$CH_3-CO-CH_2-COOC_2H_5 \xrightarrow{NaOH, H_2O} A$. The product '$A$' in the reaction is

An unknown compound $(A)$ (molar mass $= 180$) on acylation gives a product (molar mass $= 390$). Find the number of hydroxyl group present in compound $(A)$.

Which $\beta$-keto acid shown will not undergo decarboxylation?

The product is:

Compound $A$ was prepared by oxidation of compound $B$ with alkaline $KMnO_4$. Compound $A$ on reduction with lithium aluminium hydride $(LiAlH_4)$ gets converted back to compound $B$. When compound $A$ is heated with compound $B$ in the presence of $H_2SO_4$,it produces a fruity smell of compound $C$. To which family do the compounds $A$,$B$,and $C$ belong?

Compound $A$ was treated with a large excess of $CH_3MgBr$. The resulting product was exposed to $POCl_3$ /pyridine to give compound $B$,as one of many products.
Which of the following compounds can be $A$ ?