Data Sufficiency

8*10^k +j

remainder of 8*10^k when divided by 9
(-1)*(1)^k = -1

remainder of 8*10^k +j depends only on the value of j
hence statement 2 alone is sufficient

The correct option is B

Brent@GMATPrepNow wrote:Source: Magoosh Practice Questions

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

The answer should be B.

First we can check whether the remainder of 8*10^K varies when divided by 9. I took few random values of K and each time you will get the same remainder for the term. i.e. 8.

So we know that essentially the remainder of the overall term depends on the value of j rather than k. Hence B.

Easy question, but important to catch the crux of it.

What confused me at first was the way the equation was written.
I thought it was 8*10^(k +j), when in reality the question is stating 8*(10^k) +j.

1)k=13

A base of 10 to the power of any positive integer is 1 followed by a bunch of zeros.
10^1=10
10^2=100 etc..

So, 8*(10^13)+J= 8 with a lot of zeros +J. The problem said that this will be divided by 9.

***If the sum of the digits of a number are divisible by 9, then the number is divisible by 9.*** (This is on one of the GMAT flashcards found on this website).
For example, you have 48,510 that you want to divide by 9. 4+8+5+1+0=18.18 is divisible by 9, so 48,510 is divisible by 9.

Going back to: 8 with a lot of zeros +J....At this point we don't know the value of J. We cannot determine whether this is divisible by 9 (with or without a remainder). INSUFFICIENT

2) J=1
Let's plug this in: [8(10^k)+1]/9

Again, 8*10^some number is 8 with a lot of zeros. With J=1, we need to add a one. The sum of the number is 9, which is divisible by 9. We have enough information to find the remainder of the equation when it's divided by 9. SUFFICIENT

The answer is B.

Rule Of Divisibility by '9': Sum of the digits should be divisible by '9'

A) 'j' can be anything between '0' and '9'. So Insufficient
B) value of '' is irrelevant...The sum of the digits is always (8+1)=9.

So 'B' is SUFFICIENT

B is the answer

B was the answer I chose.

the same here +1 B, (10^k)/9 has always remainder of 1. Hence 8* (1/9) +j and st(1) is Not Sufficient, we don't know j; st(2) is Sufficient, j=1 returns remainder 0

Brent@GMATPrepNow wrote:Source: Magoosh Practice Questions

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

I have a question about the word "remainder" in this question. If your question is to test weather these two choices are sufficient to make 8 * (10^k) + j divisible by 9, then what is the purpose of "remainder"?

Mr.Hollywood wrote:

Brent@GMATPrepNow wrote:Source: Magoosh Practice Questions

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

I have a question about the word "remainder" in this question. If your question is to test weather these two choices are sufficient to make 8 * (10^k) + j divisible by 9, then what is the purpose of "remainder"?

Good question.

The target question here asks us to find the remainder when some value is divided by 9.
So, there are 9 possible answers: the remainder is 0, 1, 2, 3, 4, 5, 6, 7, or 8.

Since statement 2 guarantees that the value is divisible by 9, can now have enough information to conclude that the remainder is 0. So, there's the relationship between remainder and divisibility.

I could have written a different question (Is 8(10^k)+j divisible by 9?), but that would have simplified matters by turning it into a yes/no question, whereas the original question has 9 possible answers.

Cheers,
Brent

B
SImply GMAT Stuff..

I made a mistake and Read the question as 8*10*K + J so my option was D

Later after seeing the solution i realized i made a BIG mistake....

I guess these silly but unpardonable mistakes are bound to happen under pressure during actual GMAT xam....God please help ME!!!

IMP answer is B.

means 2 condition is sufficient to answer the question.

Hi Brent,

I would like to know does that rule work for all divisors...or just for 9?! Thanks...!

The answer is B )))
Since regardless of the power k 8*10^k will leave a remainder = 8,
the answer depends only on the value of J.

This seems to be an oral question...

8*10^k + j

8 multiplied by any power of 10 (0 - infinity) will always give remainder 8 when divided by 9

thus in this case, it's the value of j that will determine the remainder and not the value of k. Rather, the equation is independent of k.

Thus we can determine the value, just by having the value of j.

Thus the choice is B

:twisted: