jsk988 wrote: My question is.. what happens if the sum is incorrect? i.e. if there isn't an integer n that allows the values to add up to the sum... will it be considered insufficient?

In real GMAT questions, the information in a DS question is always 'logically consistent'. That is, it's *always* possible for all of the information given in the question and in the statements to be simultaneously true. So the situation you're asking about could never happen on the real test. If a statement says "The sum of the elements of set S is 275", there absolutely must be at least one way this could happen. Very often in DS your task is to determine whether there is only one way it could happen, or more than one way, but there's always at least one.

That said, I've seen many questions designed by test prep companies that violate this rule, so you may run across a few questions (not official questions, though) which contain inconsistent information. Logically speaking, if information is inconsistent in a DS question, there is no way to decide on a correct answer. For example, a question like the following would be nonsensical:

What is the value of x?
1) x is negative
2) x > 1

It's not possible to decide on a correct answer here. Clearly using both statements, there is no possible value of x. Many people would thus consider the two statements together sufficient; we know with certainty there is no value of x possible. Many others would consider the two statements together insufficient, since you can't find x even using all your information. Both positions are perfectly defensible, so a question like this doesn't make any sense as a DS question, since it has two different legitimate right answers. Because of this, all real GMAT DS questions must always contain consistent information.