Question

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

467*91

Answer 1

467*91
Sum of the digits at odd places 1 + * + 6 = 7 + *
Sum of the digits at even places 9 + 7 + 4 = 20
Difference = sum of odd terms – sum of even terms
= (7 + *) − 20
= * − 13
Now, (* −13) will be divisible by 11 if * = 2.
i.e., 2− 13 = −11
−11 is divisible by 11.
∴ * = 2
 Hence, the number is 467291.