Students guess that Norb\textquotesingle s age is $$24$$, $$28$$, $$30$$, $$32$$, $$36$$, $$38$$, $$41$$, $$44$$, $$47$$, and $$49$$. Norb says, "At least half of you guessed too low, two of you are off by one, and my age is a prime number." How old is Norb? ($$2011$$ AMC $$8$$ problem, Question \#$$21$$) 
Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems
If at least half the guesses are too low, then Norb\textquotesingle s age must be greater than $$36$$.  If two of the guesses are off by one, then his age is in between two guesses whose difference is $$2$$. It could be $$31$$, $$37$$, or $$48$$, but because his age is greater than $$36$$, it can only be $$37$$ or $$48$$.  Lastly, Norb\textquotesingle s age is a prime number so the answer must be $$37$$. 