Question

What least number be assigned to * so that number 653*47 is divisible by 11?

(a) 1
(b) 2
(c) 6
(d) 9

Answer 1

(a) 1

Sum of the digits at odd places = 6 + 3 + 4 = 13
Sum of the digits at even places = 5 + * + 7 = 12 + *
Difference = 13 − [12 + *] = 1 − *
If 6,53,*47 is divisible by 11, then 1 − * must be zero or multiple of 11.
1 − * = 0 or 11
* = 1 or −10
But * is a digit, so * must be 1.