Data Sufficiency (DS) | If a and b are integers, is a > b?

Is a>b ?

(1) a - 0.5b > 0
--> a> 0.5b
ie. a=3, b=3, a> 0.5b but a=b
ie. a=3, b=-3, a> 0.5b anda>b
Not Sufficient

(2)\(b^a < 0\)
Given this statement, then b is negative. Let's analyze
ie. a=3, b=-3,\((-3)^3 < 0\) and a>b
ie. a=-3, b=-3,\((-3)^{-3} < 0\) but a =b
Not Sufficient

Combining (1) and (2),
We know b<0 and a>0.5b, then a must be less negative than b. In other words, it must be true that a>b

Answer is (C)
...

---