Correct Answer - Option 4 : 2
Given:
Number = 179x091y
Concept used:
1) If the last three digits of a number are divisible by 8, then the number is completely divisible by 8
2) If the difference of the sum of alternative digits of a number is divisible by 11, then that number is divisible by 11 completely.
3) If any number is completely divisible by 88 then the number is also completely divisible by 8 and 11
Calculation:
Given number is completely divisible by 88 then it is also divisible by 11 and 8
When the number is divisible by 8 then,
91y is divisible by 8 when y = 2 ----(1)
When the number is divisible by 11 then,
(7 + x + 9 + y) – (1 + 9 + 0 + 1)
⇒ 16 + x + y – 11
⇒ x + y + 5
⇒ x + 2 + 5 ----(From eq (1))
⇒ x + 7
Now, (x + 7) is divisible by 11 when x = 4 then,
x – y = 4 – 2 = 2
∴ The required difference is 2
