Correct Answer - Option 2 : 72
Given:
The nine-digit number = 48x4923y8
Divisible by = 88
Concept used:
Divisibility rule of 8 - The last three digits of a number are divisible of 8
Divisibility rule of 11 - If the difference between the sum of the digits at odd places and even places equals 0 or divisible by 11
Calculation:
We know that the last three digits of a number are divisible of 8
⇒ The number made from the last three digits without altering their position will be divisible by 8
⇒ Possible values of y = 2 and 6
⇒ y is the largest then, y = 6
Now, check the divisibility rule of 11
⇒ (4 + x + 9 + 3 + 8) – (8 + 4 + 2 + y) = 0 or 11
⇒ (4 + x + 9 + 3 + 8) – (8 + 4 + 2 + 6) = 0 or 11
⇒ (24 + x – 20) = 0 or 11
⇒ 4 + x = 0 or 11
Then, x = (11 – 4) = 7
Now,
⇒ (6x + 5y) = (6 × 7) + (5 × 6)
⇒ 42 + 30
⇒ 72
∴ The required value is 72
