Answer is B

A number to be divisible by 9, the sum of numbers should add to 9.
With J = 1 , we don't need to look at K , as 8*10^k , will always be 8. With J = 1 , we know
8*10^K + 1 , the sum will always be = 9.
Hence B alone helps to determine the answer.

will go with D

will go with D

B.

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

Statement 1 gives [80000000000000+j]/9; as j is undefined, INSUFFICIENT
Statement 2 gives [80000...+1]/9; As the sum of the digits of the dividend equal 9, then there is no remainder, SUFFICIENT

IMO B. Only the value of J matters.

For this question of data sufficiency:-
firstly, 8 * (whatever to the power)10
= 800.....
if we add 1 to it (as j=1)
then the value becomes- 81,801,8001,80001 etc
and we know that the sum of such numbers whatsoever be is (8+1)9 thus it will
be divisible by 9 and remainder is zero.
we do not need the value of k.....
so answer is option 2 is alone sufficient no need of option 1
i Hope i am right.....

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


In case one forget divisibility by 9 rule & want to save the time;
(8 * 10^k) + j /9

statement 1 : k=13 . certainly it is insufficient as value of remainder will be dependent on "j"
statement 2 : j=1 . here we dont know value of k. so check if for j=1 and k=0,1,2 (test cases) whether we get same remainder or not.

case 1 : j=1 , k=0
--> [( 8 * 10 ^0) + 1 ]/9 = 9/9=0

case 2 : j=1 , k=1
--> [( 8 * 10 ^1) + 1 ]/9 = 81/9=0

Thus Answer=(B)

since reminder will depend upon j only ,stat2 is suff.

B.

B

If j and k and positive integers, what is the remainder then 8*10^k + j is divided by 9?

1. k = 13
2. j = 1

in this question , k and j are variables. to answer this kind of questions, we have to analyse the 8*10^k + j. Remember that 10^k always gives us extra zero , nothing else. thus regardless of the power of K, we will get 10,100,10000 etc. if we then multiply by 8 it yields 80, 800, 8000 etc. thus J is crucial as we know a number is divisible by 9 if its sum of digits divisible by 9.

1. k=13.
the power of k is inferior here as we don't know the value of j, crucial one for this question.
2. j=1
we have already determined that regardless of the power of K we will get 80,800,800000 etc. now add 1 to these numbers. it looks like 801, 8001, 80001, 8000001 etc. sum of the digits is 9. thus , statement 2 is enough. Answer is B.