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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


Team Careers360 17th Jan, 2024
Answer (1)
Team Careers360 25th Jan, 2024

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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