Question
$20x3$ is a multiple of $3$ if the digit $x$ is ______ or ______ or ______.
✓
Answer
$20x3$ is a multiple of $3$ if the digit $x$ is $1$ or $4$ or $7.$
Solution:
We know that, if a number is a multiple of $3,$ then the sum of its digits is again a multiple of $3, i.e.\ 2 + 0 + x + 3$ is a multiple of $3.\ x + 5 = 0, 3, 6, 9, 12, 15$ But, $x$ is a digit of the number $ 20\ x\ 3.\ x$ can take values $0, 1, 2, 3, 9. = x + 5 = 6$ or $9$ or $12$ Hence, $x = 1$ or $4$ or $7$
Solution:
We know that, if a number is a multiple of $3,$ then the sum of its digits is again a multiple of $3, i.e.\ 2 + 0 + x + 3$ is a multiple of $3.\ x + 5 = 0, 3, 6, 9, 12, 15$ But, $x$ is a digit of the number $ 20\ x\ 3.\ x$ can take values $0, 1, 2, 3, 9. = x + 5 = 6$ or $9$ or $12$ Hence, $x = 1$ or $4$ or $7$
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