What happens to manifold pressure reading following a reduction in both throttle and RPM? This was one of the questions in my online ground school quiz (PPL), detail as follows: 

To set climb power, you reduce the throttle (manifold pressure) and then the props (RPM lever). After setting the props you expect the manifold pressure to:

A) not change
B) temporarily rises than fall again to where it was
C) fall slightly
D) rise slightly

My original answer was there is no net change in the MP reading after performing those two reduction actions. 

My understanding of MP reading is that a reduction in throttle would mean more suction/vacuum as a result so the MP reading would decrease. On the other hand a reduction in RPM would mean less suction/vacuum so the MP reading would increase. 

Because of the above, and that there is no other detail from the question as to how much changes each action had, wouldn't it be correct to expect MP reading to first decrease (from the throttle reduction) and then rises back again (from the RPM reduction). The net change therefore should be 0. 

The correct answer however was d) slightly rises. 
The explanation that was given is because the airplane was transitioning from take off power to climb power. 

Why does MP rises slightly in this case?
I think you misread the question. Assuming you quote it properly,


  To set climb power, you reduce the throttle (manifold pressure)


… so the first step does reduce the manifold pressure and is therefore not subject of the question …


  and then the props (RPM lever). After setting the props you expect the manifold pressure to:


… only the second step is.

In the second step, the manifold pressure slightly increases, which


  On the other hand a reduction in RPM would mean less suction/vacuum so the MP reading would increase.


… you already understand.

So yes, the manifold pressure decreases first—when you retard the throttle—and then increases slightly as you reduce pitch. Just the question only targeted the second part.

The increase won't be back to the original value, because the throttle is still partially closed. With wide open throttle the manifold pressure is (for normally aspirated engine) almost ambient pressure and there is nowhere higher it can go.