Pretty straight forward.

1) many different pairs of consecutive odd numbers are possible. The only condition is that one of them should be negative. Pairs -100001, 100003 and -1, -3 as well as -1,1 will all satisfy this condition.

2) similar situation, only sign changed. Here 1 number has to be positive.

TOGETHER: The only pair that fulfils the condition is -1,1 whose sum is 0.

So D is correct.

wilderness think u meant c is answer...

Here is my soltion.

1. 3 number : atleast one is negative...
so numbers can be -1,-2 0
-1 0 1
-3 -2 -1
-100 -99 -98
all satisy atlease one -ve

2. atleast one positive again -1 0 1
1 2 3
0 1 2

now both conditions
one number needs to be +ve
one number needs to be -ve
and they all are consecutive
only soln is -1 0 1 ....abd their sum u can determine....

So C is answer.