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I was hoping someone could help explain this to me:

The first problem set for the Analytical Section (Section 4)

It is a line of nine spots occupied by 5 people, where everyone has two spots except O. Anyways, one of the conditions says that O is in a line that is after "either of K's spots" and before "at least one of L's"

I took that to mean that of the two spots that K took, O could be after one or both of them- basically that there'd have to be at least one K that was before O and at least one L that was after O...

After a lot of frustration seeing multiple scenario's work out between the answer choices, I realized that it only worked when O was after BOTH K spots. However, I've always learned that either to mean one, both, but never neither which makes this very confusing to me.

If anyone has any insight or know what I'm talking about, I'd greatly appreciate it. Thank-you!

"Either" in this case is used to convey that, whether we are talking about K1 or K2, O will always be higher than K.

However, if the rule says that "O's aisle is either numbered higher than K1 or K2, but not both," then we are talking about a situation where O is higher than only one of the Ks. I've noticed that if a rule is to convey that a certain element is before/after ONLY one of two elements without specifying which element, the phrase "but not both" is almost always used.

I think you mistook the first case for the second case.

Hope that helps