Ans C
We need to show that s+t = 0 only possible if one is +ve and other is the -ve value of it. or s=-t

St 1
s=t or s=-t

St 2
Don't know if they are same values

St1 and St2

s=-t

I'll go with A

Given: s and t are 2 different numbers.
Asked: is s+t = 0 or is s = -t?

St 1: s cannot be equal to t (since they are 2 different numbers)
So the only option left is s = -t.

So St 1 is suff.

St 2: it just means that the 2 numbers have opposite signs.

So St 2 is insuff.

IMO A

key is to understand s and t are different nos.

same explanation as mals24

by 1 distance of s and 0 will be equal to 0 and t only when 0 is the midpoint of both the nos.
hence s = -t.
suff.

2. 0 can be anywhere between s and t. hence insuff.

IMO A

Attempted this question today. I like the title "Trivial number line".

As per (1), if distance of s and t from 0 is the same (and it is given that s and t are "different" numbers), then it has to be the case that one is positive and the other is negative and they are equi-distance from 0.
=> s + t = 0
Sufficient.

As per (1), 0 is between s and t. This obviously does not tell us anything about the actual values. For example, it is possible that s = 5, t = -1; or it is possible that s = 5, t = -5.
Insufficient.

Hence, A.

A is correct here. Remember to pay attention to every bit of information you're given in the question stem; even little phrases like "two different numbers" can completely change the solution to a DS problem.