What does the incident with Mr. and Mrs. Sloan's tell us about Gatsby?

Answer: It tells us that Gatsby holds a different opinion from Tom and the Sloanes about what is appropriate and what isn't. He lacks their 'social manners.'

Explanation:

The novel Great Gatsby contrasts the aristocratic world of East Egg, and the newly-rich West Egg.

Gatsby lives in the West Egg. Having earned his money all by himself, he followed a different path and views life in a completely different way from the aristocrats. When Tom and the Sloanes arrive at Gatsby's, he invites them to stay for dinner. They refuse, but Mrs. Sloane politely invites Gatsby to have dinner with them. Gatsby fails to realize that Mr. Sloane is a troubled man who does not really want to see Gatsby in his house, and accepts their invitation. Gatsby leaves them so as to get ready for dinner, while Tom mocks him in front of Nick. In Tom's world, it is completely inappropriate of Gatsby to actually come to dinner. This demonstrates that Gatsby has a different set of values - he is naive for thinking that they were sincere with their invitation.