Question : If a nine-digit number 785$x$3678$y$ is divisible by 72, then the value of ($x$ + $y$) is:
Option 1: 20
Option 2: 12
Option 3: 10
Option 4: 5
Correct Answer: 10
Solution :
Given number = 785$x$3678$y$ is divisible by 72, then the number must be divisible by 8 and 9.
785$x$3678$y$ is divisible by 8 if the last digit three-digit 78y is divisible by 8.
78$y$ is divisible by 8 if $y$ = 4
785$x$36784 is divisible by 9 if its digit sum is divisible by 9.
= 7 + 8 + 5 + x + 3 + 6 + 7 + 8 + 4
= 48 + $x$
Put $x$ = 6
= 48 + 6
= 54
As we know, 54 is divisible by 9.
Now,
= $x$ + $y$
= 6 + 4
= 10
Hence, the correct answer is 10.
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