karthikpandian19 wrote:If j and k are positive integers, what is the remainder when (8 x 10power k + j)is divided by 9?

(1) k = 13
(2) j = 1

(sorry, i could not able write better the "10 power k")

Any number is divisible by 9 if the sum of digits of the number is divisible by 9.
Now 8 * 10^k + j, where k is any positive integer.
For any positive integer k, the sum of the digits of the expression 8 * 10^k will always be 8.
If k = 1, 8 * 10^1 = 80; sum of digits = 8
If k = 3, 8 * 10^3 = 8000; sum of digits = 8

(1) k = 13 implies 8 * 10^13 + j or the sum of the digits of 8 * 10^13 will be 8, but we do not know the value of j. Hence NOT sufficient.

(2) j = 1 clearly implies that the sum of the digits of 8 * 10^k + 1 will always be 9; SUFFICIENT.

Th correct answer is B.