Data Sufficiency

Is the product st negative?

(1) s^2 - s < 0
(2) (s-4)/(t-3) = 1

OA is C. I don't understand how B cannot be sufficient.
Stmt 2 says S=t+1, which means one of them is 0 so st=0 OR both positive OR both negative. In all these cases st is positive or 0 which means it is not negative. This should be sufficient. What am I missing here? Can some one please give me an example.
Thanks.

PGMAT wrote:Is the product st negative?

(1) s^2 - s < 0
(2) (s-4)/(t-3) = 1

OA is C. I don't understand how B cannot be sufficient.
Stmt 2 says S=t+1, which means one of them is 0 so st=0 OR both positive OR both negative. In all these cases st is positive or 0 which means it is not negative. This should be sufficient. What am I missing here? Can some one please give me an example.
Thanks.

Statement 1: s² < s.
s must be a positive fraction between 0 and 1.
In other words:
0 < s < 1.
No information about t.
INSUFFICIENT.

Statement 2: (s-4)/(t-3) = 1
s-4 = t-3
s = t+1.
If t=0 and s=1, then st is not negative.
If t=-1/2 and s=1/2, then st is negative.
INSUFFICIENT.

Statements 1 and 2 combined:
Substituting s=t+1 into 0 < s < 1, we get:
0 < t+1 < 1
-1 < t < 0.
Since s is positive and t is negative, st is negative.
SUFFICIENT.

The correct answer is C.

An important take-away:
It is important to note how a problem is RESTRICTED and how it ISN'T.
Since there is no requirement here that s and t be integers, we must consider FRACTIONS.