Members of the media often attempt to put Christians on the spot by asking a question like that.  But, when asked, an honest Christian should not try to wiggle out of it.  Since God created everything in 6 days, and man was created the same day as other land animals (assuming that the large dinosaurs we find in the fossil record are not the result of some kind of cross breeding--and we can't know that for sure), it is hard to argue against their having lived at the same time.  Furthermore, since most of the dinosaur fossils were rapidly buried in the Flood, it is an inescapable conclusion that man and dinosaurs existed together, regardless of whether or not they were created or hybridized.  Only if one buys into the evolutionary fairy tale ("the greatest hoax on earth"), is there a problem.