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If Jamal drove 240 kilometers, what was his average speed for the 240 05 Aug 2023, 05:00
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If Jamal drove 240 kilometers, what was his average speed for the 240 kilometers that he drove?

(1) Jamal's average speed for the first 160 kilometers that he drove was 64 kilometers per hour.
(2) Jamal's average speed for the last 160 kilometers that he drove was 64 kilometers per hour.
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If Jamal drove 240 kilometers, what was his average speed for the 240 05 Aug 2023, 08:06
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Bunuel
If Jamal drove 240 kilometers, what was his average speed for the 240 kilometers that he drove?

(1) Jamal's average speed for the first 160 kilometers that he drove was 64 kilometers per hour.
(2) Jamal's average speed for the last 160 kilometers that he drove was 64 kilometers per hour.
Show more

A good one!

Statements 1 and Statement 2 are individually not sufficient to answer the question as we do not know the speed Jamal drove in the remaining 80 kilometers. Hence, we can easily eliminate options A, B, and D. The answer will either be C or it will be E.

Combined

(1) Jamal's average speed for the first 160 kilometers that he drove was 64 kilometers per hour.
(2) Jamal's average speed for the last 160 kilometers that he drove was 64 kilometers per hour.

Case 1: Jamal drove at a uniform speed of 64 km/hr throughout his journey

One of the possibilities can be that Jamal drove at a uniform speed of 64 km/hr. In this case, the average speed of his entire journey will be 64 km/hr.

Case 2: Jamal did not drive at a uniform speed of 64 km/hr throughout his journey

Note, both statements tell us about the "average" speed, and we do have an overlapping distance between the two statements. So, while we know the average speed, we don't have any information on the actual speed Jamal drove in any of the segments. For example, he could have driven the first few kilometers at a very low speed and then could have sped up and slowed down again or vice versa or could have varying speeds at different intervals. Thus, while the average speed of a segment of distance is 64 km/hr, we cannot conclude that the average speed of his entire journey is 64 km/hr.

To further understand this, let's consider the journey of 240 kilometers divided into three parts -

A-B → B-C → C-D

Jamal drove at a speed of 40 km/hr from A to B, 160 km/hr from B to C, and 40 km/hr from C to D.

  • Time taken between A and B = \(\frac{80}{40} = 2\) hours
  • Time taken between B and C = \(\frac{80}{160} = 0.5\) hours
  • Average Speed between A and C = \(\frac{80}{2.5} = 64\) kmph

  • Time taken between B and C = \(\frac{80}{160} = 0.5\) hours
  • Time taken between C and D = \(\frac{80}{40} = 2\) hours
  • Average Speed between B and D = \(\frac{80}{2.5} = 64\) kmph

  • Time taken between A and D = \(2 + 0.5 + 2 = 4.5\)
  • Average Speed between B and D = \(\frac{160}{4.5} \approx 35\) kmph

Hence, the statements combined don't help us arrive at a definite answer.

Attachment:
Screenshot 2023-08-05 202838.jpg
Screenshot 2023-08-05 202838.jpg [ 45.43 KiB | Viewed 47163 times ]

Note: We don't need to do the above math in the exam. Knowing the fact that we can possibly get different values of average speed because of the overlapping region is enough to conclude that the statement combined wouldn't help us get a definite answer.

Option E
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If Jamal drove 240 kilometers, what was his average speed for the 240 14 May 2024, 04:21
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Bunuel
If Jamal drove 240 kilometers, what was his average speed for the 240 kilometers that he drove?

(1) Jamal's average speed for the first 160 kilometers that he drove was 64 kilometers per hour.
(2) Jamal's average speed for the last 160 kilometers that he drove was 64 kilometers per hour.
Show more
­
The logic here is very simple with 0 calculations.

We have total 240 km. 

Each statement alone is not sufficient since it only tells us about a part of the entire distance. 

Using both, I split the 240 km into 3 parts of 80 km each. Over 2 of these parts, the average is 64 kmph. Say I assume that over the first part the average speed was 60 and over the second it was 70. That will give about 64 average for the first 160 kms. (Just estimates)
Now if the second part has an average of 70, the third part would have an average of 60 again to get 64 overall for the last 160 kms. 

Now what if I flip it? I give 70 to the first part and 60 to the second. Still I will get the same about 64 average for the first 160 kms.
and I will give 70 to the last part and get about 64 average for the last 160 kms.

But is the average speed in both cases same? No way! In one you travel 160 kms at 60 kmph and 80 km at 70 kmph. 
In the other you travel 160 km at 70 kmph and 80 km at 60 kmph. Your average speed in the second case will be much higher. 

Attachment:
Screenshot 2024-05-14 at 4.45.34 PM.png
Screenshot 2024-05-14 at 4.45.34 PM.png [ 99.59 KiB | Viewed 32522 times ]

Hence given data is not sufficient.

Answer (E)

 ­
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If Jamal drove 240 kilometers, what was his average speed for the 240 06 Sep 2023, 18:10
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Bunuel
If Jamal drove 240 kilometers, what was his average speed for the 240 kilometers that he drove?

(1) Jamal's average speed for the first 160 kilometers that he drove was 64 kilometers per hour.
(2) Jamal's average speed for the last 160 kilometers that he drove was 64 kilometers per hour.
Show more

Total distance = 240 km, and we need to answer the question:

Average speed = ?

Statement One Alone:

=> Jamal’s average speed for the first 160 kilometers that he drove was 64 kilometers per hour.

For the first 160 kilometers, we have:

Total time = Total distance/Average speed = 160/64 = 2.5 hours

Since we don’t have information about the last 80 kilometers of the journey, we can’t answer the question. Statement one is not sufficient. Eliminate answer choices A and D.

Statement Two Alone:

=> Jamal’s average speed for the last 160 kilometers that he drove was 64 kilometers per hour.

For the last 160 kilometers, we have:

Total time = Total distance/Average speed = 160/64 = 2.5 hours

Since we don’t have information about the first 80 kilometers of the journey, we can’t answer the question. Statement two is not sufficient. Eliminate answer choice B.

Statements One and Two Together:

Average speed = Total distance/Total time

Since there is an overlap between segments of the journey we have information about, the average speed for the complete journey can be anywhere in the following interval:

240/5 < Average speed < 240/2.5
48 kmph < Average speed < 96 kmph

The two statements together are not sufficient.

Answer: E
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If Jamal drove 240 kilometers, what was his average speed for the 240 06 Oct 2023, 05:27
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Bunuel
If Jamal drove 240 kilometers, what was his average speed for the 240 kilometers that he drove?

(1) Jamal's average speed for the first 160 kilometers that he drove was 64 kilometers per hour.
(2) Jamal's average speed for the last 160 kilometers that he drove was 64 kilometers per hour.

Total distance = 240 km, and we need to answer the question:

Average speed = ?

Statement One Alone:

=> Jamal’s average speed for the first 160 kilometers that he drove was 64 kilometers per hour.

For the first 160 kilometers, we have:

Total time = Total distance/Average speed = 160/64 = 2.5 hours

Since we don’t have information about the last 80 kilometers of the journey, we can’t answer the question. Statement one is not sufficient. Eliminate answer choices A and D.

Statement Two Alone:

=> Jamal’s average speed for the last 160 kilometers that he drove was 64 kilometers per hour.

For the last 160 kilometers, we have:

Total time = Total distance/Average speed = 160/64 = 2.5 hours

Since we don’t have information about the first 80 kilometers of the journey, we can’t answer the question. Statement two is not sufficient. Eliminate answer choice B.

Statements One and Two Together:

Average speed = Total distance/Total time

Since there is an overlap between segments of the journey we have information about, the average speed for the complete journey can be anywhere in the following interval:

240/5 [/color]< Average speed < 240/2.5
48 kmph < Average speed < 96 kmph

The two statements together are not sufficient.

Answer: E
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chetan2u - can you please explain why 240/5 is used as the minimum value for the range?
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If Jamal drove 240 kilometers, what was his average speed for the 240 06 Oct 2023, 11:06
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chetan2u - can you please explain why 240/5 is used as the minimum value for the range?
Show more


It is so because you can divide 240 km in three parts of 80km each.
A+B+C = 80+80+80 = 240

Combined we are given
For A+B, he takes 2.5h and again for B+C he takes 2.5h.
That is time for (A+B)+(B+C) is 2.5+2.5

1) MAX: He covers B in 2.5h, so, hypothetically, he covers A and also C in 0 h.
Total time is 2.5h for A+B+C, so max avg speed = 240/2.5

2) MIN: He covers B in 0h, so he covers A and also C in 2.5 h each.
Total time is 2.5+2.5 or 5h for A+B+C, so max avg speed = 240/5
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If Jamal drove 240 kilometers, what was his average speed for the 240 16 Mar 2024, 08:58
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gmatophobia

Bunuel
If Jamal drove 240 kilometers, what was his average speed for the 240 kilometers that he drove?

(1) Jamal's average speed for the first 160 kilometers that he drove was 64 kilometers per hour.
(2) Jamal's average speed for the last 160 kilometers that he drove was 64 kilometers per hour.
A good one!

Statements 1 and Statement 2 are individually not sufficient to answer the question as we do not know the speed Jamal drove in the remaining 80 kilometers. Hence, we can easily eliminate options A, B, and D. The answer will either be C or it will be E.

Combined

(1) Jamal's average speed for the first 160 kilometers that he drove was 64 kilometers per hour.
(2) Jamal's average speed for the last 160 kilometers that he drove was 64 kilometers per hour.

Case 1: Jamal drove at a uniform speed of 64 km/hr throughout his journey

One of the possibilities can be that Jamal drove at a uniform speed of 64 km/hr. In this case, the average speed of his entire journey will be 64 km/hr.

Case 2: Jamal did not drive at a uniform speed of 64 km/hr throughout his journey

Note, both statements tell us about the "average" speed, and we do have an overlapping distance between the two statements. So, while we know the average speed, we don't have any information on the actual speed Jamal drove in any of the segments. For example, he could have driven the first few kilometers at a very low speed and then could have sped up and slowed down again or vice versa or could have varying speeds at different intervals. Thus, while the average speed of a segment of distance is 64 km/hr, we cannot conclude that the average speed of his entire journey is 64 km/hr.

To further understand this, let's consider the journey of 240 kilometers divided into three parts -

A-B → B-C → C-D

Jamal drove at a speed of 40 km/hr from A to B, 160 km/hr from B to C, and 40 km/hr from C to D.





  • Time taken between A and B = \(\frac{80}{40} = 2\) hours
  • Time taken between B and C = \(\frac{80}{160} = 0.5\) hours
  • Average Speed between A and C = \(\frac{80[}{color]/2.5} = 64\) kmph





  • Time taken between B and C = \(\frac{80}{160} = 0.5\) hours
  • Time taken between C and D = \(\frac{80}{40} = 2\) hours
  • Average Speed between B and D = \(\frac{80}{2.5} = 64\) kmph





  • Time taken between A and D = \(2 + 0.5 + 2 = 4.5\)
  • Average Speed between B and D = \(\frac{160}{4.5} \approx 35\) kmph

Hence, the statements combined don't help us arrive at a definite answer.

Attachment:
Screenshot 2023-08-05 202838.jpg

Note: We don't need to do the above math in the exam. Knowing the fact that we can possibly get different values of average speed because of the overlapping region is enough to conclude that the statement combined wouldn't help us get a definite answer.

[color=#00a651]Option E
Show more
­

Hi, small correction on the below
  • Time taken between A and B = \(\frac{80}{40} = 2\) hours
  • Time taken between B and C = \(\frac{80}{160} = 0.5\) hours
  • Average Speed between A and C = \(\frac{160}{2.5} = 64\) kmph
­
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If Jamal drove 240 kilometers, what was his average speed for the 240 13 May 2024, 14:59
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KarishmaB MartyMurray Can you please clarify the highlighted portion ? I dint understand that part well.
JeffTargetTestPrep

Bunuel
If Jamal drove 240 kilometers, what was his average speed for the 240 kilometers that he drove?

(1) Jamal's average speed for the first 160 kilometers that he drove was 64 kilometers per hour.
(2) Jamal's average speed for the last 160 kilometers that he drove was 64 kilometers per hour.
Total distance = 240 km, and we need to answer the question:

Average speed = ?

Statement One Alone:

=> Jamal’s average speed for the first 160 kilometers that he drove was 64 kilometers per hour.

For the first 160 kilometers, we have:

Total time = Total distance/Average speed = 160/64 = 2.5 hours

Since we don’t have information about the last 80 kilometers of the journey, we can’t answer the question. Statement one is not sufficient. Eliminate answer choices A and D.

Statement Two Alone:

=> Jamal’s average speed for the last 160 kilometers that he drove was 64 kilometers per hour.

For the last 160 kilometers, we have:

Total time = Total distance/Average speed = 160/64 = 2.5 hours

Since we don’t have information about the first 80 kilometers of the journey, we can’t answer the question. Statement two is not sufficient. Eliminate answer choice B.

Statements One and Two Together:

Average speed = Total distance/Total time

Since there is an overlap between segments of the journey we have information about, the average speed for the complete journey can be anywhere in the following interval:

240/5 < Average speed < 240/2.5
48 kmph < Average speed < 96 kmph

The two statements together are not sufficient.

Answer: E
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­
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If Jamal drove 240 kilometers, what was his average speed for the 240 13 May 2024, 15:03
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chetan2u , Please check the hightlighted portion. I think you meant "minimum avg speed " . 
chetan2u

Sonia0106


chetan2u - can you please explain why 240/5 is used as the minimum value for the range?

It is so because you can divide 240 km in three parts of 80km each.
A+B+C = 80+80+80 = 240

Combined we are given
For A+B, he takes 2.5h and again for B+C he takes 2.5h.
That is time for (A+B)+(B+C) is 2.5+2.5

1) MAX: He covers B in 2.5h, so, hypothetically, he covers A and also C in 0 h.
Total time is 2.5h for A+B+C, so max avg speed = 240/2.5

2) MIN: He covers B in 0h, so he covers A and also C in 2.5 h each.
Total time is 2.5+2.5 or 5h for A+B+C, so max avg speed = 240/5
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­
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If Jamal drove 240 kilometers, what was his average speed for the 240 Updated on: 14 May 2024, 07:18
Originally posted by MartyMurray on 13 May 2024, 15:48.
Last edited by MartyMurray on 14 May 2024, 07:18, edited 2 times in total.
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KarishmaB MartyMurray Can you please clarify the highlighted portion ? I dint understand that part well.
Quote:
Statements One and Two Together:

Average speed = Total distance/Total time

Since there is an overlap between segments of the journey we have information about, the average speed for the complete journey can be anywhere in the following interval:

240/5 < Average speed < 240/2.5
48 kmph < Average speed < 96 kmph

The two statements together are not sufficient.

Answer: E
­
Show more
­We know that 160 kilometers at the beginning and 160 kilometers at the end of the trip add up to a total of 320 kilometers. So, since Jamal went a total of 240 kilometers, the first 160 kilometers and the last 160 kilometers overlap by 80 kilometers.

So, we have 80 kilometers at the beginning, 80 kilometers of overlap, and 80 kilometers at the end.

Also, we have calculated that each 160 kilometers took 2.5 hours.

To take 2.5 hours for each 160 kilometers, Jamal could have driven at a constant rate for the entire trip. In that case he drove 64 kph from beginning to end and took 240/64 = 3.75 hours for the entire trip.

He also could have gone fast for the first 80 kilometers, slow for the second 80 kilometers, and fast for the last 80 kilometers.

To maximize the time he spent driving the middle 80 kilometers, let's say that his speed was infinity kph for the first 80 kilometers and for the last 80 kilometers.

In that case, the first and last 80 kilometers took him 0 hours each. So, to spend 2.5 hours driving the first 160 kilometers and 2.5 hours driving the last 160 kilometers, he spent 2.5 hours driving the middle 80 kilometers.

So, we have the following:

----80----|----80----|----80----
     0           2.5           0

In that case, the entire trip took 2.5 hours, and his average speed was 240/2.5 = 96kph.

He also could have gone slow for the first 80 kilometers, fast for the second 80 kilometers, and slow for the last 80 kilometers.

To minimize the time he spent driving the second 80 kilometers, let's say his speed was infinity kph for the middle 80 kilometers.

In that case, he spent 0 hours driving the middle 80 kilometers. So, to spend 2.5 hours driving the first 160 kilometers and 2.5 hours driving the last 160 kilometers, he spent 2.5 hours driving the first 80 kilometers and 2.5 hours driving the last 80 kilometers.

So, we have the following:

----80----|----80----|----80----
    2.5           0           2.5

In that case, the entire trip took 5 hours, and his average speed was 240/5 = 48 kph.­

So, the extreme times and average speeds are 2.5 and 5 hours and 96 and 48 kph, and anything between them is, at least mathematically, possible.­
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If Jamal drove 240 kilometers, what was his average speed for the 240 21 Sep 2025, 10:50
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Total distance = 240 km, and we need to answer the question:

Average speed = ?

Statement One Alone:

=> Jamal’s average speed for the first 160 kilometers that he drove was 64 kilometers per hour.

For the first 160 kilometers, we have:

Total time = Total distance/Average speed = 160/64 = 2.5 hours

Since we don’t have information about the last 80 kilometers of the journey, we can’t answer the question. Statement one is not sufficient. Eliminate answer choices A and D.

Statement Two Alone:

=> Jamal’s average speed for the last 160 kilometers that he drove was 64 kilometers per hour.

For the last 160 kilometers, we have:

Total time = Total distance/Average speed = 160/64 = 2.5 hours

Since we don’t have information about the first 80 kilometers of the journey, we can’t answer the question. Statement two is not sufficient. Eliminate answer choice B.

Statements One and Two Together:

Average speed = Total distance/Total time

Since there is an overlap between segments of the journey we have information about, the average speed for the complete journey can be anywhere in the following interval:

240/5 < Average speed < 240/2.5
48 kmph < Average speed < 96 kmph

The two statements together are not sufficient.

Answer: E
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I still don’t understand why if both statements considered together cannot be understood as 64km/hr due to the overlap between them
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If Jamal drove 240 kilometers, what was his average speed for the 240 21 Sep 2025, 11:37
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nandini14

I still don’t understand why if both statements considered together cannot be understood as 64km/hr due to the overlap between them
Show more

Marty in the post just above yours gave examples showing that the average speed is not fixed and could take many values. Check it out.

We can also reason this way: suppose the first 80 km was driven at 160 km/h, the next 80 km at 40 km/h, and the last 80 km again at 160 km/h (this gives the average speed of 64 km/h for both 160 kilometer segments ). Then the total average speed would be:

(total distance)/total time) = 240/(80/160 + 80/40 + 80/160) = 80 km/h.

But it’s also possible that each of the 80 km segments was driven at 64 km/h, in which case the overall average would be 64 km/h. Since the average speed can vary depending on what happened in that overlapping 80 km, the total average cannot be determined uniquely.
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