Hello, there. I'm happy to help with this.
What you are asking is an excellent question. It's a subtle distinction in formal logic between ordinary "or" and "exclusive or" (denoted "xor").
In formal logic:
"A
or B" means
i) the cases in which A is true and B is not true
ii) the cases in which A is not true and B is true
iii) the cases in which both A an B are true
"A
xor B" means
i) the cases in which A is true and B is not true
ii) the cases in which A is not true and B is true
So, "xor" excludes the cases in which both A and B are true, whereas ordinary "or" includes those cases.
Ordinary speech is, from a logical point of view, quite sloppy. Sometimes in ordinary speech, people use the word "or" to me the ordinary "or", and sometimes people use "or" to mean "xor". Thinking of how the word "or" is used in ordinary speech is a particularly poor guide to its use in logic.
On the GMAT, you can always assume that, when they use the word "or", they mean the ordinary "or" and NOT the "xor." If the real GMAT wants an "xor", it will spell that out by saying something roundabout like "A or B but not both at the same time."
In the problem & solutions you cite, the problem was using ordinary "or", not "xor", and the solutions were perfectly consistent with that interpretation and perfectly correct.
Does this make sense? Let me know if anyone reading this has any further questions.
Mike
_________________
Mike McGarry
Magoosh Test PrepEducation is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)