finding the state of a transistor
Yes you have assumed this, but this is still not a bad first stab analysis technique. For example, by assuming the BJT is in its active region of operation, you can do easy back of the envelope calculations to determine parameters like the voltage drop between collector and emitter to easily tell by contradiction if the transistor could not possibly be in its active region.It is worth pointing out however that the inverse of this technique is not strictly true, of course. In practical engineering, the datasheet of a transistor will have guidelines on how to ensure reliable active operation of the transistor part over its rated environmental tolerances.