Which of the following compounds reacts immediately with Lucas reagent?

In the reaction sequence $CH_2=CH_2$ $\xrightarrow{HOCl} X$ $\xrightarrow{Y} CH_2(OH)-CH_2(OH)$,$X$ and $Y$ respectively are:

Glycerol on treatment with oxalic acid at $110 \ ^oC$ forms

An alcohol having molecular weight $74$ gives white turbidity with Lucas reagent within $5-10$ minutes. It reacts with sodium metal to give $Y$. $Y$ reacts with $CH_3-Br$ to give $Z$. $Z$ is:

$A$ hydroxy compound $(X)$ with molar mass $122 \ g \ mol^{-1}$ is acetylated with acetic anhydride,using a large excess of the reagent ensuring complete acetylation of all hydroxyl groups. The product obtained has a molar mass of $290 \ g \ mol^{-1}$. The number of hydroxyl groups present in compound $(X)$ is :

The major product is: