The universal indicator is used to determine the presence of an acid or base, going from acid to base it changes in the order of the rainbow with green being neutral. Chemical X is Hydrogen Chloride (HCl) we know this because it is a strong acid therefore the indicator would turn red. Chemical Y is Sodium Hydroxide (NaOH) we know this because it is a base therefore the indicator would turn purple. Finally Chemical Z is Sodium Chloride (NaCl) which is neither an acid or base meaning it would turn green for neutral. Another thing that helped determine which one was an acid was Chemical had a reaction with the magnesium while the others did not, when reacted with bases, only the magnesium has a reaction.
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