For a Direct Broadcast Address host bits will always be 1's.
We have DBA 201.15.16.31 so we can guess that There would a class C IP address 201.15.16.X and Definitely We have done subnetting there otherwise as default mask for class C is 255.255.255.0 so in that way last octet is for host and for DBA all host bits would be converted to 1 so in that way last octet becomes 255 but as it's 31 so certainly subnetting is done and subnet bits are borrowed from host portion.
Now if we borrowed 1 bit from host portion (we borrow from left) then DBA last octet will have at least last 7 bits 1 but in 31 it's not the case
now if we borrowed 2 bit from host portion then DBA last octet will have at least last 6 bits will be 1 but that's also not the case (31 =>00011111)
Now if we borrowed 3 bits from host portion then DBA last octet will have at least last 5 bits will be 1 and yes in our given DBA last 5 bits are 1 so subnet mask can be 255.255.255.224 (/27)
Now if we borrowed 4 bits from the host portion then DBA last octet will have at least last 4 bits will be 1 so that's also possible.
and so on.