If x is a digit such that the number 18x71 -175- is divisible by 3- find possible values of x-

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Standard IV

Mathematics

Multiplication

If x is a dig...

Question

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

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Solution

$It is given that \bar{18 x 71} is a multiple of 3 . ∴ (1 + 8 + x + 7 + 1) is a multiple of 3 . ∴ (17 + x) is a multiple of 3 . ∴ 17 + x = 0, 3, 6, 9, 12, 15, 18, 21 . . . But x is a digit . So, x can take values 0, 1, 2, 3, 4 . . . 9 . 17 + x = 18 \Rightarrow x = 1 17 + x = 21 \Rightarrow x = 4 17 + x = 24 \Rightarrow x = 7 x = 1, 4, 7$

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If x is a digit such that the number 18x71¯ is divisible by 3, find possible values of x.

It is given that 18x71¯ is a multiple of 3.∴(1+8+x+7+1) is a multiple of 3.∴(17+x) is a multiple of 3.∴17+x=0, 3, 6, 9, 12, 15, 18, 21...But x is a digit. So, x can take values 0,1,2,3,4...9.17+x=18 ⇒x=117+x=21 ⇒x=417+x=24 ⇒x=7x=1,4,7

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