UNDERSTANDING DATA SUFFICIENCY??

I like to think of DS questions as puzzles where the two statements are two clues. You read the puzzle but are not given enough info to solve it. You read clue 1 and then figure out whether you can solve it. Then, you forget about clue 1 and try using clue 2 alone. If you cannot solve it, using either clue alone, you use both clues together to solve it. Obviously, since both statements (clues) are a part of the same puzzle, they CANNOT conflict.

e.g. this is not a valid question:

What is x?
(1) x - 4 = 0
(2) x^2 = 9
The two statements here are conflicting. Stmnt 1 says that x is 4. Stmnt 2 says that its square is 9 which it is not if x is 4.

This, on the other hand, is valid.
What is x?
(1) x - 3 = 0
(2) x^2 = 9
Stmnt 2 doesn't conflict with stmnt 1.