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What is the remainder when the positive integer n is divided

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seofah
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What is the remainder when the positive integer n is divided [#permalink] New post   Updated on: 24 Jan 2009, 12:24
What is the remainder when the positive integer n is divided by the positive integer k,
where k > 1?
(1) n = (k+1)^3
(2) k = 5



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Originally posted by seofah on 07 Nov 2008, 16:43.
Last edited by seofah on 24 Jan 2009, 12:24, edited 1 time in total.
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Re: What is the remainder when the positive integer n is divided [#permalink] New post   07 Nov 2008, 16:55
both n and k are positive.

dividing (1) by K, we get n/k = 3 + 3/k. Not sufficient enough to answer what the reminder is. So throw out choices A and D

with (2), we only know the value of k, so can't find out what the remainder is. So throw out choice B.

The 2 statements toegther give us n = (5+1)3 = 18 and k = 5. We can definitely say what the remainder is with the 2 statements together. So my pick Choice C
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Re: What is the remainder when the positive integer n is divided [#permalink] New post   08 Nov 2008, 03:44
I thought, it was C as well, but OA isn't C!
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Re: What is the remainder when the positive integer n is divided [#permalink] New post   08 Nov 2008, 04:37
That is strange, I had thought it to be C as well. But there is one thing i have noticed.
When k=2 remainder =1,
k=3 r=0
for k =>4 , r=3

But what difference does it make ! The QA c makes sense, else i has to be E.
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Re: What is the remainder when the positive integer n is divided [#permalink] New post   24 Jan 2009, 12:26
There was a a small typo in the question :?
I got the answer that is in line with OA, but any attempts are welcome. :)
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Re: What is the remainder when the positive integer n is divided [#permalink] New post   24 Jan 2009, 12:42
I get A..

What is the remainder when the positive integer n is divided by the positive integer k,
where k > 1?
(1) n = (k+1)^3
(2) k = 5


2) insuff..

1) n= (K+1)(K+1)^2= (K+1)(K^2+2k+1)= K^3+3K^2+K+3K+1

as you can N= will always be 1 greater than K..

therefore 1 is the remainder...

1 is suff
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Re: What is the remainder when the positive integer n is divided [#permalink] New post   24 Jan 2009, 13:22
A. You can pick k=2, k=3, k=4 and you'll see that the remainder is always 1.
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Re: What is the remainder when the positive integer n is divided [#permalink] New post   24 Jan 2009, 15:55
fresinha12 wrote:
I get A..

What is the remainder when the positive integer n is divided by the positive integer k,
where k > 1?
(1) n = (k+1)^3
(2) k = 5


2) insuff..

1) n= (K+1)(K+1)^2= (K+1)(K^2+2k+1)= K^3+3K^2+K+3K+1

as you can N= will always be 1 greater than K..

therefore 1 is the remainder...

1 is suff


agree with this solution
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Re: What is the remainder when the positive integer n is divided [#permalink] New post   24 Jan 2009, 16:56
botirvoy wrote:
What is the remainder when the positive integer n is divided by the positive integer k,
where k > 1?
(1) n = (k+1)^3
(2) k = 5



k=2,5 can be used to test. The remainder is always 1.
Rigorous proof is as follows:
n=k^3+3k^2+3k+1
Remainder is clearly 1.
1 is sufficient and hence A.



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Re: What is the remainder when the positive integer n is divided [#permalink]
24 Jan 2009, 16:56
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