https://gmat.gregmat.com/quizzes/quiz/gmat-prime-numbers (Question 4)
write your question here…In this question, with option A itself i can tell 11 can be the number since factor of 11 includes 1 and 11 where 1 is not a prime which left me with only 11.
Statement 1 alone gets you to the set \{1, 11\}. The question to ask now is whether every element in this set is prime. If it isn’t, then Statement 1 clearly isn’t sufficient, and you need “additional filtering.”
The reason you think Statement 1 alone is sufficient is because you’re mentally checking the primality of each element to do that filtering yourself. But, in the process, you are implicitly using Statement 2, because a prime by definition is a number strictly greater than 1.
Without overthinking it, just ask yourself whether every element in your possible set is prime. If they aren’t all prime, then you need additional constraints.