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
