Easy solution simplified


#1

THERE IS A PRETTY GOOD REASON WHY STATEMENT 1 HAS BETTER OFFER
Just choose 1st statement and then state “I will not get 10$ nor 500$”

Now if this statement goes true they will have to give you 10$ which makes this statement false
and if the statement is false then they have to give to 500$ or 10$ but giving 10$ makes statement true
so the only case is giving 500$ and hence offer is better because you can ask for any amount of sum.