I don't think that's the correct logic here. The quality or characteristic being compared does decide the "winner," but winning in these contexts isn't about which is the more "optimal" choice. It's about what abides by the quality/characteristic better. For example, question 2 compares how "expensive" the options are, it's not asking you what is the most cost-effective/optimal course of action. Instead, it states that one is more expensive than the other and wants to see if you can recognize which one that is. I hope this makes sense!

I think it comes down to the indicator word used and understanding the context of the conditional. By saying '"some" cats are pets,' the main concept "cats" cannot be the sufficient condition or subset because there is a chance that "some" cats aren't pets. (Although, "some" can include "all," we can't ignore the possibility that that might not be the case in this scenario.)

For something to be a sufficient condition, it needs to be fully enclosed within the bigger circle of the necessary condition, but the word "some" makes it unknown if the circle of "cats" is fully within the circle of "pets." Instead, we would imagine it as more of a venn diagram with some overlap between "cats" and "pets." This way, we are making sure to not jump to conclusion on the idea that ALL cats are pets.

If the example had explicitly stated, "All cats are pets," then we can safely conclude cats --> pets.

I understood the use of the word "require" in the sentence as an indication that the following concept is "necessary" for the preceding one. I might've jumped to conclusions on vocabulary/grammar, but in my mind, "required" is almost another way of saying "must," which we've previously learned to be a Group 2 indicator for necessary conditions.

For example, all the following sentences basically mean the same thing:

If it is a cat, then it is a mammal.

A cat must be a mammal.

A cat is required to be a mammal.

Again, there might be grammatical/vocabulary assumptions made on my part, but I found this to be a helpful way of understanding the sentence.