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If a bus took 4 hours to travel from town A to town B, what was its 09 May 2023, 13:49
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45% (02:12) correct 55% (01:55) wrong based on 193 sessions

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If a bus took 6 hours to travel from town A to town B, what was its average speed for the entire trip?


(1) In the first 2 hours, the bus covered a distance of 150 miles.

(2) The average speed of the bus for the first half of the distance was twice its average speed for the second half of the distance.


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C
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If a bus took 4 hours to travel from town A to town B, what was its 10 May 2023, 00:44
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Bunuel
If a bus took 4 hours to travel from town A to town B, what was its average speed for the entire trip?


(1) In the first 2 hours, the bus covered a distance of 150 miles.

(2) The average speed of the bus for the first half of the distance was twice its average speed for the second half of the distance.

Show more

Given:Total time taken by the bus = 4 hours

Statement 1

(1) In the first 2 hours, the bus covered a distance of 150 miles.

We are not given the information on the distance the bus covers in the subsequent two hours. Hence, the statement alone is not sufficient to find the average speed.

Eliminate A and D.

Statement 2

(2) The average speed of the bus for the first half of the distance was twice its average speed for the second half of the distance.

This statement is quite interesting!

As the average speed of the bus first half of the distance was twice the average speed for the second half of the distance, we can infer that the time taken for the bus to travel the first half of the distance was half the time taken to travel the second half of the distance.

Let's assume that the distance between A and B = 2d

Attachment:
GC1.jpg
GC1.jpg [ 28.26 KiB | Viewed 7467 times ]

Average speed = \(\frac{2d}{3t_1}\)

We also know that \(3t_1 = 4\), therefore the average speed = \(\frac{2d}{4} = \frac{d}{2}\)

While we find the values of the individual time, \(t_1 = \frac{4}{3}\) and \(t_2 = \frac{8}{3}\), we do not know the distance d, hence the statement is not sufficient on its own. We can eliminate B.

Combined

The statements combined tell us the following
  1. From statement 2 - The bus took 4/3 hours to travel half the distance (i.e. d miles)
  2. From statement 1 - The bus traveled 150 miles in 2 hours
  3. From statement 2 - The average speed of the bus for the first half of the distance was twice its average speed for the second half of the distance.

We can visualize the information as shown below -

Attachment:
GC2.jpg
GC2.jpg [ 32.94 KiB | Viewed 7366 times ]

M ⇒ Is the midpoint between A and B
N ⇒ Is the distance the bus travels in 2 hours, i.e. AN = 150 miles

The bus travels a distance 'd', denoted by AM, in \(\frac{4}{3}\) hours.

We are given information on the average speed of the bus between points AM and MB, however, no information is given if the bus travels at a constant speed between these distances. Hence, we cannot find an exact value of 'd'. In other words, for different values of 'd' we can have different average speeds.

To understand this better let's take the following cases

Case 1

Attachment:
GC3.jpg
GC3.jpg [ 29.86 KiB | Viewed 7313 times ]

AB = 160 miles
AM = MB = 80 miles

Between A and M

Distance = 80 miles
Speed of the bus between points A and M = 60 mph
Time taken by the bus to cover AM = \(\frac{80}{60}\) = \(\frac{4}{3}\) hours
Average Speed between AM= 60 mph

Between M and N

Distance = 70 miles
Speed of the bus between points M and N = 105 mph
Time taken by the bus to cover AM = \(\frac{70}{105}\) = \(\frac{2}{3}\) hours

Between N and B

Distance = 10 miles (the distance is taken as 10 miles so as to keep MB = 80 miles)
Time taken by the bus to cover NB =2 hours (because total time is 4 hours)
Speed of the bus between points M and N = 5 mph
Average Speed between MN= \(\frac{80}{ 2+\frac{2}{3}\) = 30 mph

The average speed between AB = \(\frac{160}{ 4}\) = 40 mph

Case 2

Attachment:
GC4.jpg
GC4.jpg [ 31.54 KiB | Viewed 7183 times ]

AB = 240 miles
AM = MB = 120 miles

Between A and M

Distance = 120 miles
Speed of the bus between points A and M = 90 mph
Time taken by the bus to cover AM = \(\frac{120}{90}\) = \(\frac{4}{3}\) hours
Average Speed between AM= 90 mph

Between M and N

Distance = 30 miles
Speed of the bus between points M and N = 45 mph
Time taken by the bus to cover AM = \(\frac{30}{45}\) = \(\frac{2}{3}\) hours

Between N and B

Distance = 90 miles (the distance is taken as 90 miles so as to keep MB = 120 miles)
Time taken by the bus to cover NB =2 hours (because total time is 4 hours)
Speed of the bus between points M and N = 45 mph
Average Speed between MN= \(\frac{120}{ 2+\frac{2}{3}\) = 45 mph

The average speed between AB = \(\frac{240}{ 4}\) = 60 mph

As we are getting two different values for the average speed, the statements combined are not sufficient.

Option E
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If a bus took 4 hours to travel from town A to town B, what was its 10 May 2023, 00:54
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Bunuel
If a bus took 4 hours to travel from town A to town B, what was its average speed for the entire trip?


(1) In the first 2 hours, the bus covered a distance of 150 miles.

(2) The average speed of the bus for the first half of the distance was twice its average speed for the second half of the distance.


Given:Total time taken by the bus = 4 hours

Statement 1

(1) In the first 2 hours, the bus covered a distance of 150 miles.

We are not given the information on the distance the bus covers in the subsequent two hours. Hence, the statement alone is not sufficient to find the average speed.

Eliminate A and D.

Statement 2

(2) The average speed of the bus for the first half of the distance was twice its average speed for the second half of the distance.

This statement is quite interesting!

As the average speed of the bus first half of the distance was twice the average speed for the second half of the distance, we can infer that the time taken for the bus to travel the first half of the distance was half the time taken to travel the second half of the distance.

Let's assume that the distance between A and B = 2d

Attachment:
GC1.jpg

Average speed = \(\frac{2d}{3t_1}\)

We also know that \(3t_1 = 4\), therefore the average speed = \(\frac{2d}{4} = \frac{d}{2}\)

While we find the values of the individual time, \(t_1 = \frac{4}{3}\) and \(t_2 = \frac{8}{3}\), we do not know the distance d, hence the statement is not sufficient on its own. We can eliminate B.

Combined

The statements combined tell us the following
  1. From statement 2 - The bus took 4/3 hours to travel half the distance (i.e. d miles)
  2. From statement 1 - The bus traveled 150 miles in 2 hours
  3. From statement 2 - The average speed of the bus for the first half of the distance was twice its average speed for the second half of the distance.

We can visualize the information as shown below -

Attachment:
GC2.jpg

M ⇒ Is the midpoint between A and B
N ⇒ Is the distance the bus travels in 2 hours, i.e. AN = 150 miles

The bus travels a distance 'd', denoted by AM, in \(\frac{4}{3}\) hours.

We are given information on the average speed of the bus between points AM and MB, however, no information is given if the bus travels at a constant speed between these distances. Hence, we cannot find an exact value of 'd'. In other words, for different values of 'd' we can have different average speeds.

To understand this better let's take the following cases

Case 1

Attachment:
GC3.jpg

AB = 160 miles
AM = MB = 80 miles

Between A and M

Distance = 80 miles
Speed of the bus between points A and M = 60 mph
Time taken by the bus to cover AM = \(\frac{80}{60}\) = \(\frac{4}{3}\) hours
Average Speed between AM= 60 mph

Between M and N

Distance = 70 miles
Speed of the bus between points M and N = 105 mph
Time taken by the bus to cover AM = \(\frac{70}{105}\) = \(\frac{2}{3}\) hours

Between N and B

Distance = 10 miles (the distance is taken as 10 miles so as to keep MB = 80 miles)
Time taken by the bus to cover NB =2 hours (because total time is 4 hours)
Speed of the bus between points M and N = 5 mph
Average Speed between MN= \(\frac{80}{ 2+\frac{2}{3}\) = 30 mph

The average speed between AB = \(\frac{160}{ 4}\) = 40 mph

Case 2

Attachment:
GC4.jpg

AB = 240 miles
AM = MB = 120 miles

Between A and M

Distance = 120 miles
Speed of the bus between points A and M = 90 mph
Time taken by the bus to cover AM = \(\frac{120}{90}\) = \(\frac{4}{3}\) hours
Average Speed between AM= 90 mph

Between M and N

Distance = 30 miles
Speed of the bus between points M and N = 45 mph
Time taken by the bus to cover AM = \(\frac{30}{45}\) = \(\frac{2}{3}\) hours

Between N and B

Distance = 90 miles (the distance is taken as 90 miles so as to keep MB = 120 miles)
Time taken by the bus to cover NB =2 hours (because total time is 4 hours)
Speed of the bus between points M and N = 45 mph
Average Speed between MN= \(\frac{120}{ 2+\frac{2}{3}\) = 45 mph

The average speed between AB = \(\frac{240}{ 4}\) = 60 mph

As we are getting two different values for the average speed, the statements combined are not sufficient.

Option E
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I'm so sorry, it should have been "If a bus took 6 hours" instead of "If a bus took 4 hours"
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If a bus took 4 hours to travel from town A to town B, what was its 10 May 2023, 01:19
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Bunuel
If a bus took 6 hours to travel from town A to town B, what was its average speed for the entire trip?


(1) In the first 2 hours, the bus covered a distance of 150 miles.

(2) The average speed of the bus for the first half of the distance was twice its average speed for the second half of the distance.

Show more

Bunuel

I'm so sorry, it should have been "If a bus took 6 hours" instead of "If a bus took 4 hours"
Show more

Nevermind Bunuel!

I will re-use most of my work :)

Given:Total time taken by the bus = 6 hours

Statement 1

(1) In the first 2 hours, the bus covered a distance of 150 miles.

We are not given the information on the distance the bus covers in the subsequent two hours. Hence, the statement alone is not sufficient to find the average speed.

Eliminate A and D.

Statement 2

(2) The average speed of the bus for the first half of the distance was twice its average speed for the second half of the distance.

This statement is quite interesting! (what - not again!)

As the average speed of the bus first half of the distance was twice the average speed for the second half of the distance, we can infer that the time taken for the bus to travel the first half of the distance was half the time taken to travel the second half of the distance.

Let's assume that the distance between A and B = 2d

Attachment:
GC1.1.jpg
GC1.1.jpg [ 28.26 KiB | Viewed 6938 times ]

Average speed = \(\frac{2d}{3t_1}\)

We also know that \(3t_1 = 6\), therefore the average speed = \(\frac{2d}{6} = \frac{d}{3}\)

While we find the values of the individual time, \(t_1 = \frac{6}{3}= 2\) and \(t_2 = 4\), we do not know the distance d, hence the statement is not sufficient on its own. We can eliminate B.

Combined

From statement 1, we know that the distance traveled in two hours = 150 miles.

From statement 2, we were able to infer that \(t_1\) = 2 hours, and the bus traveled half the distance at that time. Hence d = 150 miles

Therefore we can now find the average speed = \(\frac{d}{3}\)

The statements combined are sufficient to answer the question.

Option C

P.S. - I still like the previous version of the question, it was trickier to fall for the C trap in that version :twisted:

Nevertheless - Great Questions as always!
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If a bus took 4 hours to travel from town A to town B, what was its 03 Jun 2023, 08:45
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Bunuel
If a bus took 4 hours to travel from town A to town B, what was its average speed for the entire trip?


(1) In the first 2 hours, the bus covered a distance of 150 miles.

(2) The average speed of the bus for the first half of the distance was twice its average speed for the second half of the distance.


Try this fresh challenging question from our new edition of GMAT Club Tests.

 


Enjoy this brand new question we just created for the GMAT Club Tests.

To get 1,600 more questions and to learn more visit: user reviews | learn more

 

Show more

If a bus took 6 hours to travel from town A to town B, what was its average speed for the entire trip?

(1) In the first 2 hours, the bus covered a distance of 150 miles.

This information provides the average speed of the bus for the first 150 miles, which was 75 miles per hour. However, we don't know its average speed for the remaining 4 hours of the journey. Not sufficient.

(2) The average speed of the bus for the first half of the distance was twice its average speed for the second half of the distance.

This statement implies that the bus covered the first half of the distance in half the time it took to cover the second half of the distance. Since the journey took a total of 6 hours, the bus took 2 hours to cover the first half of the distance and 4 hours to cover the second half of the distance. Not sufficient.

(1)+(2) From (1), we know that in the first 2 hours, the bus covered a distance of 150 miles. From (2), we know that it took the bus 2 hours to cover the first half of the distance. Consequently, the entire journey was 300 miles long. As it took 6 hours to cover this distance, the average speed for the entire trip was 300/6 = 50 miles per hour. Sufficient.


Answer: C
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