Clarification on DS

Basically in DS there are two types of question :

The value type : What is the value of x ? What is the length of AB ?
For this type of question you need to find one only value to conclude about the sufficiency

The Yes/ NO type, the type you were mentioning in your question : Is X prime ? is Y even ?

For this type of question you just need to answer a definitive YES or a definitive NO the sufficiency will be the ability to have only ONE answer.

As an example, is x prime ?

1) x has three different factors
2) x+y is prime

Statement 1 indicates that x has three different factors, therefore x is not prime.
Hence we have enough information to answer the question, so statement 1 is SUFFICIENT, we answered with a DEFINITIVE NO, there is NO AMBIGUITY.

Statement 2 indicates that x+y is prime, since we have no information about x and about y we can think that :
x = 2 and y = 1 therefore x+y = 3 (prime) and x = 2 prime, YES
x = 4 and y = 1 thetford x+y = 5 (prime) and x = 4, not prime, NO

In this case we have TWO DIFFERENT ANSWERS Yes and NO, so the statement is INSUFFICIENT.

The answer is A, Statement 1 is sufficient.