That is a competency based interview mate
The interviewer asks you these kind of questions so that you give them examples of how you illustrated a particular competency. For example the question above would be asked to measure your ability to work in teams. Every question is supposed to measure one or more competency.
Its not easy answering such questions, but i suggest you read tips on "how to answer competency based interview questions" next time. Most organizations that try and adopt sound HR practices use the competency based interview at some stage.
I work in human resources for a university.