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I am told that all three sugars below can be oxidized to their corresponding carboxylic acids using potassium permanganate.

This strikes me as bloody wrong because only hemiacetal sugars interconvert in solution with their open chain forms, and we need that open chain form to access the aldehyde/ketone for oxidation. Potassium permanganate as far as we know creates C-O bonds while not breaking any C-C bonds ... hence ... the general rule in our class is that ketones cannot be further oxidized (further oxidation would rupture C-C bonds).

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Each of your molecules also contains at least one primary alcohol appendage. Primary alcohols are readily oxidized by potassium permanganate to the corresponding carboxylic acid (see this link for more information).

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