In this question all six places are filled with only A or B and each column has an A+B addition. Also from the options in the answer choices we can infer that A+B has to be less than or equal to 9 because any higher sum of A+B would result in a four digit number as you can see by performing the hundreds place addition. For Example, take A & B as 5,5 and you would see that the hundreds place addition itself would lead you to 1000 which makes it a 4 digit number which none of our answer choices are.
As A+B is less than or equal to 9 we can see that addition in each and every position(ones, tens and hundreds) would result in a number which is less than 10 and hence there won't be any carryover.
Therefore we get A+B as the number in each of the ones tens and hundreds position which tells us that all three places have the same number(A+B)
In the answer choices only 999 fits this criteria.(you can also cross check this by taking {A,B} as {4,5} and vice versa)