Integer Properties - DS

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by Brent@GMATPrepNow » Wed Jul 11, 2012 6:19 am
UmangMathur wrote:This seems to be an oral question... :idea: :idea: :idea: :idea: :idea: :idea:

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:
Nice.

Once we've rephrased the target question as, "What is the value of j?", we can see that the correct answer must be B.

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by [email protected] » Thu Jul 12, 2012 4:51 am
answer is 8

this is very poor logic question.

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by Brent@GMATPrepNow » Thu Jul 12, 2012 9:01 am
[email protected] wrote:answer is 8
The answer is 8?

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by cuddytime » Mon Jul 16, 2012 8:13 am
Could we have the question modified as follows to clear any confusion?

(8*10^k)+ J?

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by Brent@GMATPrepNow » Mon Jul 16, 2012 4:34 pm
cuddytime wrote:Could we have the question modified as follows to clear any confusion?

(8*10^k)+ J?
The old question still followed orders of operation, but I have changed it nonetheless.

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by Shubhu@MBA » Wed Jul 18, 2012 10:02 am
8*10^k + j when divided by 9 will always give a remainder of 8(provided k & j are both positive integers)

Thus this question can be answered by any of the options given in the question

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by Brent@GMATPrepNow » Fri Jul 20, 2012 6:51 am
Shubhu@MBA wrote:8*10^k + j when divided by 9 will always give a remainder of 8(provided k & j are both positive integers)

Thus this question can be answered by any of the options given in the question
I think you're reading the expression as 8 * 10^(k+j) in which case you're right; the remainder will always be 8
However, the expression is actually meant to be 8*(10^k)+j, in which case the remainder varies, depending solely on the value of j.

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by Shubhu@MBA » Fri Jul 20, 2012 1:45 pm
Brent@GMATPrepNow wrote:
Shubhu@MBA wrote:8*10^k + j when divided by 9 will always give a remainder of 8(provided k & j are both positive integers)

Thus this question can be answered by any of the options given in the question
I think you're reading the expression as 8 * 10^(k+j) in which case you're right; the remainder will always be 8
However, the expression is actually meant to be 8*(10^k)+j, in which case the remainder varies, depending solely on the value of j.

Cheers,
Brent
Thanks for the clarification.

(8 * 10^k )/9 will always leave a remainder 8.

Thus, it is "j" which will determine what the the remainder will be for the expression 8*(10^k)+j.

Hence Option B will be the answer.

If J=1 then the remainder for above expression will always be 0, as the expression will always be completely divided by 9, no matter what is the value of K.

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by Brent@GMATPrepNow » Sat Jul 21, 2012 6:30 am
Shubhu@MBA wrote:
Brent@GMATPrepNow wrote:
Shubhu@MBA wrote:8*10^k + j when divided by 9 will always give a remainder of 8(provided k & j are both positive integers)

Thus this question can be answered by any of the options given in the question
I think you're reading the expression as 8 * 10^(k+j) in which case you're right; the remainder will always be 8
However, the expression is actually meant to be 8*(10^k)+j, in which case the remainder varies, depending solely on the value of j.

Cheers,
Brent
Thanks for the clarification.

(8 * 10^k )/9 will always leave a remainder 8.

Thus, it is "j" which will determine what the the remainder will be for the expression 8*(10^k)+j.

Hence Option B will be the answer.

If J=1 then the remainder for above expression will always be 0, as the expression will always be completely divided by 9, no matter what is the value of K.
Exactly.

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by pablo_vish » Mon Jul 23, 2012 5:17 pm
Hi Brent,
Nice question.. I was able to get this one quickly thanks to your online course.. :) :)
Was just wondering, whether it would be fine to solve this by choosing numbers and then applying the divisibility rule?
Aiming for a 740+ in GMAT

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by Brent@GMATPrepNow » Thu Jul 26, 2012 6:41 am
pablo_vish wrote:Hi Brent,
Nice question.. I was able to get this one quickly thanks to your online course.. :) :)
Was just wondering, whether it would be fine to solve this by choosing numbers and then applying the divisibility rule?
Thanks for the feedback, Pablo :-)

We can choose numbers for statement 1 to show that it is not sufficient.
When we choose numbers for statement 2, we can't definitively show that the statement is sufficient, but with each set of numbers, we can gain more confidence that it is, indeed, sufficient.

If anyone would like to learn more about choosing numbers (and using a table to organize your information), you can watch the following free video: https://www.gmatprepnow.com/module/gmat- ... cy?id=1101

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by Selwyn » Thu Jul 26, 2012 4:22 pm
I have added a new question on the same area Number Properties. First of my posts here, if you guys enjoy this I will post more


If a, b and c are all prime numbers then how many ordered pairs of {a,b,c} exist that satisfy the equation a + b = c
1. 0 < a,b,c < 99
2. 50 < a,b,c < 151

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by hemant_rajput » Sun Aug 26, 2012 1:49 am
hardly took 15 sec to solve this.

10^k = (9+1)^k = 9^k + 1^k. So 8*10^k will always give remainder 1. with the value of j know we can find the final answer.

Hence B is the answer

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by deepalimittal26 » Tue Oct 23, 2012 1:03 pm
Answer should be B.

Divisibility rule of 9 works well with second option.

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by mparakala » Wed Oct 24, 2012 11:50 am
Ans: B

1) not sufficient to say that there will be one fixed remainder. the remainder is going to be "8" no matter what the power of 10 is. so, " k" value s not imp . "j"is!

2) gives the value of j.
so, the number 8*10 + 1= 801 or 8 * 100 + 1 = 8001 , the remainder will always be "0".
SUFFICIENT!