Correct Answer - Option 4 : 2
Given:
Given number is 785x3678y
The number is divisible by 72
Concept used:
If a number is divisible by 72 then the number will be divisible by 8 and 9
A number is divisible by 8 if the last three digits are divisible by 8.
A number is divisible by 9 if the sum of its digits is divisible by 9.
Calculation:
As, the number 785x3678y is divisible by 8
⇒ 78y is divisible by 8
For y = 4, the number is divisible by 8
As, the number 785x3678y is divisible by 9
⇒ 7 + 8 + 5 + x + 3 + 6 + 7 + 8 + y is divisible by 9
⇒ 44 + x + y is divisible by 9
⇒ 44 + x + 4 is divisible by 9
⇒ 48 + x is divisible by 9
Nearest integer to 48 is 54 which is divisible by 9
48 + x = 54
⇒ x = 6
x – y = 6 – 4
⇒ 2
∴ The value of (x – y) is 2
