I'm not even sure how to approach this question. At first, I thought that because the flux of the field $F$ through the smaller sphere was $20$, then the flux through the larger sphere should also be $20$ (Does the flux of $F$ represent the rate of flow of gas?) but that doesn't necessarily have to be true.
I'm not sure how to use the divergence either. I think the divergence theorem states that the flux through the larger sphere is equal to the volume integral of the divergence throughout the larger sphere, but I only have the divergence on the surface of the smaller sphere. Am I supposed to calculate the divergence at all points from that information?