Question in Quant Algebra Section, Under Hard Section

GRE Quant Problem Solving
1

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In this question, when I tried plugging in numbers for a and b in the respective orders,
a: 15, 5, -1, -3
b: 1, 3, -15, -5
I am able to get the answer as D.

But if I am factoring Quantity B: a^2-b^2 as (a+b)(a-b), and then dividing both Quantity A and Quantity B by (a+b), it results in the following:
Quantity A: 1
Quantity B: a-b

Since a>b, (a-b) will always be a positive integer greater than 1, leading to answer choice B.

2

What if a + b < 0?

3

Even if a+b<0, if it is divided on both sides, the Quantity A will turn out to be 1, right?

4

But the comparison changes. Put it this way: 3 > 2 but -3 < -2.