All numbers that are divisible by neither $$5$$ nor $$11$$ were removed from a sequence of consecutive natural numbers from $$1$$ to $$5500$$. A new sequence was formed. How many terms are there in this new sequence? (Adapted from $$2004$$ Math Kangaroo Problems, Level $$9-10$$, Question \#$$30$$) 
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Method $1$:  $5500\div5=1100$; $5500\div11=500$; $5500\div(5\times11)=100$.  $1100+500-100=1500$.  Method $2$:  In each group formed by $55$ consecutive numbers, $55-(11+5-1)=40$ numbers will be removed.  $5500\div55\times(55-40)=1500$ numbers will remain in this new sequence. 