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In the movie, set in 1922, Leonardo DiCaprio as Gatsby drives a 1929 Duesenberg Model J.
As Jerry Garrett at the New York Times points out, it's unlikely that Gatsby would be driving a Duesenberg of any kind: The company had just gone into business in 1922, and the Model J — the car that made it a popular brand — did not enter production until 1928.
In F. Scott Fitzgerald's novel, Gatsby drives a yellow Rolls-Royce, and since the most popular model from the British automaker in 1922 was the 40/50 HP, aka the Silver Ghost, it's a good bet that's what the image-obsessed Gatsby would have purchased.
Rolls-Royce also produced the "baby" Rolls-Royce 20 HP in 1922, a less grandiose car unlikely to appeal to the Long Island bootlegger.
This 1922 Silver Ghost was sold by RM Auctions in 2012, for £112,000 (182,574 in 2013 USD). Imagine it in yellow, and that's what Gatsby should be driving:
In contrast, here's a Duesenberg Model J:
