Is there a intuitive way to solve this rather than with equations, quadratics. I guesses for a sec that A is very sufficient information. Since only two variables are unknown - distance covered by B before it intersects A and the speed of train B. Two variables and two equations will be fine.
But then I looked at B and suddenly the difficulty jumped up. A or D appear likely. I thought train B is super fast so increasing the distance will make even more likely that train B arrives before A. This is the same as stem 1)
hence I guessed D.
Interesting question. I would like to share my thoughts on it. The first thing I notice is that the statements do not provide any concrete data. I cannot solve anything using them so most probably I will be able to get an answer from the data in the question stem but I will get multiple possible answers. The statements will probably help me choose one of them. (all a speculation based on the statements. The answer may be E) I know a quadratic gives me multiple answers.
Attachment:
Ques2.jpg
The diagram above incorporates the data given in the question stem. Let x be the distance from meeting point to Boston.
Speed of train A = 100 mph
Speed of train B = x/(10 min) = 6x mph (converted min to hr)
Total time taken by both is 2 hrs. Already accounted for is 1hr + (1/6) hr
The remaining (5/6) hrs is the time needed by both together to reach their respective destinations.
Time taken by train A to reach B + time taken by train B to reach NY = 5/6
x/100 + 100/6x = 5/6
3x^2 - 250x + 5000 = 0 (Painful part of the question)
x = 50, 33.33
(1) Train B arrived in New York before Train A arrived in Boston.
If x = 50, time taken by train A to reach B = 1/2 hr, time taken by train B to reach NY = 1/3 hr
If x = 33.33, time taken by train A to reach B = 1/3 hr, time taken by train B to reach NY = 1/2 hr
Since train B arrived first, x must be 50 and B must have arrived at 4:20. Sufficient.
(2) The distance between New York and Boston is greater than 140 miles.
x must be 50 to make total distance more than 140. Time taken by train B must be 1/3 hr and it must have arrived at 4:20. Sufficient.