# A number 78x19y07 is divisible by 99, Find the value of x - y

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A number 78x19y07 is divisible by 99, Find the value of x - y

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Correct Answer - Option 1 : 0

Given-

78x19y07 is divisible by 99

Concept Used-

A number is divisible by 9 if the sum of all the digits of the number is divisible by 9.

A number is divisible by 11 if the difference of the sum of alternate digits of the number(starting from 1st number) and the sum of alternate digits of the number(starting from the 2nd number) is divisible by 11.

Calculation-

For a number to be divisible by 99 it must be divisible by both 9 and 11

Hence, 78x19y07 is divisible by 9 and 11.

It means (7 + 8 + x + 1 + 9 + y + 0 +7) should be divisible by 9

⇒ 32 + x + y should be multiple of 9, i.e x + y can be 4,13

Again, {(7 + x + 9 + 0) - (8 + 1 + y + 7)} is multiple of 11, i.e x - y = 0,11

∵ x and y are unit digit integers the only values possible are x + y = 4 and x - y = 0

∴ Value of x - y = 0