A Train Traveled from Station A to Station B at an Average Speed of 80 GMAT Data Sufficiency

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?

1. 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
2. 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

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. 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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