I had almost exactly this same engineering test when google interviewed me in 2006. It was terrible, and left a bad taste in my mouth. Given the complexity of the work I was doing at the time, the entire thing seemed ridiculous.
replies(2):
Recruiter: "I was looking for you to say it's a fingerprint"
So I guess I was wrong, because despite explaining them in decent detail, I didn't use the one keyword.
So he asked "how did you figure this out so fast?". I told him I didn't, I just remember all the "important" powers of 2. He said "well... that's not what I was looking for, I wanted you to calculate it, but... I guess a candidate who memorizes powers of 2 is a positive sign?". I passed.