1. Doesn't mean anything, a and b can both be positive for instance and a can be negative b can be positive.

2. If a and b were on the same side (both positive or both negative) the module of their sum will equal the distance from 0 to a + the distance from 0 to b. However, it is said that the distance is greater so this simply means a and b are not on the same side so 0 is certainly between them.

therefore, B

We can also solve this using absolute values.

The distance between a number and 0 is the absolute value of that number.

Let's start by rephrasing the question (often a great first step in DS):

Q: If neither a nor b is 0, do a and b have different signs?

Then we rephrase the statements as:

(1) |a| > |b|

(2) |a| + |b| > |a + b|

(1) says nothing about the signs of a and b: insufficient.

(2) if a and b have the same sign, then |a| + |b| = |a + b|. The only way that (2) can be true is if a and b have different signs: sufficient.

(2) is sufficient but (1) is not: choose (B).