Note that $$45=5\times 9$$. As $$5$$ and $$9$$ are coprime, a positive integer is a multiple of $$45$$ if and only if it is a multiple of both $$5$$ and $$9$$. The units digit of all five options is $$5$$, so they are all multiples of $$5$$. An integer is a multiple of $$9$$ if and only if the sum of its digits is also a multiple of $$9$$. The sums of the digits of the five options is $$18$$, $$18$$, $$18$$, $$18$$ and $$8$$. So $$305$$ is the only one of the options which is not a multiple of $$9$$ and hence is not a multiple of $$45$$. 
Which of the following integers is not a multiple of $$45$$? 
a) $$765$$ 
b) $$675$$ 
c) $$585$$ 
d) $$495$$ 
e) $$305$$ 