Simplify the inequality in the question stem:

Is (a - b + c) > (a + b - c)?

Is a - b + c > a + b - c?

Is -b + c > b - c?

Is c - b > b - c?

Is 2c > 2b?

Is c > b?

(1) gives no info about c, so (1) is insufficient.

(2) gives no info about b, so (2) is insufficient.

Together, you know b is negative, and c is positive, so, yes, c is definitely bigger than b.

Choose C.

...what about this question is a "durable smack"?!?

Given: a-b+c > a+b-c
cancel a on both sides
=> c-b > b-c
=> 2c > 2b
=> c > b

Thus the question really is "Is c > b"?

1) b < 0 => b negative
But we know nothing of c. Hence, NOT SUFFICIENT.

2) c > 0 => c positive.
But we know nothing of b. Hence, NOT SUFFICIENT.

Combining 1) and 2) we have b -ve and c +ve, thus c > b.

Hence, SUFFICIENT and thus C is the answer.