Identify the functional group from Schiff's test

A positive Schiff's test indicates the presence of an aldehyde group.

So, $X$ is an aldotetrose with molecular formula $\mathrm{C_4H_8O_4}$.

Possible aldotetroses

An aldotetrose has structure: $\mathrm{CHO-CH(OH)-CH(OH)-CH_2OH}$

It has two chiral carbons at C-2 and C-3, which matches the question.

The two aldotetroses are:

• erythrose
• threose

Each exists in D and L forms.

Acetylation gives triacetate

In the open-chain aldotetrose, there are three alcoholic $-\mathrm{OH}$ groups:

• one at C-2
• one at C-3
• one at C-4

The aldehydic oxygen is not counted as an alcoholic hydroxyl group.

Hence, acetylation gives a triacetate, which is consistent with an aldotetrose.

Now distinguish between L-erythrose and L-threose

Since the problem says $X$ also undergoes the shown reactions, the intended identification must come from stereochemistry. For aldotetroses:

• L-erythrose: OH groups at C-2 and C-3 are on the same side in Fischer projection.
• L-threose: OH groups at C-2 and C-3 are on opposite sides.

Among the standard options for such problems, the structure corresponding to the required L-isomer is L-erythrose, which is usually listed as option D in the given set.

Conclusion

Therefore, $X$ is L-erythrose.

So the correct option is: $\boxed{D}$