A train traveled from Station A to Station B at an average speed of 80

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 to travel from Station A to Station B is 3 times the amount of time that it took the train to travel from Station B to Station C.

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Official Answer

D

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balamoon · Accepted Answer

The clear way to handle this answer -

chetan2u · Answer

Hi  ElCorazon ,
the Q stem tells us the speed in two different routes and asks us the average speed..
for this we require the distance or the ratio of distances..
lets see the statement..
1)statement 1 gives us the ratio of distance .. so sufficient..
2) statement two tells us the ratio of time so multiplying this ratio with speed would give us the ratio of distance .. again sufficient

ans D

manpreetsingh86 · Answer

Average speed = total distance/ total time.

1) A-----B-------C

let bc=x, therefore AC=4x, and AB=3x

thus average speed = 4x/{(3x/80)+(x/60)}

we can easily calculate the value of avg. speed from the above exp. hence sufficient

2) A---------B----------c

let distance between AB=x and BC=y
x/80=4(y/60)

x=(16/3)y-------------1)

average speed = x+y/{(x/80)+(y/60)}

we can substitute the value of x in terms of y in the above expression to find out the average speed. hence sufficient

therefore correct answer should be D

ElCorazon · Answer

Is there a quicker way to see that the distance variable cancels out, rather than going through the entire algebraic calculation? I made the assumption that the variable would remain, and struggle to finish in ~ 2 minutes once I start getting into algebra for DS questions. Thanks..

EMPOWERgmatRichC · Answer

Hi ElCorazon,

The 'goal' to try to answer each Quant question in under 2 minutes is NOT practical. While some questions can be solved relatively quickly (in under 30 seconds), certain questions are designed to take longer to solve (upwards of 3 minutes, and that's if you KNOW what you're doing). These types of "multi-step trip" questions are usually wordier, take more steps to solve and require a higher degree of organization and attention-to-detail than most prompts, so it's understandable that you would need MORE than 2 minutes to solve it.

Instead of having a "2 minutes or less" goal, focus more on your overall efficiency - you should try to get this question correct without wasting time.

GMAT assassins aren't born, they're made,
Rich

Konstantin1983 · Answer

Hi Rich!
I watched EMPOWERGmat course and you said that if we have a ratios that means that statement is sufficient. Hence answer is D. Do i think logically?=))

VeritasPrepBrandon · Answer

This question is not correct, because the statements conflict each other. It is impossible that, given A to B is 80 mph and B to C is 60 mph, both of these statements could be true. Think about this example:

Statement 1 - assume distance from A to C is 320 miles. Because A to C is 4x B to C, then A to B is 3x B to C. Its a 3:1 ratio in the distances. Therefore we have 240 miles from A to B and 80 miles from B to C. That leaves us with time of 3 hours from A to B and time of 1 hour 20 minutes from B to C.

Statement 2- this can't be possible given what we just figured out in statement 1. 3:1.33 does not equal 3:1.

The question is flawed.

Bunuel · Answer

Thank you for noticing this. Edited the question.

XYZABCABC · Answer

Hello Sir,

I have understood the question and the answer to it. However, this question has put questions on my understanding.

For "Averages", we take the ratios. I have always understood that when it is average speeds, ratio of "time" needs to be taken and not the ratio of "distances". But here by ratio of distances, we are able to arrive at the average speed. Has my understanding been wrong?

Please assist.

Bunuel · Answer

This is a data sufficiency question. Options for DS questions are always the same.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

I suggest you to go through the following posts: 
 ALL YOU NEED FOR QUANT .
 Ultimate GMAT Quantitative Megathread

Hope this helps.

dabaobao · Answer

Avg Speed = Total Distance/Total Time

Stmt 1) D1 = 4x; D2 = x
Avg Speed = 5x/((4x/8) + (x/60)
Sufficient

Stmt 2) T1 = 3t; T2 = t
Avg Speed = (3t*80 + t*60)/4t
Sufficient

ANSWER: D

Basshead · Answer

We're looking for the average speed at which the train traveled from Station A to C.

We are given the average speed from Station A to Station B and the average speed from Station B to Station C.

A couple things we can take away right away:
- The average speed must be between 60 kilometers and 80 kilometers.
- Since we're 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.

Statement 1 gives us a ratio of the 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.

Statement 2 tells us a ratio of the time spent in each part. With a ratio of time spent, we can determine an average speed. Sufficient.

AnishPassi · Answer

No, your understanding isn't wrong.
If we are given the speeds and the ratio of distances, we can still figure out the ratio of 'times'.

The average speeds are 80 and 60 kmph.
Say the distance from
A to B is 120 km
B to C is 30 km

Then, the time taken from
A to B would be 1.5 hours
B to C would be 0.5 hours

The two times are in a ratio of 3:1

Even if you take some other distances, the ratio would remain the same.

The average speeds are 80 and 60 kmph.
Say the distance from
A to B is 240 km
B to C is 60 km

Then, the time taken from
A to B would be 3 hours
B to C would be 1 hour

Ratio of 3:1

Basically, if the distances are 4x and x km, and the speeds are 80kmph and 60kmph, , the times would be in the following ratio:

4x/80 : x/60
--> 1/20 : 1/60
--> 60 : 20
--> 3 : 1

2019ms8915 · Answer

use weighted average with time as the weight - super fast

Gaurav07 · Answer

What would roughly be the level of this question?

Bunuel · Answer

You can always check the stats on the question in the tags and the original post: https://gmatclub.com/forum/download/file.php?id=87075 GMAT-Club-Forum-hhzuwe1j.png

A train traveled from Station A to Station B at an average speed of 80

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GMAT Data Sufficiency (DS) Questions

A train traveled from Station A to Station B at an average speed of 80

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