Partial Information

There are 2011 people in the group, where an unknown number of people are male and female. Person A engages in a conversation with you. You know that there are between 500 and 700 males at the party, exclusive. A knows that too, but he also knows some additional information that you don't know.

The conversation:

A: That guy's over there is wearing a purple shirt.

You: Yeah, he's a mathematician studying perfect squares.

A: By the way, the total number of females can be expressed as a sum of 3 squares.

You: Nice! But I still don't know how many males and females there are.

A: See that guy over there wearing a bandana? His name's Jack. I think he can tell you the number!

(You walk over to Jack)

Jack: The number of females is either odd, a triangular, or a fibonacci number.

You: I still don't know.

Jack: The number of males is the shape of my moustache.

You: (Stares at moustache) Thanks a lot!!! I've figured out the number of males and females!

If the ratio of number of males to females can be expressed as a/b, where a and b are positive coprime integers, then what is a+b?


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