Answer: D
In the dark the ionic mechanism gives the secondary cation (CHX3)X3C−CHX+−CHX3, which undergoes a 1,2-methyl shift to the tertiary cation (CHX3)X2CX+−CH(CHX3)X2 and gives 2-bromo-2,3-dimethylbutane. With peroxide, Br⋅ adds to the terminal carbon; the radical does not rearrange and the product is (CHX3)X3CCHX2CHX2Br.