Believe the Bible -- Why?

Today on Focus on the Family I heard Josh McDowell speaking to some group somewhere and he was talking about asking young people and their Christian leaders a question -- "Do you believe the Bible? Is it your authority on life?" Well in these Christian groups he always heard the same answer -- "Well, yes."
Then he asked them a deeply penetrating question -- "Why do you believe the Bible?" McDowell reports that no one could really answer. Except on one occaison.
One time he asked a youth leader the "Why?" question, and the guy responded, "Because I have faith." He said the others in the crowd started cheering. Sadly.
Does just because I have faith in something, does that make it authoritative and true? What about a Muslim, they have faith that the Koran is true -- does that make it true?
In this post-modern culture, truth becomes personal truth. What is true for me is true for me, I believe it and have faith in it. You may not. You may have your own truth.
I have often thought about going to someone in a witnessing encounter and saying to them, "The Bible says you must repent of your sins and trust Christ for salvation."
And their response would be, "Well what do I care what the Bible says. I don't believe the Bible. I've never read the Bible. Why should I put any stock in what that book says. Why not listen to what the Mormons say, they have a book of their own don't they? What makes the Bible the authority?"
Do we as Christian men and women, evangelical believers, know how we would respond to that response from our neighbors?
Hopefully in the next few days I will be posting here some reasoned responses.