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Question:

If 24x is a multiple of 3, where x is a digit, what is the value of x?

Solution:

Since24xis a multiple of3, its sum of digits6+xis a multiple of3;So,6+xis one of these numbers:0,3,6,9,13,15,18,….Sincexis a digit, it can only be that6+x=6or9or12or15.Therefore,x=0or3or6or9.Thus,xcan have any of four different values.