Statement 1 tells us that train P had traveled at an average speed of 70 mph until the trains crossed, and we know it has traveled for 2 hours when the trains cross. Thus, it had traveled:
d =r*t
d=70(m/h)*2h=140 mi

Since we know station X and Y are 250 miles apart, we know that the trains meet at a point that is 140 mi from station X (where P left), and 110 miles from station Y (where Q left).

We thus know that train P is closer to its destination, and we have sufficient information from statement 1.

Statement 2 tells us that train Q had traveled at an average speed of 55 mph for the whole trip. However, we don't know what its average was at the point the trains met, and thus we can't figure out how far it had traveled when they met. Thus, statement 2 is insufficient.

Since statement 1 is sufficient and statement 2 is not, the answer is A.

zagcollins wrote: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.

Let's try answering this with a lot less math, which should always be your goal in data sufficiency. Remember, we don't care what the answer is, we just care if we can get an answer!

Let's start by really understanding the question. We know the distance and we know at what time the trains pass each other. In order to determine which one is closer to its destination, we need to know their relative speeds (we don't even need to know their actual speeds - just knowing that one is moving faster than the other would be sufficient).

(1) Gives us the speed of P up until the trains met. Well, we can certainly figure out exactly where train P would be (and since it's where they pass, we know where Q would be as well) if we know P's time and rate, so we could see which one is closer to the end of the trip: sufficient.

(2) This statement is kind of nasty! Just because train Q averaged 55mph for the entire trip, we can't assume that train Q was moving at a constant speed. For all we know, train Q traveled part of the trip at 80mph and another part at 30mph. Since we don't know how quickly Q was traveling for the first part of the journey (i.e. until they met), we have no way of calculating how close the two trains were to their destinations: insufficient.

(1) is suff and (2) isn't: choose (A).