Rather than go into great detail on why I don't like their questions, I'm going to pick out one that stands out as an example. It starts:
"Suppose I want to <description of some user story>, so I want you to design a system that <vague description of an implementation method>."
Okay, I'm thinking, done this before a lot of times, it's bland but not an unreasonable way to find out how somebody approaches problems. But they haven't finished talking, and they add one more sentence:
"Make sure you show me the objects and classes that your system will use."
This is the point when I try not to let my disappointment and irritation show. It's not just that they've completely prejudiced the question, by forcing it down one particular design path, it's that they've made it clear this is not a test of my ability to design systems, it's a test of my ability to mimic their design of the system. Worse yet, in one stroke this destroys any hope of finding out how the candidate thinks; instead, it just measures how well they can think along certain lines.
I don't have a problem with object-oriented designs - I'd probably have done things that way anyway. But I do have a problem with companies that hire based on conformity to groupthink. I don't want to work with a group of people who were selected based on their performance at this kind of question.