# If a nine-digit number 43x1145y2 is divisible by 88, then the value of (2x - y), for the largest value of y, is:

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If a nine-digit number 43x1145y2 is divisible by 88, then the value of (2x - y), for the largest value of y, is:
1. 1
2. 5
3. 0
4. -1

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Correct Answer - Option 1 : 1

Given:

A nine-digit number 43x1145y2 is divisible by 88, then the value of (2x - y), for the largest value of y

Concept used:

Divisibility

Calculation:

A nine-digit number 43x1145y2 is divisible by 88

A number is divisible by 88 means its divisible by 11 and 8

⇒ 11 × 8 = 88

To check the divisibility of 8 check the last three digits

5y2 should be divisible by 8

y should be 9 or 5 or 1

⇒ 592 or 512

But as per the question we have to consider the largest value ∴ y = 9

⇒ $\frac{{592}}{8} = 74$ which is completely divisible

The nine digit becomes 43x114592

Checking it with divisibility of 11 : (Sum of digits at odd places - Sum of digits at even places) = 0 or 11

⇒ (2 + 5 + 1 + x + 4) - (3 + 1 + 4 + 9) = 0

⇒ (12 + x) - (17) = 0

⇒ x - 5 = 0

⇒ x = 5

Value of (2x - y) = 10 - 9 = 1