distance or a ratio of time spent in each part in order to find a conclusive answer.
S1 gives us a ratio of distance traveled. With a ratio of the distance traveled, we can determine the time spent in each part and come up with an average speed
Sufficient
S2 tells us a ratio of the time spent in each part. With a ratio of time spent, we can determine an average speed.
Sufficient
Correct Option: D
Approach Solution (3):
Let \(d_1\)km be the distance between Station A and Station B, and let \(d_2\)km be the distance between Station B and Station C.
Then \(\frac{d_1}{80}\)is the amount of time, in hours, the train took to travel from Station A to Station B, and \(\frac{d_2}{60}\)is the amount of time, in hours, the train took to travel from Station B to Station C.
Determine the value of \(\frac{d_1+d_2}{\frac{d_1}{80}+\frac{d_2}{60}}\)\(\)
(1) It is given that. Therefore,
\(\frac{d_1+d_2}{\frac{d_1}{80}+\frac{d_2}{60}} =\frac{4d_2+d_2}{\frac{4d_2}{80}+\frac{d_2}{60}} =\frac{d_2(4+1)}{d_2(\frac {4}{80}+\frac{1}{60})} = \frac{(4+1)}{(\frac {4}{80}+\frac{1}{60})}\)\(\)
Sufficient
(2) It is given that \(\frac{d_1}{80}=3\frac{d_2}{60}\) or \(\frac{d_1}{80} = \frac{d_2}{20}\)
It follows that \(20d_1=80d_2\)or \(d_1 = 4d_2\), which is the same relationship given in (1)
Sufficient
Correct Option: D
“A train traveled from Station A to Station B at an average speed of 80 kilometers per hour and then from Station B to Station C at an average speed of 60 kilometers per hour. If the train did not stop at Station B, what was the average speed at which the train traveled from Station A to C?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.
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