If x denotes the digit at hundreds place of the number 67x19 -175- such that the number is divisible by 11- Find all possible values of x-

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Standard VIII

Mathematics

Divisibility by 9

If x denotes ...

Question

If x denotes the digit at hundreds place of the number $\bar{67 x 19}$ such that the number is divisible by 11. Find all possible values of x.

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Solution

$A number is divisible by 11, if the difference of the sum of its digits at odd places and the sum of its digits at even places is either 0 or a multiple of 11 . Sum of digits at odd places - Sum of digits at even places = (6 + x + 9) - (7 + 1) = (15 + x) - 8 = x + 7 ∴ x + 7 = 11 \Rightarrow x = 4$

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If x denotes the digit at hundreds place of the number $\bar{67 x 19}$ such that the number is divisible by 11. Find all possible values of x.

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If x denotes the digit at hundreds place of the number 67x19¯ such that the number is divisible by 11. Find all possible values of x.

Anumberisdivisibleby11,ifthedifferenceofthesumofitsdigitsatoddplacesandthesumofitsdigitsatevenplacesiseither0oramultipleof11.Sumofdigitsatoddplaces-Sumofdigitsatevenplaces=(6+x+9)-(7+1)=(15+x)-8=x+7∴x+7=11⇒x=4

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If x denotes the digit at hundreds place of the number $\bar{67 x 19}$ such that the number is divisible by 11. Find all possible values of x.