It is currently 20 Oct 2017, 16:39

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# What is the remainder when the positive integer n is divided

Author Message
TAGS:

### Hide Tags

Intern
Joined: 18 Oct 2008
Posts: 2

Kudos [?]: 11 [0], given: 0

What is the remainder when the positive integer n is divided [#permalink]

### Show Tags

18 Sep 2011, 19:19
9
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

68% (00:30) correct 32% (00:37) wrong based on 423 sessions

### HideShow timer Statistics

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: what-is-the-remainder-when-the-positive-integer-n-is-divided-96366.html
[Reveal] Spoiler: OA

Kudos [?]: 11 [0], given: 0

Manager
Status: Retaking next month
Affiliations: None
Joined: 05 Mar 2011
Posts: 211

Kudos [?]: 177 [2], given: 42

Location: India
Concentration: Marketing, Entrepreneurship
GMAT 1: 570 Q42 V27
GPA: 3.01
WE: Sales (Manufacturing)

### Show Tags

18 Sep 2011, 19:41
2
KUDOS
2
This post was
BOOKMARKED
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.

Kudos [?]: 177 [2], given: 42

Math Forum Moderator
Joined: 20 Dec 2010
Posts: 1964

Kudos [?]: 2051 [4], given: 376

### Show Tags

19 Sep 2011, 03:15
4
KUDOS
1
This post was
BOOKMARKED
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:
$$\frac{(k+1)^3}{k}=Remainder Of(\frac{Remainder Of(\frac{k+1}{k})*Remainder Of(\frac{k+1}{k})*Remainder Of(\frac{k+1}{k})}{k})=Remainder Of(\frac{1*1*1}{k})=1$$

Sufficient.

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
_________________

Kudos [?]: 2051 [4], given: 376

Manager
Status: Retaking next month
Affiliations: None
Joined: 05 Mar 2011
Posts: 211

Kudos [?]: 177 [1], given: 42

Location: India
Concentration: Marketing, Entrepreneurship
GMAT 1: 570 Q42 V27
GPA: 3.01
WE: Sales (Manufacturing)

### Show Tags

19 Sep 2011, 03:19
1
KUDOS
1
This post was
BOOKMARKED
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:
$$\frac{(k+1)^3}{k}=Remainder Of(\frac{Remainder Of(\frac{k+1}{k})*Remainder Of(\frac{k+1}{k})*Remainder Of(\frac{k+1}{k})}{k})=Remainder Of(\frac{1*1*1}{k})=1$$

Sufficient.

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

Gud Explanation Fluke. Hope my explanations above were also correct although a little traditional

Kudos [?]: 177 [1], given: 42

Math Forum Moderator
Joined: 20 Dec 2010
Posts: 1964

Kudos [?]: 2051 [0], given: 376

### Show Tags

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.
_________________

Kudos [?]: 2051 [0], given: 376

Manager
Status: Retaking next month
Affiliations: None
Joined: 05 Mar 2011
Posts: 211

Kudos [?]: 177 [0], given: 42

Location: India
Concentration: Marketing, Entrepreneurship
GMAT 1: 570 Q42 V27
GPA: 3.01
WE: Sales (Manufacturing)

### Show Tags

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??

Kudos [?]: 177 [0], given: 42

Manager
Status: Bell the GMAT!!!
Affiliations: Aidha
Joined: 16 Aug 2011
Posts: 176

Kudos [?]: 81 [0], given: 43

Location: Singapore
Concentration: Finance, General Management
GMAT 1: 680 Q46 V37
GMAT 2: 620 Q49 V27
GMAT 3: 700 Q49 V36
WE: Other (Other)

### Show Tags

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
_________________

If my post did a dance in your mind, send me the steps through kudos :)

Kudos [?]: 81 [0], given: 43

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7676

Kudos [?]: 17369 [3], given: 232

Location: Pune, India

### Show Tags

19 Sep 2011, 22:22
3
KUDOS
Expert's post
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/
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Kudos [?]: 17369 [3], given: 232 Math Forum Moderator Joined: 20 Dec 2010 Posts: 1964 Kudos [?]: 2051 [0], given: 376 Re: Number propierties [#permalink] ### Show Tags 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. _________________ Kudos [?]: 2051 [0], given: 376 Director Joined: 29 Nov 2012 Posts: 868 Kudos [?]: 1412 [0], given: 543 Re: What is the remainder when the positive integer n is divided [#permalink] ### Show Tags 04 Jul 2013, 03:00 The expansion of $$(K+1)^3$$ needs to be memorized? BTW great explanation @fluke _________________ Click +1 Kudos if my post helped... Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/ GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html Kudos [?]: 1412 [0], given: 543 Math Expert Joined: 02 Sep 2009 Posts: 41892 Kudos [?]: 129034 [3], given: 12187 Re: What is the remainder when the positive integer n is divided [#permalink] ### Show Tags 04 Jul 2013, 03:12 3 This post received KUDOS Expert's post 3 This post was BOOKMARKED What is the remainder when the positive integer n is divided by the positive integer k, where k>1 (1) $$n=(k+1)^3= k^3 + 3k^2 + 3k + 1=k(k^2+3k+3)+1$$ --> first term, $$k(k^2+3k+3)$$, is obviously divisible by $$k$$ and 1 divide by $$k$$ yields the remainder of 1 (as $$k>1$$). Sufficient. (2) $$k=5$$. Know nothing about $$n$$, hence insufficient. Answer: A. OPEN DISCUSSION OF THIS QUESTION IS HERE: what-is-the-remainder-when-the-positive-integer-n-is-divided-96366.html _________________ Kudos [?]: 129034 [3], given: 12187 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7676 Kudos [?]: 17369 [3], given: 232 Location: Pune, India Re: What is the remainder when the positive integer n is divided [#permalink] ### Show Tags 04 Jul 2013, 20:07 3 This post received KUDOS Expert's post fozzzy wrote: The expansion of $$(K+1)^3$$ needs to be memorized? BTW great explanation @fluke In case you do forget the expansion/don't know it, just multiply: $$(K+1)^3 = (K+1)(K^2 + 2K + 1)$$ (We certainly know the expansion of $$(K+1)^2$$ or we can find it my multiplying (K+1)(K+1)) $$(K+1)^3 = K^3 + 3K^2 + 3K + 1$$ _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Kudos [?]: 17369 [3], given: 232

Re: What is the remainder when the positive integer n is divided   [#permalink] 04 Jul 2013, 20:07
Display posts from previous: Sort by