Bob
Please don't say "NO"!!
I know for sure that it is possible, because it happened to me once.
I added my friend on a new WhatsApp account registered by a new mobile number and didn't text him about it. To my surprise, he came to me the next day and said he knew it because he saw my number, name and profile photo!
I think there is some trick, or an advanced 3rd party app maybe, which tells you when someone add you on WhatsApp, even without any contact between you.
Please help

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