On a real GMAT question, the two statements will never give incompatible answers. You can't see a question like this:

What is the value of x?

1) x is an even integer
2) x is an odd integer

nor could you see a question like this:

What is the value of x?

1) x = 2
2) x = 25

Because in DS questions you are asked to decide whether the information in both statements is sufficient, it must be logically possible for both statements to be simultaneously true. It would make no sense for x to be both odd and even; nor would it make any sense for x to be equal to both 2 and 25. On the real GMAT, the statements cannot contradict each other.

Now, just because the real GMAT structures their questions in this way is no guarantee that test prep companies will always do the same. I've certainly seen published questions from test prep companies, not real GMAT questions of course, which have inconsistent statements.