hatemnag wrote:

Hi Bunuel. Actually, i understand your logic in algebraic approach in statement 1 while i can not as you mentioned that such statement tells us directly that c (either) in green area or red area. Isn't "either" in a DS Q. means that it has two solutions and is insufficient ?

You are confusing getting "either" in the form of 2 differnet answers for the same statements and have 2 cases for the same statement that give you the same answer.

Example, if the question is " what is the value of x?

Statement 1 tells you that x is either 1 or 2, then in this case the statement is

NOT sufficient.

BUT

if the question asks " is x>0?"

Statement 1 tells you that x is either 1 or 2, then in this case the statement is

sufficient as for x=1, you get "YES" for the question asked, similar to the case when x=2. FYI, if you ended with different values of negative values of 'x' , even then this statement sould have been SUFFICIENT, as you would have obtained a "NO" for all possible values of 'x'.

Thus, a statement or a combination of statements is SUFFICIENT if and only if you get 1 UNIQUE/UNAMBIGUOUS answer.

Hope this helps.