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

(Since 24*x* is a
multiple of 3, its sum of digits 6 + *x* is a multiple of 3; so
6 + *x* is one of these numbers: 0, 3, 6, 9, 12, 15, 18….
But since *x* is a digit, it can only be that 6 + *x* = 6
or 9 or 12 or 15. Therefore, *x* = 0 or 3 or 6 or 9. Thus, *x*
can have any of four different values)

Since 24*x* is a
multiple of 3, the sum of its digits is a multiple of 3.

Sum of digits of 24*x*
= 2 + 4 + *x* = 6 + *x*

Hence, 6 + *x* is
a multiple of 3.

This is possible when 6
+ *x* is any one of these numbers 0, 3, 6, 9, and so on …

Since *x* is a
single digit number, the sum of the digits can be 6 or 9 or 12 or 15
and thus, the value of *x* comes to 0 or 3 or 6 or 9
respectively.

Thus, *x* can have
its value as any of the four different values 0, 3, 6, or 9.

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