Google User Experience Designer interview questions

I had a phone call with the recruiter and hiring manager. Answered several questions on the phone about process and experience. After the call they asked me to complete an unpaid homework assignment. This assignment took about a week to do. After submitting the work, I received a generic decline letter. I know this is a very competitive job, but I don’t understand why they think it is acceptable to ask for a week of unpaid work from a candidate without giving any explanation on their decision. In my opinion they should revise their interview process.

I applied quite late online, only a day or two before the deadline. A day after applying I received a questionnaire. Filled out a questionnaire and had a design project. Had one interview but no response after. There was no indication whether I was rejected or still in the application pool