If two objects collide and are stationary, what must the total momentum of the sum of the objects have been before collision?

Explanation:

Concept: In collision between two isolated bodies momentum is always conserved.

Also, if the collision is elastic kinetic energies are also conserved

m1v1i + m2v2i = m1v1f + m2v2f.

and in elastic collision

Momentum is preserved in collisions between two objects. The initial moment not being zero, the final momentum is not zero. This means both object has to be in motion.

However, it may be possible for one of the objects to be at rest after the collision.  For instance, if the masses of the two objects are same, then after a head-on elastic collision the object initially at rest is moving and the object initially moving is at rest.