Forces on frictionless surface

I chose be because sum of x and y is equal to F. Would appreciate if each choice was analyzed

Answer credited to @Asafmen

This uses Newton’s Third Law, which states: when two bodies interact, they apply forces to one another that are equal in magnitude and opposite in direction.

In order to push the box X, the force must be great enough to overcome the force X exerts on Y.

After the force does so, the “rest” of the force is pushing the box, which is why the force experienced by X is less than that Y experiences.

Since they are in contact, we can treat this as a plastic collision- where the total Kinetic Energy does not remain the same.

M changes here, F is constant, so acceleration for Y+X will be smaller than Y- meaning X will experience less force.

F is needed to push both objects, but X experiences the force only after Y is moved. Therefore, the force is smaller.

The frictionless surface reduced this effect, but we cannot neglect it.