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Sodium Sulfate vs Sodium Sulfite

I recently took a test and one of the questions was:

Which procedures will allow a student to differentiate between solid sodium sulfate and solid sodium sulfite?

I. Make solutions of each and look for a precipitate when added to $0.10$ M barium nitrate.

II. Add crystal of each to $0.10$ M HCl and watch for bubbles.

III. Make solutions of each and test with a pH indicator.

The answer is 2 and 3, however, I incorrectly answered 2 only. I have actually thought a long time about this question.

Why is III also correct, if sodium sulfate and sodium sulfite are both basic and would turn pH indicator the same color?