Draw an inverter. Draw the layout. No, I use a P-well process (or whatever is opposite of what you draw) Redraw it.
Draw a 4-1 mux using transmission gates (or whatever they think you don't know based on how you answered #1)
What tools do you know? Do you know Verilog (or VHDL)? How many pins was the biggest project you have made? What was the die area? Power dissipation? How could you have made the power dissipation smaller? (answer - smaller/better process!)
Some places will give you a big schematic - why won't this circuit work? They want to see you work a problem - noone can solve it by looking at it!!! Trace it out, and explain why you make the choices you do. Be calm and simply work the way you do. Even if you turn out wrong, they will know you are well prepared to understand how to approach things.
Those are some of the questions I remember I liked, and turned out good for me. Or you could use Intel's "famous" question to some of their candidates (no not me - they work you too hard!!)..
You have one match, and 10 inches of candle wick that will burn in one hour. The candle wick does NOT burn at an even rate, meaning if you cut it in half, one half may burn in 50 minutes, the other in 10. You need to make a timer to count out 15 minutes, 30 minutes after it it lit. Good luck.
If you think, it is like a current source problem..