If the nine-digit number 48x4923y8 is divisible by 88, then the value of (6x + 5y) for the maximum value of y, will be:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 72
Concept Used:
If a number is divisible by 88, then the number is divisible by both 8 and 11.
Divisibility of 8: When the last three digits of tye given number is divisible by 8, the number is divisible by 8.
Divisibility of 11: Ifthe difference between the sum of the alternate digits of a number is either 0 or multiple of 11, then the number is divisible by 11.
Explanation:
According to the given question,
The last three digits of the number 48x4923y8 are 3y8
For this number to bt divisible by 8, 3y8 should be divisible by 8
⇒ y = 6 (for maximum value of y)
Now, the number 48x492368 to be divisible by 11,
(4 + x + 9 + 3 + 8) - (8 + 4 + 2 + 6) = 11
⇒ 24 + x - 20 = 11
⇒ 4 + x = 11
⇒ x = 7
Now, the required value = (6x + 5y) = 6(7) + 5(6) = 42 + 30 = 72
Hence the required answer is 72.