OO Design questions in Interviews

I was rather surprised when several companies I've been interviewing with, asked me to solve a modelling question as a part of the initial written test. The questions were vague and open ended and ranged from designing a restaurant reservation system to designing a library for borrowing and renewing books. The expectation was to create a class diagram using any of your favorite uml tool (I chose Visio and have to admit i hadn't used it in a while) and send it as a part of their online test.
 
Since this was a part of an online test, I didn't have an opportunity to ask for use cases without which the questions are difficult to answer. Do you find these questions useful in interviewing developers?