A. β -ionone contains carbon-carbon double bonds, which can discolor acidic KMnO4 solution, so A is correct;

B. If both carbon-carbon double bonds and -CHO react with hydrogen, and 1mol intermediate X can react with 3molH2 at most, then B is wrong;

C vitamin A 1 contains a large hydrocarbon group, so it cannot be dissolved in water, so c is correct;

D. β -ionone is different from intermediate X in molecular formula by 1 CH2 group, so it is not an isomer, so D is wrong;

So choose AC.