As a promotional single, it aimed for radio airplay only and was the number one most added R&R mainstream rock track in America during the week of its release.

Both releases featured artwork, with the main CD single using a similar design to the album cover, using a red spiraling background and a drawing of a woman and a man.

[9] The CDr single featured artwork which highlighted a close-up of each band member in front of a circular black and white checkered background.

[11] No music video was created for the single, although the song became part of the band's live set before and after the album's release, often as an encore.

[15] On April 5, 2005, a five track extended play "Sessions@AOL" was released by the band, which included "Scent of a Woman".

[17] Upon release, Billboard said of Special One: "Fans and rock programmers will find plenty to love in such tracks as "Scent of a Woman," "My Obsession" and "If I Could."

"[21] Asbury Park Press highlighted the song as the "most notable" of the album's "first-rate tunes", describing it as a "rousing rocker with a killer melody and a walloping beat".

[24] The Worcester Telegram Gazette felt Special One was "pure Cheap Trick, from the big-gun blast of "Scent of a Woman"..."[25] Concert Shots writer Chris McKay said the song "sounds like AC/DC if they'd spent more time listening to The Move".

"[27] MelodicRock.com commented: ""Scent of a Woman" is a cracking feel good rocker that goes right back to the heart of what makes Cheap Trick special.

"[32] Shortly before the album's release, the Chicago Tribune reviewed a Cheap Trick live concert and mentioned the song: "...and "Scent of a Woman" came on like gangbusters to open the encore, sexual politics turned into a blue-eyed soul rampage, underscored with bombastic Who-like power chords.

"[33][34] In a 2004 concert review by Pittsburgh Post-Gazette, Ed Masley stated: "Two new songs, "My Obsession" and "Scent of A Woman," held up surprisingly well".