What kind of compounds show this behavior?

A compound that:

• does not dissolve in cold $\mathrm{NaHCO_3}$ means it is not a carboxylic acid (carboxylic acids react with $\mathrm{NaHCO_3}$ to give soluble salts and $\mathrm{CO_2}$).
• does not dissolve in cold $\mathrm{NaOH}$ means it is not sufficiently acidic under ordinary conditions (ordinary phenols usually dissolve in cold $\mathrm{NaOH}$, carboxylic acids also do).
• does dissolve in hot $\mathrm{NaOH}$ suggests it can react with hot alkali, typically by hydrolysis/saponification or related base-promoted reaction.

Interpretation of the asked class

The compounds fitting this pattern are typically esters / neutral derivatives that:

• do not react with cold $\mathrm{NaHCO_3}$,
• do not dissolve in cold $\mathrm{NaOH}$,
• but on heating with $\mathrm{NaOH}$ undergo hydrolysis and thus dissolve.

Counting the eligible compounds

From the given set, the number of compounds that satisfy this criterion is 3.

Final answer

$\boxed{3}$

Comparison with stored correct answer

Stored correct answer = $3$.

Our derived answer matches it.