Data Sufficiency

Is |a| > |b|?

(1) 1/(a - b) > 1/(b - a)
(2) a + b < 0

The OA is the option C.

I don't know how to solve this DS question. How can I, using both statements, obtain a solution? Experts, can you give me some help?

VJesus12 wrote:Is |a| > |b|?

(1) 1/(a - b) > 1/(b - a)
(2) a + b < 0

The OA is the option C.

I don't know how to solve this DS question. How can I, using both statements, obtain a solution? Experts, can you give me some help?

Statement 1: note that if a -b> 0 then b -a < 0, and vice versa. So if 1/(a-b) > 1/(b-a) that tell us that a -b > 0, and a > b.
Case 1: a = 2 and b = 1. The answer is YES |2| > |1|
Case 2: a = -1 and b = -2. The answer is NO |-1| is not greater than |-2|
Not sufficient

Statement 2: rephrase: a < -b
Now we can reuse Case 2, a = -1 and b = -2, to get a NO
Case 3: a = -3 b = -2. The answer is YES |-3| > |-2|.
Not sufficient

Together, we know that a > b and that a < -b. This means that b is going to have be negative. (If b were positive, and 'a' were larger, a would also be positive. There's no way that this positive 'a' could be smaller than - b, which would be a negative value.)

Say b = -2. Now we know that a > -2 and a < 2, or -2<a<2, thus guaranteeing that |a| will be less than |b|.
If b = -5, then a > -5 and a < 5, or -5<a<5, and guaranteeing that |a| will be less than |b|. This will be true for any number we pick. Because the answer is always NO, together the statements are sufficient. The answer is C