If at least half the guesses are too low, the Norb\textquotesingle s age must be greater than $34$. If two of the guesses are off by one, then his age is between two guesses whose difference is $2$. It could be $29$, $35$ or $37$, but because his age is greater than $34$, it can only be $35$ or $37$. Lastly, Norb\textquotesingle s age is a prime number so the answer must be $37$. 
Students guess that Norb's age is $28$, $30$, $34$, $36$, $38$, and $41$. Norb says, "At least half of you guessed too low, two of your guesses are off by one, and my age is a prime number."~How old is Norb? (adapted from 2011 AMC 8 Problem, Question \#21) 
[a] $$25$$ 
[b] $$29$$ 
[c] $$31$$ 
[d] $$37$$ 
[e] $$14$$ 