You are right.
There was some confusion about the sign of charges. The problem text said that "The sphere has a total charge of 2Q and the shell has a total charge of 3Q."
The charge locates on the surfaces. So there is 2Q charge on the surface of the inner sphere of radius a. By induction, there is -2Q charge on the inner surface of the shell, a sphere of radius b, and to make the total charge of the shell 3Q, there must be 5Q charge on the outer surface of radius c.