VJesus12 wrote:If ab=0, is |a-b|>0?

1) a=0
2) b<0

The OA is the option B.

Experts can you tell me why is not sufficient the statement (1)? I don't understand. I think the correct option is D.

If ab = 0, then we have three states of the world:

1. a = 0, b doesn't equal 0
2. a doesn't equal zero, b = 0
3. a = 0, b = 0

For |a-b|>0 we need to be in state 1 or 2.

(1) doesn't tell which state of the world I am in, I know a = 0, but I don't know what b is - not sufficient
(2) b < 0 tells me I'm in state 1 and hence, |a-b|>0 (I can't be in any other state of the world and don't need to told the value for a because I know it is zero) - sufficient

Answer is B.