Batman: Arkham City) has shipped 6 million units, as of December 31, 2011. Now, "shipped" is a much different statistic than "sold," but it's a strong figure nonetheless.
It's difficult to tell how Warner Bros. Interactive did on its own in 2011, since its financial results are lumped in with two other Time Warner subsidiaries, (Warner Bros. Pictures and Warner Bros. Television), both of which brought in astounding amounts of money with their respective Harry Potter and Big Bang Theory licenses. Overall, Time Warner's "Filmed Entertainment" (tv, movies and gaming) reported revenues of $12.6 billion; a 9 percent year-over-year increase.
The statement also mentions Mortal Kombat and "several LEGO titles" as key contributors to the division's successful year.