Can every question be answered?

This morning I attended a small church service...maybe 10 people were there. The format of this church service is conducive to my learning style. One of the great things about this morning's service was that the pastor asked a few questions of us and we had a chance to have some small discussions. One of the questions was, "Can every question be answered?". I thought this was an awesome discussion topic, and one that could be debated indefinitely. 


What is the definition of a question?


Definition of QUESTION
1. a (1): an interrogative expression often used to test knowledge (2): an interrogative sentence or clause; b (1): a subject or aspect in dispute or open for discussion (2): a subject or point of debate or a proposition to be voted on in a meeting (3) the specific point at issue


2. a: an act or instance of asking, also: a judicial or official investigation b: torture as part of an examination c: room for doubt or objection


Knowing this, is a question necessarily something that has to have an answer? And if all questions had answers, would the mystery of the world be lost? 


Thoughts abound...