If the formula of the sodium salt of an anion X is Na₂X, then the form

If the formula of the sodium salt of an anion X is Na₂X, then the formula of its aluminium salt would be

AlX
AlX₂
Al₂X₃
AlX₃
This question was previously asked in
UPSC CAPF – 2019
The correct answer is C, Al₂X₃.
The formula Na₂X indicates that the anion X has a charge of -2 (X²⁻) because sodium (Na) has a charge of +1, and there are two sodium ions balancing the charge of one X anion (2 * +1 + charge of X = 0, so charge of X = -2). Aluminium (Al) forms ions with a charge of +3 (Al³⁺).
To form a neutral compound between Al³⁺ and X²⁻, the total positive charge must equal the total negative charge. The least common multiple of the absolute charges (3 and 2) is 6. We need two Al³⁺ ions to get a total positive charge of +6 (2 * +3) and three X²⁻ ions to get a total negative charge of -6 (3 * -2). Therefore, the formula for the aluminium salt of anion X is Al₂X₃.