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## Integer Properties - DS

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This topic has 11 expert replies and 70 member replies
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tgou008 Rising GMAT Star
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What level difficulty do you think this is / was?

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svsan_81 Just gettin' started!
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Thu Mar 10, 2011 3:51 am
good Question

niazsna786 Just gettin' started!
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Wed Mar 23, 2011 5:08 am
B looks correct to me .
for j = 1 given in 2.
the equation can 81, 801, 8001, 80001.... so on. what ever be the value of 'k' the expression is divisible by 9(sum of the digits always remain 9)
with only k = 13 we cannot be sure.

lawri Just gettin' started!
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Thu Mar 24, 2011 6:27 am
Good question. I misread the question as 8*10^(k+j). Were I immediately concluded the answer would be D.

So, lesson learned: Avoid careless errors by reading stem carefully.

Here's the break down

A - Insufficient becuase can't determine the value 8*10^13 + j given that j is unkown.
B - Sufficient becasue we know that 8*10^k +1 will alway yield a number that is divisble by 9,
C - N/A given that be is true
D - N/A given that be is true
E - N/A given that be is true

sayanchakravarty Just gettin' started!
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Sun May 29, 2011 8:54 am
B

subhashghosh Rising GMAT Star
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jainnikhil02 Really wants to Beat The GMAT!
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Wed Jun 08, 2011 11:36 am
IMO B

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Wed Jun 08, 2011 9:30 pm
Quote:
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
if sum of digits of a number is divisible by 9, then that no. is divisible by 9.
8*10^k + j has sum of digits = 8+j
a)k=13; the remainder depends on j
insufficient
b)j=1
sum=9, thus no. divisible by 9.
remainder=0
Sufficient
IMO B

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cmmancin Just gettin' started!
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Tue Jun 14, 2011 8:30 am
What level question would you say this is?

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Brent@GMATPrepNow GMAT Instructor
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Wed Jun 15, 2011 7:38 am
cmmancin wrote:
What level question would you say this is?

It pretty much comes down to whether or not one realizes that, with statement 2, the number will be of the form 8000....01 and that the sum of the digits will be 9

That said, I'd say the question is of above-average difficulty (650+)

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krishp84 Just gettin' started!
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Fri Jul 08, 2011 11:12 pm
lawri wrote:
Good question. I misread the question as 8*10^(k+j). Were I immediately concluded the answer would be D.

So, lesson learned: Avoid careless errors by reading stem carefully.

Here's the break down

A - Insufficient becuase can't determine the value 8*10^13 + j given that j is unkown.
B - Sufficient becasue we know that 8*10^k +1 will alway yield a number that is divisble by 9,
C - N/A given that be is true
D - N/A given that be is true
E - N/A given that be is true

Similar thing with me but not the same
I took (8.10^k+j)/9

Substituted values
1) k=13..
If k=1 ,80/9 = 8
If k=2, 800/9 = 8

So k=13, (8.10^13)/9=8

But forgot about j....So concluded A will satisfy

2) (8.10^k+1)/9
If k=1 ,81/9 = 0
If k=2, 801/9 = 0

So k=13, (8.10^13+1)/9=0
So B will satisfy
Therefore chose D....

But correct ans. is B
Takeaway for me : when solving fastly, watch out not to miss any variable carelessly.
Takeaway for others : when solving problems like these, it is much more easy to pick smart numbers because you cannot depend upon standard formulaes at all places in GMAT.

I solved this in less than 60 secs.

amit2k9 GMAT Destroyer!
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Sat Jul 09, 2011 2:04 am
a 8*10^13+ j where j can have any value. for j=0 remainder = 0, for j=1 remainder = 1.
not sufficient.

b remainder = 0 as 8+1 = 9/9 = 1 remainder =0 always.

B it is.

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shoot4greatness Really wants to Beat The GMAT!
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Sat Jul 09, 2011 11:37 am
The question, I think, may be in the low 600 range question. Just need a little knowledge in number theory. Statement 1 is not sufficient because J is still unknown. Statement 2 allows us to come to a conclusion that the numerator will be a multiple of 9. K is positive integer, thus K must be greater than 0. 0 is an integer, but not positive nor negative. When J is 1, the numerator will be 1 greater than 8x10^k. The division rule of 9 is when the sum of all numbers in a given integer is multiple of 9, the integer is a multiple of 9, or 9 is a factor/divisor of the given integer. For example, if K=1, then the numerator will be 81. If K=2, numerator will be 801. There will be k-1 number of zeros in-between 8 and 1. Add the sum of all numbers in the numerator: 8+1=9, so no remainder. Question can be answered with statement 2. Pick B.

akhilsuhag Really wants to Beat The GMAT!
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Sun Jul 10, 2011 11:59 pm
Here:

(8*10^k+j)/9 = (8*10^k)/9 + j/9

Now (8*10^k)/9 will always give a remainder of 0.8 for any value of k. So if we are supplied a value of k then it is insufficient. We would need the value of j to find the answer

Therefore, statement A is INSUFFICIENT.

and statement B is SUFFICIENT.

Please tell me if this way is correct or not..

Thanks

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Tue Jul 12, 2011 9:06 pm
B.. I felt it was an easy one

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