GMAT Set 8 Q35

[Abhijit K]

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
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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.

Is the answer C or E?

[GMATGuruNY]

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.

Since the distance between the two stations is 250 miles, P and Q meet when the sum of their distances = 250.

Statement 1:
Since P and Q meet after each has traveled for 2 hours, the distance traveled by P in these 2 hours = r*t = 70*2 = 140 miles.
Thus, the distance traveled by Q in these 2 hours = 250-140 = 110 miles.
Since P has traveled farther than Q, P is closer to its destination.
SUFFICIENT.

Statement 2:
Q's average speed for the entire trip does not constrain Q's average speed for the FIRST 2 HOURS.

Case 1: Q travels at 1mph the first 2 hours
Here, Q's distance = r*t = 1*2 = 2 miles, implying that P's distance = 250-2 = 248 miles.
In this case, P is closer to its destination.

Case 2: Q travels at 100mph for the first 2 hours
Here, Q's distance = r*t = 100*2 = 200 miles, implying that P's distance = 250-200 = 50 miles.
In this case, Q is closer to its destination.

Since P is closer in Case 1, but Q is closer in Case 2, INSUFFICIENT.

The correct answer is A.