Hydrolysis of 4-chloro-3,3-dimethylbut-1-ene forms which products much faster than primary alkyl halides?
Apparently, (B) is wrong for obvious reasons.


The product formed fastest will be kinetically determined. Shifting of bonds takes time so the fastest formed product will be the the one where minimum migrations occur hence (A). 
As @orthocresol stated below, a stable compound similar to cyclopropylmethyl carbocation is forming here. "The double bond helps to kick out the chloride ion to give a stabilised carbocation, which makes it react much faster than usual". Hence product (A) will be favored thermodynamically too (refer).