Recurring Decimal Integer Product

Let D be a recurring decimal of the form, D = 0.a₁a₂a₁a₂a₁a₂ ......., where digits a₁ and a₂ lie between 0 and 9. Further, at most one of them is zero. Then which of the following numbers necessarily produces an integer, when multiplied by D?

SELECT ONE OPTION

Ask about this question