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.

Please can you explain your ans.Thanks

If they both leave at the same time, the one that has been traveling faster up to that point in time will be nearer to its destination. Note that the faster one could slow down considerably afterwards - but I don't care about that or about when they actually reach their destinations. I only care about where they are when they pass.

First, sketch this out on paper.

(1) At the time they pass, they've been going for 2 hours. If P has averaged 70mph to that point, then P has gone 140 miles. The tracks are 250 miles long, so P still has 110 miles to go. At this "passing" point, Q has then gone 110 miles and still has 140 miles to go. So P is closer to its destination. Sufficient.

(2) Q averaged 55mph for the whole trip. I'll try to see if I can both make Q the "closer" train and P the "closer" train with this info. To average 55mph over 250 miles, the train has to run about 4.5 hours (because 250/4.5 is just about 55).
First, let's say Q goes 10mph for the first 2 hours and then some really fast speed after that to up the overall average to 55mph. (Note: it'd have to approach 450+ mph, but the problem doesn't tell us there's a max speed the train can travel!) After 2 hours, Q has gone 20 miles and P has gone 230 miles. P is closer to its destination.

Now let's say Q goes 100mph for the first 2 hours and then some really slow speed after that to bring the overall average down to 55mph. After 2 hours, Q has gone 200 miles and P has gone 50 miles. Q is closer to its destination.

I can't say one is definitely closer than the other. Insufficient. Answer is A.

Thanks.
That clarity helped.
I really like the patience with which experts post their analysis here.
It really helps.

You're welcome! We love teaching and we're all big GMAT geeks, so we enjoy it. :)

[Should'nt the answer be C.

From 1 we know P had covered 140m but we know nothing of train Q INSUFFICIENT

From 2 we do not know anything abt train P.

TOGETHER we can solve.

Did I miss something.

If we know that the trains are meeting each other, then we know that "combined" they have traveled a combined distance of 250 miles. When we know that P has traveled (70*2) 140 miles, so Q has traveled 110 miles.

As such, statement A is sufficient.

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

That is given, but we do not know train P's average speed for the entire trip, so we can't say exactly how many mile train P has traveled.

Statement A is insufficient.

Hi, Where do u get the GMAT paper ? . Its mentioned in the post .. PAPER 18 ? . Is it hardcopy or softcopy?

I would happy to get a clarification on (1) "At the time when the two trains passed, train P had averaged a speed of 70 miles per hour. " as well.
"At the time" doesn't mean the whole period from the start up to the encounter, it mean only the time of the encounter.
Since I understood it that way, I thought that E was the answer.

Thanks

b.t.w
Really great forum.

that interpretation is impossible, because there's no such thing as an average speed for an instantaneous observation. if the problem cites an average speed, then the entity in question MUST have been traveling for a time interval, of nonzero length.

also, segue to the sentence correction: the sentence uses the past perfect ('had averaged'), so you know that it means to refer to a situation whose relevance continued up until the 2 trains passed each other. more evidence that they're talking about an interval, not a single point in time.

the average thingy is the clincher, though. as soon as you see that, you can throw out any thoughts about instantaneous speeds, because they don't apply.