Stations X and Y are connected by two separate, straight, parallel

Stations X and Y are connected by two separate, straight, parallel rail lines that are 250 miles long. Train P and train Q simultaneously left Station X and Station Y, respectively, and each train traveled to the other’s point of departure. The two trains passed each other after traveling for 2 hours. When the two trains passed, which train was nearer to its destination?
(1) At the time when the two trains passed, train P had averaged a speed of 70 miles per hour.
(2) Train Q averaged a speed of 55 miles per hour for the entire trip.

(1) As P averaged 70 miles per hour at the time when the two trains passed, hence when they passed each other P traveled 2*70=140 miles, so for P it was 110 miles left to cover and for Q 140. P was closer to its destination. Sufficient.

(2) Knowing average speed for entire trip won't help us to determine the distance either of train coverd at the time they passed each other (as the average speed at the time the met could have been different). Not sufficient.

Answer: A.
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Given: Total track distance is 250 miles. Trains P and Q left at same time. The two trains passed each other after 2 hours.

Target question: When the two trains passed, which train was nearer to its destination?

Statement 1: At the time when the two trains passed, train P had averaged a speed of 70 miles per hour.
KEY INFO: The two trains passed each other after traveling for 2 hours
During those two hours, train P averaged 70 mph

distance = (rate)(speed)
So, during those two hours, train P's travel distance = (70)(2) = 140 miles
Since the trains MEET after 2 hours, and since the total track distance is 250 miles, we can conclude that train Q traveled the 110 miles during the 2 hours.
The answer to the target question is train P is closer to its destination
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: Train Q averaged a speed of 55 miles per hour for THE ENTIRE TRIP.
Note the ENTIRE TRIP part. Statement 2 doesn't really tell us much about the first 2 hours (until the trains met)

Let's examine two possible scenarios:
NOTE: time = distance/rate
This means train Q's TOTAL travel time = 250/55 ≈ 4.5 hours
So, as long as train Q's TOTAL travel time is 4.5 hours, then statement 2 is satisfied

Case a: Train Q travels 150 miles in the first 2 hours and then travels 100 miles in the next 2.5 hours. Train P travels 100 miles in the first 2 hours and then travels 150 miles in the next 2.5 hours.
In this case, the answer to the target question is train P is closer to its destination

Case b: Train Q travels 100 miles in the first 2 hours and then travels 150 miles in the next 2.5 hours. Train P travels 150 miles in the first 2 hours and then travels 100 miles in the next 2.5 hours.
In this case, the answer to the target question is train Q is closer to its destination
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

Stations X and Y are connected by two separate, straight, parallel rail lines that are 250 miles long. Train P and train Q simultaneously left Station X and Station Y, respectively, and each train traveled to the other’s point of departure. The two trains passed each other after traveling for 2 hours. When the two trains passed, which train was nearer to its destination?

(1) At the time when the two trains passed, train P had averaged a speed of 70 miles per hour.
(2) Train Q averaged a speed of 55 miles per hour for the entire trip

SOLUTION:

D = 250 miles
P and Q travel 2 hrs each before they meet

From (1): P speed = 70 mph i.e. in 2 hrs it covers 140 miles
Therefore, Q must have traveled = 110 miles ---- SUFFICIENT

From (2): Q speed for ENTIRE trip = 55 mph ---- Clearly INSUFFICIENT

ANSWER: A

Stations X and Y are connected by two separate, straight, parallel rail lines that are 250 miles long. Train P and train Q simultaneously left Station X and Station Y, respectively, and each train traveled to the other’s point of departure. The two trains passed each other after traveling for 2 hours. When the two trains passed, which train was nearer to its destination?

(1) At the time when the two trains passed, train P had averaged a speed of 70 miles per hour.
Train P has been running for 2 hours with an average speed of 70 miles per hour so it has covered 140 km .
The total distance is 250; so P was 250-140= 90 miles away from its destination .
We can use logic to see that since the train are crossing each other then train Q must also travelled 90 kilometres and thus it was 250-90 = 160 km away from its destination
Train P was closer
SUFFICIENT

(2) Train Q averaged a speed of 55 miles per hour for the entire trip.
Well the speed for first hour can vary from the second's hour's speed and so on.
We don know at what speed train Q travelled for the first 2 hours so we cannot figure out its distance.
INSUFFICIENT

ANSWER IS A

Sorry but the explanation for statement 1 is not clear from the above thread. Can someone please explain how do we know the speed of Q and how do we derive that equation. Thank you.

X------(140 miles)--------(meeting point)------(110 miles)-----Y
P -->..........................................................................<--Q

Trains meet after 2 hours. Train P's rate was 70 miles per hour at the time when the two trains met, hence P traveled 2*70=140 miles. Thus Q traveled 250 - 140 = 110 miles. We don't need the rate of Q to answer the question but we can get it. It would be (distance traveled)/(time) = 110/2 = 55 miles per hour.
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Bunuel
I did not understand still that even if option 1 gives us P is 110 miles away from destination how can we conclude that P is nearer at that time without knowing anything about Q?
If we are to compare P & Q's distance from the destination when they pass each other, we need to know Q's distance too at that time right?
Please help me understand this.
Thanks!

P is 110 miles from the destination at the moment when P and Q meet. Since the whole distance is 250 miles, then Q is 250 - 110 = 140 miles from the destination.
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hi, i have one query. when we already know that in option B the average speed for the whole trip is 55 KMPH, therefor we can sufficiently derive that when the passed each other the speed for Q was 55 KMPH.

Hence we can derive that after 2 hours train Q hasd travelled 2*55= 110 kM, and hence train P travelled 140 KM.

Why cant both be sufficient.

Also i have a doubt that in option 1. Train P had averaged the speed to 70 KMPH so we donot know that whether further it will go with the same speed or increase the speed or reduce the speed.

Please suggest a suitable explanation for the doubt.

Thanks.

Hi Bunuel,

Thank you for your explanation.

Yet, I'm quite confused with this question.

The question doesn't state that the two travel at the constant speed for the entire trip.
That is why B alone is incorrect: the speed at which Train Q travels can vary with time.
However, if I interpret the the statement B and then apply to A, I think ,from the statement ,"At the time when the two trains passed, train P had averaged a speed of 70 miles per hour." At the time when the two trains passed can be just a one point of time; perhaps, the speed before that time can be different from 70 miles per hour.

That's why I think A is incorrect too.
Please explain.
Thank you.

Your interpenetration is not correct.

"(1) At the time when the two trains passed, train P had averaged a speed of 70 miles per hour" means that the average speed of P before the meeting was 70 miles per hour.
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Given:
1. Stations X and Y are connected by two separate, straight, parallel rail lines that are 250 miles long.
2. Train P and train Q simultaneously left Station X and Station Y, respectively, and each train traveled to the other’s point of departure.
3. The two trains passed each other after traveling for 2 hours.

Asked: When the two trains passed, which train was nearer to its destination?

(1) At the time when the two trains passed, train P had averaged a speed of 70 miles per hour.
Train P travelled = 70 *2 = 140 km and is 110km away from destination.
While Train Q travelled = 110 km and was 140 km away from destination.
Train P is closer to the destination.
SUFFICIENT

(2) Train Q averaged a speed of 55 miles per hour for the entire trip.
Average speed at the time of meeting is important and not for entire trip.
NOT SUFFICIENT

IMO A

Stations X and Y are connected by two separate, straight, parallel rail lines that are 250 miles long. Train P and train Q simultaneously left Station X and Station Y, respectively, and each train traveled to the other’s point of departure. The two trains passed each other after traveling for 2 hours. When the two trains passed, which train was nearer to its destination?

We're told that the rail line is 250 miles long. If Train P and Train Q leave simultaneously and at the same speed, they would meet when each train travels 125 miles. Lets keep this in mind before reading the statements:

(1) At the time when the two trains passed, train P had averaged a speed of 70 miles per hour.

If they met after traveling for 2 hours, then Train P had traveled 140 miles when the trains passed. 140 miles > 125 miles. Train P was closer to its destination. SUFFICIENT.

(2) Train Q averaged a speed of 55 miles per hour for the entire trip.

We don't know how far Train Q traveled in the first 2 hours -- it's possible train Q could have not moved in the first 2 hours. Statement 1 is different because we could conclude that Train P has traveled 140 miles per hour in the first two hours. We can make that conclusion here with train Q. Without more information, we can't conclude anything. INSUFFICIENT.

Answer is A.
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OFFICIAL GMAT EXPLANATION

Arithmetic Applied problems; Rates

(1) This indicates that Train P had traveled 2(70) = 140 miles when it passed Train Q. It follows that Train P was 250 − 140 = 110 miles from its destination and Train Q was 140 miles from its destination, which means that Train P was nearer to its destination when the trains passed each other; SUFFICIENT.

(2) This indicates that Train Q averaged a speed of 55 miles per hour for the entire trip, but no information is given about the speed of Train P. If Train Q traveled for 2 hours at an average speed of 55 miles per hour and Train P traveled for 2 hours at an average speed of 70 miles per hour, then Train P was nearer to its destination when the trains passed. However, if Train Q traveled for 2 hours at an average speed of 65 miles per hour and Train P traveled for 2 hours at an average speed of 60 miles per hour, then Train Q was nearer to its destination when the trains passed. Note that if Train Q traveled at (120)(55)/140 = 47 1/7 miles per hour for the remainder of the trip, then its average speed for the whole trip was 55 miles per hour; NOT sufficient.

Statement 1 alone is sufficient.

Solution:

Statement One Alone:

At the time when the two trains passed, train P had averaged a speed of 70 miles per hour.

Since train P had averaged a speed of 70 miles per hour when the two trains passed each other, we see that, after traveling for 2 hours, train P had traveled 70 x 2 = 140 miles. Therefore, train P was 250 - 140 = 110 miles from Station Y, whereas train Q was 140 miles from Station X. Therefore, train P was closer to its destination (Station Y) than train Q was to its destination (Station X).

Statement one alone is sufficient.

Statement Two Alone:

Train Q averaged a speed of 55 miles per hour for the entire trip.

Even though we know train Q averaged a speed of 55 miles per hour for the entire trip, we don’t know how many miles train Q had traveled for the first 2 hours. If it indeed traveled an average speed of 55 miles per hour for the first 2 hours, then it traveled 55 x 2 = 110 miles and was 250 - 110 = 140 miles from its destination, whereas train P was 110 miles from its destination. In this case, train P was closer to its destination than train Q was to its destination. However, if train Q traveled at a faster speed, say an average speed of 70 miles per hour, for the first 2 hours, then it traveled 70 x 2 = 140 miles and was 250 - 140 = 110 miles from its destination whereas train P was 140 miles from its destination. In this case, train Q was closer to its destination than train P was to its destination.

Statement two alone is not sufficient.

Answer: A
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yep, I messed it up. marked E because of how the answer choices were placed. "Averaged for whole trip"/ "average at the point of passing each other". it's on the same concept as other relative speed questions. here's what the 'equation" looks like:

\(Time taken= total distance/relative speed\)

relative speed when bodies are travelling towards each other= \(Rp+Rq\)
time=2hrs
dis=250
Rp=70

\(2= 250/Rp+Rq\)
Rp=70
\(2=250/70+Rq\) -----------> Rq will come out as 55.

who travelled more? that's rate*2 -----> \(70*2=140\) is > than \( 55*2 \)
So yep. this is suff. can't believe it was this easy and I missed it.. sigh*

I am a bit confused here. I thought the question already specifies that the two trains passed each at the 2 hour mark. Isn't it implied then in an RTD table that
R T D
Train P 2 140
Train Q 55 2 110
Total 250

Am I misinterpreting the information?

Why is there no official answer for this? Bunuel can you add that? This is clearly A

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Added the OA. Thank you!
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