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Question
If x is a digit such that the number \[\overline{{18x71}}\] is divisible by 3, find possible values of x.
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Solution
\[\text{ It is given that }\overline{{18x71}}\text{ is a multiple of 3}. \]
\[ \therefore (1 + 8 + x + 7 + 1)\text{ is a multiple of 3} . \]
\[ \therefore (17 + x)\text{ is a multiple of 3 }. \]
\[ \therefore 17 + x = 0, 3, 6, 9, 12, 15, 18, 21 . . . \]
\[\text{ But x is a digit . So, x can take values }0, 1, 2, 3, 4 . . . 9 . \]
\[17 + x = 18 \Rightarrow x = 1\]
\[17 + x = 21 \Rightarrow x = 4\]
\[17 + x = 24 \Rightarrow x = 7\]
\[x = 1, 4, 7\]
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