No. Despite an article I just read on Cincinnati's Fox19.com. This is just not accurate, or at least not in the manner in which Fox19.com claims.
According to Fox19.com, truthfully answering the Facebook profile questions regarding where you were born and how old you are gives identity thieves enough information to reverse engineer your Social Security number. While the answers to those questions might accidently help an identity thief guess your SSN, its not that much help and not for the reasons Fox19 claims.
The Fox19.com article claims that the first three numbers of your SSN are based on where you were born. If that were true, then, yes, correctly providing the city and state where you were born would help ID thieves guess the first three digits of your SSN.
BUT ... the first three digits are not based on where you were born but instead are based on the zip code given on your SSN application. So it could be in the state where you were born. But in many, many instances, that's not so.
For instance, I was born in Louisiana. At the time that I was born, my parents and siblings lived in Arkansas. However, we moved to Mississippi when I was four years old and, after moving to the Magnolia State, my parents applied for my SSN. So the first three digits of my SSN match one of the various sets of 3 digit numbers for Mississippi, not Louisiana where I was born or Arkansas where my family was living when I was born.
Another example - my wife was born in Tennessee but her family lived at the time in Mississippi. Apparently, her parents also applied for her SSN in Mississippi, because the first three numbers of her SSN also match one of the 3 digit Mississippi combinations, but not the same 3 digit combination that I have.
So its simply not as easy as knowing where you are born.
As for the second part of your SSN, called the grouping, correspond to when you applied for your SSN, which does not necessarily relate to when you were born. For instance, my grouping would be approximately 4 years after I was born. My daughter's SSN was also not requested when she was born but years later. Some people get their kids' SSNs as soon as they are born only to lose them later and have to do it all over again.
So feel free to be honest on Facebook about where and when you were born, unless of course you don't want the internet knowing how old you really are.