Chemical Kinetics - change to system conditions This is a question from a very old AP Chem exam (2006) prep book which I am amusing myself with in my spare time which is kind of humbling. There is something I am missing with this question, one of several similar questions in the kinetics section.

Given the following reaction (which doesn't establish an equilibrium) :
$\ce{A (g) + B (g) -&gt; C (g)}$
which of the following would increase the concentration of $\ce{A}$?

addition of $\ce{A}$ at constant $T$ and $V$
addition of $\ce{A}$ at constant $T$ and $P$
addition of $\ce{A}$ at constant $V$ and $P$


Now my first thoughts are to reason as follows :
If you add $\ce{A}$ and the volume is constant obviously the concentration of $\ce{A}$ increases. If you add $\ce{A}$ and keep $T$ and $P$ constant the $V$ will just expand and the concentration will be the same. But if I ignore the reaction this is a gas law / concentration question so it is out of place. But it isn't an equilibrium so none of that reasoning applies either.
Now if the reaction happens so slow it takes a year for $1\,\%$ of $\ce{A}$ to react I could just consider the reaction not even happening? If the reaction happens so fast that it is essentially over in 1 second then it seems like any change to A would be undone as fast as you could increase it. But it seems like I am missing something basic as there is nothing given regarding the rate.
There are several questions almost identical to this in the same section which just have other than $1:1$ coefficients in the equation.
As you said, your statement "If you add A and the volume is constant obviously the concentration of A increases" indeed does not apply.  In fact, the number of mols of A never changes.  Add a mol of A, and it reacts irreversibly with B and is gone forever as part of C.  

This means that the total volume must decrease for the concentration to increase, which means that "addition of A at constant T and P" must be correct, as it is the only answer that allows for a decrease in volume and therefore an increase in the concentration of A.  

An assumption made here that is not explicitly stated in the question, is that we never run out of B.