Question

A crystal of formula $A{B}_3$ has $A$ ions at the cube corners and $B$ ions at the edge centres. The coordination numbers of $A$ and $B$, respectively, are $x$ and $y$, then the sum of $x$ and $y$ is:

Answer 1

Each $A$ atom present at the centre is surrounded by 6 $B$ atoms present at the edges it is connected to (2 in the plane, 2 above the plane and 2 below the plane). Thus the coordination number of $A=6$.
Each $B$ atom present at edge centre is surrounded by two $A$ atoms at the corners.
$x=6$
$y=2$
$x+y=8$