SAT Question Everyone Got Wrong

[Albert Chan]

Paper models to count faces when joining tetrahedron and pyramid, is not convincing enough.
We could have what is claimed as 1 face really is 2, just visually too close to call.

From https://math.stackexchange.com/a/1856243, adding an extra pyramid is much better.
Pink bottom angle = 180° - 2*60° = 60°, which make Pink region a tetrahedron.