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## Integer Properties - DS

tagged by: Brent@GMATPrepNow

This topic has 11 expert replies and 70 member replies
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rijul007 GMAT Destroyer!
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Sat Oct 22, 2011 11:27 am
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

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immaculatesahai Rising GMAT Star
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Sun Nov 06, 2011 1:34 am
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

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.

SaeedaJ Just gettin' started!
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Wed Nov 09, 2011 3:49 pm
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

ArunangsuSahu GMAT Destroyer!
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Wed Nov 09, 2011 7:40 pm
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

krishna88 Just gettin' started!
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bpdulog Really wants to Beat The GMAT!
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Sun Nov 20, 2011 12:38 pm
B was the answer I chose.

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pemdas GMAT Titan
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Sun Nov 20, 2011 4:05 pm
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

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Mr.Hollywood Rising GMAT Star
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Wed Dec 07, 2011 2:41 am
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"?

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Brent@GMATPrepNow GMAT Instructor
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Wed Dec 07, 2011 8:00 am
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

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him1985 Rising GMAT Star
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B
SImply GMAT Stuff..

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Thu Feb 02, 2012 9:01 am
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!!!

gmattest001 Just gettin' started!
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Sun Feb 05, 2012 7:01 am

means 2 condition is sufficient to answer the question.

sullykma Just gettin' started!
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Sun Mar 04, 2012 9:10 pm
Hi Brent,

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

ka_t_rin Rising GMAT Star
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Wed Mar 14, 2012 4:38 am
Since regardless of the power k 8*10^k will leave a remainder = 8,
the answer depends only on the value of J.

UmangMathur Just gettin' started!
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Wed Jul 11, 2012 6:12 am
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

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