If n is a positive integer and r is the remainder when n^2 - 1 is divi : GMAT Data Sufficiency (DS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 06 Dec 2016, 08:22

# Yale SOM:

### 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

# If n is a positive integer and r is the remainder when n^2 - 1 is divi

Author Message
TAGS:

### Hide Tags

Intern
Joined: 05 Aug 2009
Posts: 8
Followers: 0

Kudos [?]: 28 [0], given: 0

If n is a positive integer and r is the remainder when n^2 - 1 is divi [#permalink]

### Show Tags

11 Feb 2010, 13:52
8
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

62% (02:23) correct 38% (01:30) wrong based on 268 sessions

### HideShow timer Statistics

If n is a positive integer and r is the remainder when n^2 - 1 is divided by 8, what is the value of r?

(1) n is odd
(2) n is not divisible by 8

[Reveal] Spoiler:
Could anyone explain to me why the number 1 would work in the first situation? I understand why 3, 5, 7 or others work. But why 1 works, too? Thank you so much for this great help!!
[Reveal] Spoiler: OA

Last edited by Bunuel on 28 Jul 2015, 05:52, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Manager
Joined: 26 May 2005
Posts: 208
Followers: 2

Kudos [?]: 114 [1] , given: 1

Re: If n is a positive integer and r is the remainder when n^2 - 1 is divi [#permalink]

### Show Tags

11 Feb 2010, 14:06
1
KUDOS
2
This post was
BOOKMARKED
given, n is positive interger and
n^2 - 1 = 8 * k + r -> r remainder
what is r??

st 1) n is odd
n^2-1 = (n+1) * (n-1)
so n+1 and n-1 are consequetive even numbers... one of them will be multiple of 2 and the other will be multiple of 4. So n^2 - 1 will be evenly divided by 8 and r=0
Sufficient
st 1) n is not divisible by 8. Not sufficient

A
GMAT Tutor
Joined: 24 Jun 2008
Posts: 1183
Followers: 409

Kudos [?]: 1475 [1] , given: 4

Re: If n is a positive integer and r is the remainder when n^2 - 1 is divi [#permalink]

### Show Tags

11 Feb 2010, 14:19
1
KUDOS
Expert's post
2
This post was
BOOKMARKED
I like the approach in the post above best for this problem; when you see something like n^2 - 1 in a GMAT question, it will almost always be useful to use the difference of squares factorization: n^2 - 1 = (n+1)(n-1). A less elegant alternative is to write n = 2k + 1. Then n^2 - 1 = (2k + 1)^2 - 1 = 4k^2 + 4k + 1 - 1 = 4k^2 + 4k = 4(k)(k + 1), and since k and k+1 are consecutive integers, one of them must be divisible by 2, so 4(k)(k + 1) must be divisible by 4*2 = 8.

To answer the question in the original post, if n=1, then n^2 - 1 = 0. So the question becomes, what is the remainder when 0 is divided by 8? Well, 0 is divisible by every positive integer; the quotient is zero and the remainder is zero. If you think back to how you first learned division, this should hopefully be clear: if you have, say, 11 apples and 8 children, we can give each child 1 apple and we have 3 left over, so the quotient is 1 and the remainder is 3 when you divide eleven by eight. If we have 0 apples and 8 children, we can give each child 0 apples and we have 0 left over, so the quotient is 0 and the remainder is 0 when we divide zero by eight.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Intern
Joined: 05 Aug 2009
Posts: 8
Followers: 0

Kudos [?]: 28 [0], given: 0

Re: If n is a positive integer and r is the remainder when n^2 - 1 is divi [#permalink]

### Show Tags

11 Feb 2010, 15:11
Thanks for the great help.

But I still feel very confused.
The question is asking "what's the value of r"?
I understand when n is 3,5,7, the r will be 1. However, if n is 1, r will be 0. In this case, we have two answers for r and we can't really tell the exact value for r, right? This is the reason why I don't think the first one work and the answer should be "E". Am I in the right path? Thanks for the help again.
GMAT Tutor
Joined: 24 Jun 2008
Posts: 1183
Followers: 409

Kudos [?]: 1475 [0], given: 4

Re: If n is a positive integer and r is the remainder when n^2 - 1 is divi [#permalink]

### Show Tags

11 Feb 2010, 15:18
YTT wrote:
Thanks for the great help.

But I still feel very confused.
The question is asking "what's the value of r"?
I understand when n is 3,5,7, the r will be 1. However, if n is 1, r will be 0. In this case, we have two answers for r and we can't really tell the exact value for r, right? This is the reason why I don't think the first one work and the answer should be "E". Am I in the right path? Thanks for the help again.

No, the remainder will be zero for any of the values 1, 3, 5, or 7 (or for any other odd value of n). If, say, n=5, then n^2 - 1 = 25 - 1 = 24, and the remainder when we divide 24 by 8 is zero.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Intern
Joined: 05 Aug 2009
Posts: 8
Followers: 0

Kudos [?]: 28 [0], given: 0

Re: If n is a positive integer and r is the remainder when n^2 - 1 is divi [#permalink]

### Show Tags

11 Feb 2010, 15:26
Yes, You are right! Sorry that I forgot that we have to "-1". Thank you so much for this!! Now, I got it!
Manager
Joined: 26 Nov 2009
Posts: 175
Followers: 3

Kudos [?]: 56 [0], given: 5

Re: If n is a positive integer and r is the remainder when n^2 - 1 is divi [#permalink]

### Show Tags

15 Feb 2010, 00:45
given n is postive integer n^2-1/8

1. n is odd

if n is odd then the values goes 1,3,5,7,...

if n=1 thn 0/8 = 0 so remainder is 0
if n=3 then 8/8= 1 so remanider is 0
if n=5 then 34/8 = 3 so remainder is 0

so clearly A is sufficient
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12882
Followers: 561

Kudos [?]: 158 [0], given: 0

Re: If n is a positive integer and r is the remainder when n^2 - 1 is divi [#permalink]

### Show Tags

28 Aug 2015, 01:19
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.
_________________
VP
Joined: 08 Jul 2010
Posts: 1432
Location: India
GMAT: INSIGHT
WE: Education (Education)
Followers: 65

Kudos [?]: 1339 [0], given: 42

Re: If n is a positive integer and r is the remainder when n^2 - 1 is divi [#permalink]

### Show Tags

23 Aug 2016, 20:03
YTT wrote:
If n is a positive integer and r is the remainder when n^2 - 1 is divided by 8, what is the value of r?

(1) n is odd
(2) n is not divisible by 8

[Reveal] Spoiler:
Could anyone explain to me why the number 1 would work in the first situation? I understand why 3, 5, 7 or others work. But why 1 works, too? Thank you so much for this great help!!

Please check the solution in the file attached
Attachments

File comment: www.GMATinsight.com

SOL.jpg [ 124.97 KiB | Viewed 630 times ]

_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com
Call us : +91-9999687183 / 9891333772
http://www.GMATinsight.com/testimonials.html

Feel free to give a Kudos if it is a useful post .

Intern
Joined: 01 Jun 2013
Posts: 7
Followers: 0

Kudos [?]: 0 [0], given: 127

Re: If n is a positive integer and r is the remainder when n^2 - 1 is divi [#permalink]

### Show Tags

08 Oct 2016, 07:55
YTT wrote:
If n is a positive integer and r is the remainder when n^2 - 1 is divided by 8, what is the value of r?

(1) n is odd
(2) n is not divisible by 8

[Reveal] Spoiler:
Could anyone explain to me why the number 1 would work in the first situation? I understand why 3, 5, 7 or others work. But why 1 works, too? Thank you so much for this great help!!

n^2-1=(n+1)(n-1)
(1) when n is odd, given expression is always mutiple of 8 hence zero(0) remainder- Sufficient
(2) put the various nos. except multiple of 8 and you will get various remainder- unsufficient
Re: If n is a positive integer and r is the remainder when n^2 - 1 is divi   [#permalink] 08 Oct 2016, 07:55
Similar topics Replies Last post
Similar
Topics:
14 If n is a positive integer and r is the remainder when n^2-1 9 21 Jan 2012, 17:04
16 If n is a positive integer and r is the remainder when (n-1) 14 04 Aug 2010, 02:47
3 If n is a positive integer and r is the remainder when (n-1) 9 03 Jul 2010, 21:19
2 If n is a positive integer and r is the remainder when (n-1) 6 31 Aug 2009, 04:03
8 If n is a positive integer and r is the remainder when (n-1)(n+1) is 8 21 Mar 2009, 09:52
Display posts from previous: Sort by