Two hours after X leaves college, Y leaves his home to intercept him. If Y travels twice as fast as X, how long will it take Y to meet X?
Speed Y = 2x(1) X's college is 50 miles due north of Y’s home
There are two problems here. a.) I wouldn't put it past the GMAT to trick us by saying the distance between x and home is 50 miles but the route traveled is longer than 50 miles. b.) Though we know that Y travels twice as fast as X, we don't know what speed Y travels at. For example, X may travel at 1 mile/hour and Y may travel at 2 miles/hour or X may travel at 10 miles/hour and Y at 20 miles/hour. Obviously, depending on the rate they travel at, the time it takes them to meet will vary.
INSUFFICIENT(2) Y’s rate is 30 mph
This tells us Y's rate (and X's as well, given the information in the stem) but we know nothing about the distance they both travel.
I think the "due north" bit should raise some red flags in people's mind. This is an uncommon way to refer to distance in any real application. For example, when I refer to the distance from NYC to Boston (a route I travel often) I don't mean the distance they are from one another in a straight line, but rather the distance they are from one another by the road way or in my case, the train tracks. Straight line distance is meaningless unless you're taking a helicopter or plane, something I doubt comes into play with X and Y!
That being said, unless we know the actual distance they traveled, we cannot solve for this problem.