TMUAmockz Set 1 Paper 2 · Question 6

Let $x$ be an integer. Consider the expression

\frac{5x}{12}+\frac x8.

Which of the following statements about $x$ are true whenever this expression is an integer?

I $x$ being a multiple of 24 is both necessary and sufficient for the expression to be an integer.
II $x$ being a multiple of 12 is sufficient for the expression to be an integer.
III $x$ must be a multiple of 8.
IV $x^2$ must be a multiple of 576.

AI and III only

BI and IV only

CI, III and IV only

DI, II, III and IV

EII, III and IV only

FIII and IV only

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