If the net work on a particle is zero, can the speed change? The following question was on a quiz in physics class:

If the net work done on a particle is zero, which of the following statements must be true?
a) The velocity is zero
  b) The velocity is decreased
  c) The velocity is unchanged
  d) The speed is unchanged
e) There is no displacement for the object 

The correct answer was e.  In what scenario would the speed change?
There was an explanation beside the question:

Since the work done is zero, it indicates that the applied force is zero. Since Force = Mass X Acceleration, and the mass is not zero, this implies that the acceleration is zero.

When asked about this question, the teacher responded:

If there is no displacement, then only work done is zero.  If the speed is unchanged, then there is no acceleration.  This will lead to an absence of a force.  Hope it explains the situation. 

 A: If you've accurately described the problem and answer, your teacher made a mistake. The answer is d). Work is the change in kinetic energy, so if work is zero, kinetic energy is fixed and speed is fixed. Velocity can change by having the particle change direction. Velocity need not be zero, and therefore displacement need not be zero.
A: Work is $\vec{F}.d\vec{s}$ so your teachers answer holds only if the force is nonzero. Otoh, if the force is zero, the object could have been displaced (for eg: moved at a constant speed). So unless there is some other information specifying that the external force is nonzero (for eg: multi part problem, or other information) the answer cannot be option (e).
Note that anyways, option (e) is a subset of option (d). If an object is not displaced, then its speed stays unchanged and is zero. So option (d) can not be wrong.
EDIT: The description in the picture seems crazy in multiple ways! O_o
A: In addition to the previous answers. You can have a good example showing that the answer (e) is incorrect. If you considered a charged particle entering a magnetic field. The magnetic field will NOT exert work on the particle, it will change its velocity but NOT its speed.
The particle will keep moving in the magnetic field although no work is exerted on it. A net displacement could be obtained if the magnetic field was chosen properly. That proves your teacher is wrong. The correct answer is (d)
A: Using this from my book (Physics for Scientists and Engineers with Modern Physics 9th Ed):

If more than one force acts on a system and the system can be modeled as a particle,
  the total work done on the system is just the work done by the net force. If we
  express the net force in the x direction as o Fx, the total work, or net work, done as
  the particle moves from xi to xf is  
ΣW = the integral of ΣF from xi to xf

A proof that d) the speed of the particle must be unchanged is true:

If ΣW  =  the integral of ΣF from xi to xf   =  0, then Δx = 0  OR  ΣF = 0 (this alone is proof that e) there must be no displacement is false).  In the case that Δx = 0, the particle is not displaced and the speed is unchanged.  If ΣF  =  ma0+ma1+ . . . + man  =  m(Σa)  =  0 and m ≠ 0, then Σa = 0 and the speed is again unchanged.  Therefore, if ΣW = 0, then it is necessarily true that the speed remains unchanged.

A: Oh dear, I don't like it when physics teachers make conceptual mistakes like this. It certainly option d) the speed remains unchanged. Option e) is only valid if and only if the body is at rest with the inertial frame to begin with.
We cannot say velocity remains unchanged because the body could be rotating about an axis (change in direction alludes to change in velocity, but there is NO work done when an object is rotating about a fixed point).
