Can someone with a "master" key open any lock?

We recently changed outer door locks on my mom's apartment because she doesn't want her apartment manager going in while she is away from home. With their "master" key, would they still be able to unlock her door without having the new key? Are these keys capable of opening other doors in any... show more We recently changed outer door locks on my mom's apartment because she doesn't want her apartment manager going in while she is away from home. With their "master" key, would they still be able to unlock her door without having the new key? Are these keys capable of opening other doors in any place--say, outside of the apartment complex?
Update: We got permission from the management to change the locks with the understanding that if an emergency occurred, they would not be able to enter, so there is no violation on our part.
Update 2: Also, I know they have a master key because I had to borrow it once to check on my mom when she didn't answer her door. They didn't search through keys, they just went to a closet and handed me a key.
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