Question : If a nine-digit number 785$x$3678y is divisible by 72, then the value of ($x$ – $y$) is:
Option 1: –2
Option 2: 0
Option 3: 2
Option 4: –1
Correct Answer: 2
Solution : 785$x$3678y is divisible by 72. ⇒ 785$x$3678y is divisible by 8 and 9. 78$y$ is divisible by 8 only when $y$ = 4 So, the number becomes 785$x$36784. 785$x$36784 is divisible by 9 when the sum of digits of the number is divisible by 9. 7 + 8 + 5 + $x$ + 3 + 6 + 7 + 8 + 4 = 48 + $x$ At $x$ = 6, the sum of the digits of the number is divisible by 9. So, we found, $x = 6$ and $y =4$ $\therefore(x-y) = 6 - 4 = 2$ Hence, the correct answer is 2.
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