Find all School-related info fast with the new School-Specific MBA Forum

It is currently 30 Jul 2014, 22:02

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

700 Algrbra! Need help again. Thanks so much!

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 05 Aug 2009
Posts: 8
Followers: 0

Kudos [?]: 3 [0], given: 0

700 Algrbra! Need help again. Thanks so much! [#permalink] New post 11 Feb 2010, 13:52
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

50% (00:00) correct 50% (01:17) wrong based on 6 sessions
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!!
Attachments

GMAT.png
GMAT.png [ 66.03 KiB | Viewed 1403 times ]

Manager
Manager
avatar
Joined: 26 May 2005
Posts: 210
Followers: 2

Kudos [?]: 63 [0], given: 1

GMAT Tests User
Re: 700 Algrbra! Need help again. Thanks so much! [#permalink] New post 11 Feb 2010, 14:06
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 Instructor
avatar
Joined: 24 Jun 2008
Posts: 967
Location: Toronto
Followers: 247

Kudos [?]: 633 [0], given: 3

GMAT Tests User
Re: 700 Algrbra! Need help again. Thanks so much! [#permalink] New post 11 Feb 2010, 14:19
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.
_________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

Private GMAT Tutor based in Toronto

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

Kudos [?]: 3 [0], given: 0

Re: 700 Algrbra! Need help again. Thanks so much! [#permalink] New post 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 Instructor
avatar
Joined: 24 Jun 2008
Posts: 967
Location: Toronto
Followers: 247

Kudos [?]: 633 [0], given: 3

GMAT Tests User
Re: 700 Algrbra! Need help again. Thanks so much! [#permalink] New post 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.
_________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

Private GMAT Tutor based in Toronto

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

Kudos [?]: 3 [0], given: 0

Re: 700 Algrbra! Need help again. Thanks so much! [#permalink] New post 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
Manager
avatar
Joined: 26 Nov 2009
Posts: 178
Followers: 3

Kudos [?]: 53 [0], given: 5

GMAT ToolKit User GMAT Tests User
Re: 700 Algrbra! Need help again. Thanks so much! [#permalink] New post 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
Re: 700 Algrbra! Need help again. Thanks so much!   [#permalink] 15 Feb 2010, 00:45
    Similar topics Author Replies Last post
Similar
Topics:
Suggestions Welcomed! Thanks so much! sofalee 1 08 Oct 2012, 23:39
Please kindly evaluate profile. Thanks so much cucussa 0 28 Jul 2008, 06:40
Experts publish their posts in the topic please evaluate my Profile , thanks so much fuvictory 1 16 Jun 2008, 22:26
Experts publish their posts in the topic Profile evaluation - thanks so much rita112358 1 30 Jul 2007, 00:58
Thank you so much for the advice, Linda peterpan 0 16 Dec 2004, 16:02
Display posts from previous: Sort by

700 Algrbra! Need help again. Thanks so much!

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.