Question

In the following number, replace * by the smallest number to make it divisible by 11:

9*8071

Answer 1

9*8071
Sum of the digits at odd places 1+0+* = 1 + *
Sum of the digits at even places 7 + 8 + 9 = 24
Difference = sum of odd terms – sum of even terms
=1 + * – 24
= * − 23
Now, (* − 23) will be divisible by 11 if * = 1.
i.e., 1 − 23 = −22
−22 is divisible by 11.
∴ * = 1
Hence, the number is 918071.