How does Nick react when Gatsby says, "look here old sport, what's your opinion of me, anyhow?"
The easiest way to answer this question is by going to the text. Nick says Gatsby "surprisingly" asks Nick, "what's your opinion of me anyhow?" Then he admits, "A little overwhelmed, I began the generalized evasions which that question deserves."
But this question is very Great Gatsby-esque in that it's upfront and in Nick's face. This is like a magician who performs tricks in front of an audience, but does not want the audience to really think about it too much.
In fact, the rest of what Gatsby tells Nick in this scene is much like a magic show, full of half truth.
Did Gatsby go to Oxford? Yes. But did he really go to Oxford? Not really.
Did Gatsby travel around the world? Yes. But did he live like a "rajah"? No.
So Gatsby's blunt question does what it's intended to, which is to distract Nick from figuring out what he really thinks about Gatsby.