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What is the remainder when the positive integer n is divided [#permalink]
 18 Sep 2011, 19:19
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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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Re: Number propierties [#permalink]
18 Sep 2011, 19:41
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andresfigue 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 Algebraic way: 1) eXPAND (K+1)^3 = k^3+3.(K^2)+3k+1. So definitely remainder of 1 as the first 3 terms are multiples of K. Sufficient 2) Insufficient. Numerical way: Take k= 2 & 3 . u will get remainder 1 in both cases. So A.
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Re: Number propierties [#permalink]
19 Sep 2011, 03:15
andresfigue 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 Sol: 1) \frac{(k+1)^3}{k}Remainder: \frac{(k+1)^3}{k}=Remainder Of(\frac{Remainder Of(\frac{k+1}{k})*Remainder Of(\frac{k+1}{k})*Remainder Of(\frac{k+1}{k})}{k})=Remainder Of(\frac{1*1*1}{k})=1Sufficient. Ans: "A" ************************************************ I think there is some principle of induction that we can apply here. For more on the formula I used to solve this: compilation-of-tips-and-tricks-to-deal-with-remainders-86714.html
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Re: Number propierties [#permalink]
19 Sep 2011, 03:19
fluke wrote: andresfigue 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 Sol: 1) \frac{(k+1)^3}{k}Remainder: \frac{(k+1)^3}{k}=Remainder Of(\frac{Remainder Of(\frac{k+1}{k})*Remainder Of(\frac{k+1}{k})*Remainder Of(\frac{k+1}{k})}{k})=Remainder Of(\frac{1*1*1}{k})=1Sufficient. Ans: "A" ************************************************ I think there is some principle of induction that we can apply here. For more on the formula I used to solve this: compilation-of-tips-and-tricks-to-deal-with-remainders-86714.htmlGud Explanation Fluke. Hope my explanations above were also correct although a little traditional 
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Re: Number propierties [#permalink]
19 Sep 2011, 03:27
GMATPASSION wrote: Gud Explanation Fluke. Hope my explanations above were also correct although a little traditional Oh, absolutely!! In fact, Kudos for that. I believe you used the concept of mathematical induction, in which all terms but one are divisible by the denominator. I remember Karishma's describing it once. I don't remember that exactly.
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Re: Number propierties [#permalink]
19 Sep 2011, 03:30
fluke wrote: GMATPASSION wrote: Gud Explanation Fluke. Hope my explanations above were also correct although a little traditional Oh, absolutely!! In fact, Kudos for that. I believe you used the concept of mathematical induction, in which all terms but one are divisible by the denominator. I remember Karishma's describing it once. I don't remember that exactly. Thanks for my first kudos buddy. 'Mathematical Induction' Wats dat? Never Heard of that??
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Re: Number propierties [#permalink]
19 Sep 2011, 03:59
GMATPASSION wrote: andresfigue 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 Algebraic way: 1) eXPAND (K+1)^3 = k^3+3.(K^2)+3k+1. So definitely remainder of 1 as the first 3 terms are multiples of K. Sufficient 2) Insufficient. Numerical way: Take k= 2 & 3 . u will get remainder 1 in both cases. So A. Good explanation GMATPASSION. Kudos for that
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Re: Number propierties [#permalink]
19 Sep 2011, 22:22
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GMATPASSION wrote:
Thanks for my first kudos buddy. 'Mathematical Induction' Wats dat? Never Heard of that??
Responding to a PM: Actually it was a discussion on 'Binomial Theorem' (Induction is an altogether different concept which is out of GMAT scope) Binomial theorem comes in handy in many remainder questions. With a power of 3, it is easy to expand the expression and see that only 1 will be the remainder (as GMATPASSION did). For higher powers, binomial theorem can be used. I have put up a post on the Veritas blog discussing it and its applications. Here is the link. Get back in case there are any doubts. http://www.veritasprep.com/blog/2011/05 ... ek-in-you/
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Re: Number propierties [#permalink]
20 Sep 2011, 00:24
VeritasPrepKarishma wrote: GMATPASSION wrote:
Thanks for my first kudos buddy. 'Mathematical Induction' Wats dat? Never Heard of that??
Responding to a PM: Actually it was a discussion on 'Binomial Theorem' (Induction is an altogether different concept which is out of GMAT scope) Binomial theorem comes in handy in many remainder questions. With a power of 3, it is easy to expand the expression and see that only 1 will be the remainder (as GMATPASSION did). For higher powers, binomial theorem can be used. I have put up a post on the Veritas blog discussing it and its applications. Here is the link. Get back in case there are any doubts. http://www.veritasprep.com/blog/2011/05 ... ek-in-you/Got it!!! thanks a lot Karishma.
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Re: Number propierties
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20 Sep 2011, 00:24
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