If a nine-digit number 9m2365n48 is completely divisible by 88 , what is the value of (m2 × n2), for the smallest value of n, where m and n are natural numbers?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 64
Concept used :
Divisibility of 8 : If the last three digits of a number is divisible by 8, the number is divisible by 8.
Divisibility of 11 : If the difference of the sum of alternative digits of a number is equal to 0 or divisible by 11, then that number is divisible by 11 completely.
Solution :
The number 9m2365n48 is divisible by 88, i.e., 8 and 11
So, n48 is divisible by 8.
Put n = 2, 248 is divisible by 8
Hence n = 2 (smallest value)
Now 9m2365248 should be divisible by 11
(9 + 2 + 6 + 2 + 8) - (m + 3 + 5 + 4) should be divisible by 11
27 - m - 12 should be divisible by 11
15 - m should be divisible by 11
Putting m = 4, 15 - 4 = 11 is divisible by 11
Hence m = 4 and n = 2
Now the required result (m2 × n2) = (16 × 4) = 64.