If $x$ is a digit such that the number $18 x 71$ is divisible by $3$ , find possible values of $x$ .

1

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4

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7

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All of these

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Solution

The correct option is D All of these
If the sum of digits of a number divisible by $3$ , then it is a multiple of $3$ .
$∴ 1 + 8 + x + 7 + 1 = 3 n$
$\Rightarrow 17 + x = 3 n$
Here, $n = 6, 7, 8,$
$\Rightarrow 17 + x = 18, 21, 24$
$\Rightarrow x = 1, 4, 7$

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