Lucas reagent is a mixture of $HCl$ and anhydrous zinc chloride.
Tertiary alcohols react immediately with Lucas reagent as evidenced by turbidity owing to the low solubility of the organic chloride in the aqueous mixture. Secondary alcohols react within five or so minutes (depending on their solubility). Primary alcohols do not react appreciably with Lucas reagent at room temperature. B is a secondary alcohol, C and D are primary alcohol. Only $A$ is a tertiary alcohol, so the reaction of Lucas reagent is fast with $A$.