In this construction, used with "not", it should be considered as meaning "even a little". When "remotely" is used without "not", it indicates "hardly" or "scarcely". She asked, "Is it possible?" He replied, "Remotely." He means there is a chance, although slight. "Not remotely" indicates zero chance. The word is used in oral English frequently.

Yep, I agree with what they all said. Remotely here is an adverb and it means, "a little, a bit" It is at times synonymous with, "slightly", although remotely is more on degree, content and distance. Yes, you may use remotely in conversations, but when using NOT + REMOTELY, you are placing STRONG EMPHASIS on zero possibility. Although I suggest putting 'even' after 'not' to complete the thought. EXAMPLE: A: Wow, the seminar was so great. The speaker was so eloquent. B: What? Are you kidding me? The seminar was not even remotely challenging! Yes, the speaker was so eloquent, but all the exercises were too elementary for Middle Managers. Using remotely in other ways: A: Are you done with the report? B: Yes, I'm, handing it in tomorrow. You done, too? A: Hah! Not remotely. Gotta work overtime tonight. (Meaning: Not close. Far from done. Not in the slightest) Another more formal conversation: A: Last quarter was a letdown. We almost reached the sales quota! B: Yeah. I hope we get to this quarter. The new manager's very capable. A: I doubt it. It's still remotely possible even if the management set a lower quota. B: You're such a pessimist.

In this case remotely means: in the slightest degree. To say something isn't remotely possible means there's absolutely no way it's possible. People usually use the word remotely like this to really emphasize something. If I said: He's not remotely funny. I would be placing a strong emphasis that I don't find him funny in even the slightest degree. I think we tend to use this phrase when its needed. It's a current way of speaking that people use today. It's not an old way of speaking.

"It's not remotely possible" means that the subject is very unlikely. Synonymous with "It's a long shot", and "It's doubtful", etcetera. In this instance, remotely means something far off or in a hidden place. Like a remote island. http://www.thefreedictionary.com/remote