Is a>0?

Statement 1:

Scenarios when (a-b)>0..........................................................(a)
i) a>0, b>0
ii) a<0, b<0
iii) a>0, b=0
iv) a=0, b<0

Clearly insufficient. "a" can have values with both the signs or zero too..

Statement 2:

Scenarios when \(a^2-b^2>0\)
i) a>0 or a<0, b>0 or b<0 & |a|>|b| ; since square term always yields positive value

Clearly insufficient. "a" can have values with both the signs.

Combining, (1)+(2),
we can re-write St2 as
(a+b)(a-b)>0--------------------(b)

hence from (a) & (b), we have (a+b)>0 -----(c)

Now adding (a) with (c) we have,

(a+b+a-b)>0 or 2a>0 or a>0

Hence sufficient.

Ans. C

P.S:- We can only add inequalities when their signs are in the same direction.