I'm not sure when I should be asking if X exist and when I can assume it does. I feel like I get similar questions wrong on the daily drills, because I wrongly assume all variables exist. I got this one wrong because I didn't assume X existed.
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The daily drills are tough insofar as we are trying to teach ideas about the structure of logical arguments, and sometimes the abstraction makes them confusing. In general, a real question passage will likely make it more clear whether X (whatever X is) exists or not.
But for the daily drills, and for symbolic logic in general, it is safe to assume that every premise/variable mentioned in the passage is on the table. It is not so much whether it “exists†or not — if it is mentioned in a premise, it (or its contrapositive) can be used in a logical chain to get to the conclusion.
I hope that helps! Please let us know if you have further questions.
