If x is a digit of the number $\bar{66784 x}$ such that it is divisible by 9, find possible values of x.

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Solution

$It is given that \bar{66784 x} is a multiple of 9 . Therefore, (6 + 6 + 7 + 8 + 4 + x) is a multiple of 9 . And, (31 + x) is a multiple of 9 . Possible values of (31 + x) are 0, 9, 18, 27, 36, 45, . . . But x is a digit . So, x can only take value 0, 1, 2, 3, 4, . . . 9 . ∴ 31 + x = 36 \Rightarrow x = 36 - 31 \Rightarrow x = 5$

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If x is a digit of the number 66784x¯ such that it is divisible by 9, find possible values of x.

It is given that 66784x¯ is a multiple of 9.Therefore, (6+6+7+8+4+x) is a multiple of 9.And,(31+x) is a multiple of 9. Possible values of (31+x) are 0, 9, 18, 27, 36, 45,...But x is a digit. So, x can only take value 0, 1, 2, 3, 4,...9.∴31+x=36 ⇒x=36-31⇒x=5

If x is a digit of the number $\bar{66784 x}$ such that it is divisible by 9, find possible values of x.