Statement 1.
Either both x &y are positive or one of them is +ve, other is -ve
Hence x & y can be +ve or -ve
Insufficient
Statement 2
Either both x &y are -ve or one of them is +ve, other is -ve
Hence x & y can be +ve or -ve
Insufficient
Combining both equations
one of them is +ve and other is -ve
xy<0
Sufficient
IMO C
Either both x &y are positive or one of them is +ve, other is -ve
Hence x & y can be +ve or -ve
Insufficient
Statement 2
Either both x &y are -ve or one of them is +ve, other is -ve
Hence x & y can be +ve or -ve
Insufficient
Combining both equations
one of them is +ve and other is -ve
xy<0
Sufficient
IMO C