Answer:
<em>A) the moment of inertia of the system decreases and the angular speed increases.
</em>
Explanation:
The complete question is 
A merry-go-round spins freely when Diego moves quickly to the center along a radius of the  merry-go-round. As he does this, It is true to say that
A) the moment of inertia of the system decreases and the angular speed increases.
B) the moment of inertia of the system decreases and the angular speed decreases.
C) the moment of inertia of the system decreases and the angular speed remains the same.
D) the moment of inertia of the system increases and the angular speed increases.
E) the moment of inertia of the system increases and the angular speed decreases
In angular momentum conservation, the initial angular momentum of the system is conserved, and is equal to the final angular momentum of the system. The equation of this angular momentum conservation is given as
 ....1
    ....1
where  and
 and  are the initial and final moment of inertia respectively.
 are the initial and final moment of inertia respectively.
and  and
 and  are the initial and final angular speed respectively.
 are the initial and final angular speed respectively.
Also, we know that the moment of inertia of a rotating body is given as
 ....2
    ....2
where  is the mass of the rotating body,
 is the mass of the rotating body,
and  is the radius of the rotating body from its center.
 is the radius of the rotating body from its center.
We can see from equation 2 that decreasing the radius of rotation of the body will decrease the moment of inertia of the body.
From equation 1, we see that in order for the angular momentum to be conserved, the decrease from  to
 to  will cause the angular speed of the system to increase from
 will cause the angular speed of the system to increase from  to
 to  .
 .
From this we can clearly see that reducing the radius of rotation will decrease the moment of inertia, and increase the angular speed.