It may not matter because the question talks about the faces of the cell, not the corners of the cell. Here is a list of all the common unit cells in an undergraduate class:
- Primitive cubic (also known as simple cubic)
- Face-centered cubic (FCC; also known as cubic close-packed, CCP)
- Body-centered cubic (BCC)
- Hexagonal close-packed (HCP)
Although the question doesn't specify which unit cell (though it should, to not confuse the student!), we can figure out that the only ones that have an atom on a face are the FCC and the HCP unit cells.
The FCC unit cell has six 1/2-atoms total on the faces, while the HCP, from what I can tell, has two 1/2-atoms total on the top and bottom faces.
No unit cell that you would need to know about has any different than 1/2 an atom on a face.