You sometimes have to trust the GMAT a little. Most problems do have easy solutions, well-hidden. Have faith in this and go boldly forth!
Your instinct should be to realize "hm, there aren't that many possible ways to do this. It could be 13 and 31 or 17 and 71 or ... probably a few more. But not many." Thus (D) is the initial guess. After all, almost ANY information should narrow it down.
Statement (1): What numbers add up to 110 that fit this description? Since the digits are reversed it has to be numbers whose digits add up to 10. And are prime. Not 19/91 (91 isn't prime); not 28/82 (neither is prime), but 37 and 73, yup, that works. Done. 30 seconds.
Statement (2): The same logic. You already know that 37 and 73 work. If you change the numbers it will be a different difference -- keeping the digits reversed, any smaller first number makes the difference larger, any bigger second number makes the difference smaller. Although we can't use Statement (1) when analyzing Statement (2), we CAN remember what we've figured out about the problem (in this case, the answer!) to analyze Statement (2). Clearly it has to be 37 and 73 again. Done. 15 seconds.
That's how to do it fast: having faith that the answers make sense and remembering everything you learn as you move from Prompt to Statement to Statement.
