Vincen 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.

OA is A.

I don't know how can I solve this DS question. Experts, can you give me some help.

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 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 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

Vincen wrote: ↑

Wed Oct 11, 2017 6:19 pm

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.

OA is A.

I don't know how can I solve this DS question. Experts, can you give me some help.

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