Crystal Structure: Primitive base vectors etc

[ApeXaviour]

This is the question:
http://www.maths.tcd.ie/~cockburd/Question.jpg
It's not a homework question, merely one from a previous years tutorial sheet.
Okay so it's tetragonal conventional unit cell, has a sort of face centered structure right?
Em.. so that would mean it has a four point basis.
My attempt at labelling the vectors of the basis was:

Mn at 0, a/2*(A+B)
Ni at c/2*C + a/2*A, c/2*C + a/2*B

A, B and C being unit vectors.. (I changed them to capitals to avoid confusion with the magnitudes a,b and c). I really have absolutely no idea if this is correct. I took the origin to be the bottom rear left Mn atom and took the 3 nearest face centre ones to it. I brought it to the lecturer, explained my confusion, he took a quick glance and told me my answer too complicated, that it was cubic. Then he realised it wasn't, stated as much and proceeded to lose attention.
Then for the primitive vectors of the bravais lattice.
Well there are three right? lets call them a1, a2 and a3.

a1 = a/2*B +c/2*C
a1 = a/2*(A + B)
a3 = a/2*A +c/2*C

So am I close or have I completely misconceived what the bravais lattice and primitive base vectors are?
Thanks
-Declan

[inha]

Looks ok to me. You get the tetragonal unit cell by stretching the cubic cell along one of the lattice vectors so keeping it closely analogous to cubic FCC is the right way to go.