That would be considered an affirmative representation of fact that was false and there would be a claim under NJ Consumer Fraud Act. Looks like a bait and switch to me which is not permitted under NJ law.
I would immediately save all advertisements for this complex in order to prove intent when they say it was a MISTAKE. How many mistakes can they make? I would be willing to assume that this is not an isolated incident and you are not the only one to have responded!
The issue would be one of damages. Did you agree to the $1,200? Did you go elsewhere?
See a NJ class action attorney. This seems likely to have multiple potential plaintiffs against a single defendant engaged in false advertising.
I am not your lawyer and you are not my client. Free advice here is without recourse and any reliance thereupon is at your sole risk. This is done without compensation as a free public service. I am licensed in IL, MO, TX and I am a Reg. Pat. Atty. so advice in any other jurisdiction is strictly general advice and should be confirmed with an attorney licensed in that jurisdiction.
I think you have already received good answers to your question, which was limited to false advertising as a cause of action. The NJ Dept of Consumer affairs is a good place to take your complaint to see if this particular landlord has a history here. Their website is http://www.njconsumeraffairs.gov/ocp/
I would look beyond the advertising issue or bait and switch issue - which of course is a standard tactic especially in the used car sales industry, and think about whether you might also have a housing discrimination claim (i.e., they offered YOU a higher price because of your race, sex, religion, or some other classification which the law prohibits).
Take a look here: http://portal.hud.gov/hudportal/HUD?src=/topics/housing_discrimination