# If the 8-digit number 179x091y is divisible by 88, then what is the value of (x – y)?

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If the 8-digit number 179x091y is divisible by 88, then what is the value of (x – y)?
1. 3
2. 4
3. 1
4. 2

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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