What is the remainder when the positive integer n is divided : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 22 Jan 2017, 18:38

### 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

Manager
Joined: 10 Sep 2009
Posts: 119
Followers: 3

Kudos [?]: 66 [1] , given: 10

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

### Show Tags

17 Nov 2009, 09:50
1
KUDOS
2
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

76% (01:43) correct 24% (01:08) wrong based on 116 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
[Reveal] Spoiler: OA

Attachments

gmat_prep2.jpg [ 41.1 KiB | Viewed 2904 times ]

VP
Joined: 05 Mar 2008
Posts: 1473
Followers: 11

Kudos [?]: 261 [0], given: 31

Re: Division by K - Remainder - Gmat Prep [#permalink]

### Show Tags

17 Nov 2009, 10:44
pierrealexandre77 wrote:
Hi guys,

easiest way is just start substituting numbers for K

if K = 2 n = 27 27/2 leaves remainder 1
if k = 3 n = 64/3 leaves remainder 1
Senior Manager
Joined: 30 Aug 2009
Posts: 286
Location: India
Concentration: General Management
Followers: 3

Kudos [?]: 163 [0], given: 5

Re: Division by K - Remainder - Gmat Prep [#permalink]

### Show Tags

17 Nov 2009, 10:46
pierrealexandre77 wrote:
Hi guys,

given that both n and k are +ve integers and k>1 with option 1 for any value of k>1 the remainder will always be 1. hence suff

option 2 says nothing abt n.hence insuff

hence A
Manager
Joined: 24 Jul 2009
Posts: 73
Location: United States
GMAT 1: 590 Q48 V24
Followers: 2

Kudos [?]: 125 [0], given: 124

Re: Division by K - Remainder - Gmat Prep [#permalink]

### Show Tags

17 Nov 2009, 10:52
A: Sufficient as we get a unique value of remainder = 1 when for K=2,3,4,5.....
B: Not Sufficient.

Ans: A
Manager
Joined: 10 Sep 2009
Posts: 119
Followers: 3

Kudos [?]: 66 [0], given: 10

Re: Division by K - Remainder - Gmat Prep [#permalink]

### Show Tags

17 Nov 2009, 10:53
kp1811 wrote:
pierrealexandre77 wrote:
Hi guys,

given that both n and k are +ve integers and k>1 with option 1 for any value of k>1 the remainder will always be 1. hence suff

option 2 says nothing abt n.hence insuff

hence A

I understand with the picking number methodology, but is there a formal way to prove that?
Senior Manager
Affiliations: PMP
Joined: 13 Oct 2009
Posts: 312
Followers: 4

Kudos [?]: 161 [0], given: 37

Re: Division by K - Remainder - Gmat Prep [#permalink]

### Show Tags

17 Nov 2009, 11:20
I tried to expand S1 as

$$K^3+3K+3K^2+1$$ using formula for $$(a+b)^3 = a^3+b^3+3a^2b+3ab^2$$
when we divide $$K^3+3K+3K^2+1$$ by K

k^3 , 3K and 3k^2 can be evenly divided by K , the remaining 1 would be remainder since K >1; 1 divide K, we get remainder 1 for any k>1

_________________

Thanks, Sri
-------------------------------
keep uppp...ing the tempo...

Press +1 Kudos, if you think my post gave u a tiny tip

Senior Manager
Joined: 30 Aug 2009
Posts: 286
Location: India
Concentration: General Management
Followers: 3

Kudos [?]: 163 [0], given: 5

Re: Division by K - Remainder - Gmat Prep [#permalink]

### Show Tags

17 Nov 2009, 19:00
pierrealexandre77 wrote:
kp1811 wrote:
pierrealexandre77 wrote:
Hi guys,

given that both n and k are +ve integers and k>1 with option 1 for any value of k>1 the remainder will always be 1. hence suff

option 2 says nothing abt n.hence insuff

hence A

I understand with the picking number methodology, but is there a formal way to prove that?

we can expand (k+1)^3 and see that all terms are divisible by k except 1 (where k>1) which is the remainder
VP
Joined: 08 Jun 2010
Posts: 1402
Followers: 3

Kudos [?]: 115 [0], given: 813

Re: Division by K - Remainder - Gmat Prep [#permalink]

### Show Tags

20 Dec 2010, 02:07
we do not need to remember the formular. Do like this

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

all the element can be divided by K, 1 is left. Answer A
Math Expert
Joined: 02 Sep 2009
Posts: 36601
Followers: 7097

Kudos [?]: 93479 [0], given: 10563

Re: Division by K - Remainder - Gmat Prep [#permalink]

### Show Tags

20 Dec 2010, 02:21
thangvietnam wrote:
we do not need to remember the formular. Do like this

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

all the element can be divided by K, 1 is left. Answer A

What is the remainder when the positive integer n is divided by the positive integer k, where k > 1?

Given: $$n=qk+r$$. Question: $$r=?$$

(1) $$n=(k+1)^3$$ --> you don't actually need to expand at all, since you understand what will happen after expansion: all term but the last will have $$k$$ as the multiple and thus will be divisible by $$k$$ and the last term will be 1 and 1 divide by $$k$$ yields remainder of 1 (as $$k>1$$). Sufficient.

(2) $$k=5$$. Know nothing about $$n$$, hence insufficient.

_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13508
Followers: 577

Kudos [?]: 163 [0], given: 0

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

### Show Tags

13 Jul 2016, 04:50
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: What is the remainder when the positive integer n is divided   [#permalink] 13 Jul 2016, 04:50
Similar topics Replies Last post
Similar
Topics:
17 What is the remainder when the positive integer n is divided 9 14 Oct 2012, 03:46
25 What is the remainder when the positive integer n is divided 11 18 Sep 2011, 18:19
3 What is the remainder when the positive integer n is divided 4 26 Sep 2010, 10:44
22 What is the remainder when the positive integer n is divided 11 25 Jun 2010, 22:42
29 What is the remainder when the positive integer n is divided 17 10 May 2009, 20:09
Display posts from previous: Sort by