There's a really handy technique called, "casting out 9s," which is good to use whenever a problem comes up that involves "summing up the digits." It's a way to compare all the numbers to each other.
In this problem, instead of laboriously adding up all the digits of every answer choice, you can quickly reduce them by "casting out the nines:"
Step 1: cross out all nines and any two or more digits that add up to nine or multiples of 9 (3,6 or 4,2,3, or 6,4,8, etc).
Step 2: add up the digits you have left
Step 3: keep adding the digits together until you have a single digit (keep in mind 9=0)
Step 4: compare all the single digits of each answer choice and see which is greatest in order to answer this question.
This is really quick:
Step 1: cross off 9, and then cross off 4,2,3 b/c they add to 9.
Step 2: what's left is 1, so that's your single digit for this number
Step 1: cross off 9, and 9
Step 2: add 1+6+4, which equals 11
Step 3: add 1+1, which equals 2, so that's your single digit for this number
Step 1: cross off 6,4,8
Step 2: add 6+7, which equals 13
Step 3, add 1+3, which equals 4, so that's your single digit for this number
Step 1: cross off 6,3
Step 2: add 2+5+5, which equals 12
Step 4: add 1+2=3, so that's your single digit for this number
Step 1: cross of 4,5, and 9
Step 2: add 6+8, which equals 14
Step 3: add 1+4, which equals 5, so this is your single digit for this number, and this is also the greatest one, and thus the answer.
This method is so easy you can do it in your head. Try it!