Using pure reasoning to solve this question will take less than a minute without doing any kind of calculations.
Using Statement (1):
Car X is going 50 mph and Car Y 40 mph, so Car X is 10 mph faster. That means every hour Car X gains 10 miles on Car Y. Since the current gap is 1 mile and we need an extra 1 mile for a 2-mile lead, Car X must gain 1 mile. At 10 miles per hour, gaining 1 mile takes 1/10 of an hour—which is 6 minutes => Sufficient/
Using Statement (2):
Three minutes ago, Car X was only 1⁄2 mile ahead, and now it is 1 mile ahead. That means in 3 minutes, the lead increased by 1⁄2 mile. So, Car X is gaining 1⁄2 mile every 3 minutes. To gain an additional 1 mile (which is twice 1⁄2 mile), it would take twice as long—6 minutes => Sufficient.
Hence (D)