Compound A is an optically active alcohol. Treatment with chromic acid converts A into a ketone, B. In a separate reaction, A is treated with PBr3, converting A into compound C. Compound C is purified, and then it is allowed to react with magnesium in ether. Compound B is added to the resulting solution of Grignard reagent. After hydrolysis, this solution if found to contain 3,4-dimethyl-3-hexanol. Propose structures for compounds A,B and C.