Let A and B two sets. The set A has 2016 more subsets than B. If  $A\cap B$  has 3 members, then the number of members in  $A\cup B$  is

If A has m members and B has n members, then
$2^m-2^n=2016=2^5.63$
$\Rightarrow 2^n(2^{m-n}-1)=2^5(64-1)=2^5(2^6-1)$
 $\Rightarrow n=5$   and  $m-n=6\Rightarrow m=11$
The number of members in  $A\cup B$ $=11+5-3=13$