There are 2 variables in the original condition. Hence there is a high chance that C is the correct answer. If we apply the common mistake type 4(A) just like tip 4. In case of con 1), we always get y^2≥0. So, from 0<x=1/(3+y^2)≤1/3<1, the answer is yes and the condition is sufficient. The correct answer, thus, is A.

@ Max@Math Revolution - given: |X|<1, as asked in the question. implies --> -1<x<1.
from [A] we got 0<x<1/3.

My question is if the domain of x is a subset of what is asked, such as we got 0<x<1/3 as subset of -1<x<1, then can that given condition said to be sufficient?

Further, the only insufficient condition would be any number or domain outside of what is asked, say anything beyond -1<x<1.

Thank you

dustystormy wrote:@ Max@Math Revolution - given: |X|<1, as asked in the question. implies --> -1<x<1.
from [A] we got 0<x<1/3.

My question is if the domain of x is a subset of what is asked, such as we got 0<x<1/3 as subset of -1<x<1, then can that given condition said to be sufficient?

The question is "Is ∣x∣<1?"

Do you know the answer to the question?

If you can define the answer to the question by using the statement, along with any information given in the question, then the statement is sufficient.

Further, the only insufficient condition would be any number or domain outside of what is asked, say anything beyond -1<x<1.

Yes, basically. Still let's be clear about this.

The statement is only insufficient if members of the set of all possible values of x are both within and beyond the boundaries defined by the question.

In other words, if the answer to the question cannot be defined by using a statement, then that statement is insufficient.