achal46 wrote:If j and k are positive integers, what is the remainder when 8 * (10^k) + j is divided by 9?
(1) k = 13
(2) j = 1

As per my understanding -

If k=13, then the remainder is j
If j=1, then remainder is 0 always

In either case the remainder is known (j or 0), so shouldn't the answer be 'Both are independently sufficient'??

Target question: What is the remainder when 8 * (10^k) + j is divided by 9?

Statement 1 is not sufficient.
If k=13, there are different values of j that will change the remainder when the entire number is divided by 9. Some examples:
case 1) k=13 and j=1: The remainder when 8*(10^k)+j is divided by 9 is 0
case 2) k=13 and j=2: The remainder when 8*(10^k)+j is divided by 9 is 1
Since we get conflicting answers to our target question, statement 1 is not sufficient.

Statement 2
To solve this question, we need to know a divisibility rule that says "If a number x is such that the sum of its digits is divisible by 9, then the original number, x, is divisible by 9"

Take 1000000320048 for example. It would take a while to determine whether this number is divisible by 9. However, we can use the rule. The sum of the digits is 18, and 18 is divisible by 9. So, we can conclude that 1000000320048 is divisible by 9.

Back to the original question. We know that 8 x 10^k will be an 8 followed by several 0's

If j=1 [from statement (2)], then 8 * 10^k + j will be 8 followed by several 0's and then 1 (e.g., 80000001 or 800000000000000001)
We can see that the sum of the digits will always equal 9, so this number will be divisible by 9.
As such, the remainder will always equal 0.
This tells us that statement 2 is sufficient.

Answer = B

Cheers,
Brent