If the 10-digit number 897359y7x2 is divisible by 72, then what is the value of(3x-y), for the possible greatest value of y ?

Given, 897359y7x2 is divisible by 72 then the number is divisible by 8 and 9

If the number is divisible by 8, then the last three digits should be divisible by 8

$$\Rightarrow$$  7x2 is divisible by 8

$$\Rightarrow$$  x = 1, 5, 9

If the number is divisible by 9, then the sum of the digits of the number should be divisible by 9

$$\Rightarrow$$  8 + 9 + 7 + 3 + 5 + 9 + y + 7 + x + 2 = multiple of 9

$$\Rightarrow$$  50 + y + x = multiple of 9

For x = 1

50 + y + 1 = multiple of 9

$$\Rightarrow$$  51 + y = multiple of 9

The only possible value of y is 3

For x = 5

50 + y + 5 = multiple of 9

$$\Rightarrow$$  55 + y = multiple of 9

The only possible value of y is 8

For x = 9

50 + y + 9 = multiple of 9

$$\Rightarrow$$  59 + y = multiple of 9

The only possible value of y is 4

So when x = 5, y has the greatest value 8.

$$\therefore\ $$3x - y = 3(5) - 8 = 7

Hence, the correct answer is Option C