I didn't see Kate today, she ... have taken the day off.

The correct answer is must. Explanation: The sentence "I didn't see Kate today, she ... have taken the day off" requires a modal verb that expresses a strong possibility or deduction. 'Must' is used to express that the speaker believes it is very likely that Kate has taken the day off, based on the fact that they didn't see her. 'Need' doesn't fit the context, and 'can't' would imply impossibility, which doesn't align with the likely scenario.