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

It is currently 30 Jun 2015, 11:50

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

For some integer q, q^2 - 5 is divisible by all of the follo

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 5678
Location: Pune, India
Followers: 1412

Kudos [?]: 7308 [1] , given: 186

Re: q^2 - 5 [#permalink] New post 08 Jan 2011, 20:10
1
This post received
KUDOS
Expert's post
dimitri92 wrote:
For some integer q, q^2 - 5 is divisible by all of the following EXCEPT
(A) 29
(B) 30
(C) 31
(D) 38
(E) 41


The way I would approach this question:

So q^2 - 5 is divisible by all of the following except:
29, 31, 41 - big prime numbers, don't know any divisibility rules for these, forget them for the time being.. 38 = 19*2. (q^2 - 5) can be divisible by 2 (e.g. when q^2 ends with a 5, q^2 - 5 ends with a 0). As for 19, again a big prime number. Leave it for the time being.

(If the question is anywhere close to an actual GMAT question, they will not expect you to do many calculations with 29, 31, 41 etc. I see these big prime numbers and am quite convinced that they are just a smokescreen.Try and focus on what they could ask you like divisibility by 2, 3 etc. )

As for 30, q^2 - 5 is divisible by 10 (using the logic shown above). What about 3?
\(q^2 - 5 = q^2 - 1 - 4 = (q - 1)(q + 1) - 4\)
In any 3 consecutive numbers, (e.g. \((q - 1), q, (q + 1)\)), one and only one number will be divisible by 3.
If either (q - 1) or (q + 1) is divisible by 3, (q - 1)(q + 1) is divisible by 3, which means \((q - 1)(q + 1) - 4\) cannot be divisible by 3. If q is divisible by 3, then q^2 will be divisible by 3 and q^2 - 5[/m] will not be divisible by 3.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews


Last edited by VeritasPrepKarishma on 08 Jan 2011, 20:17, edited 1 time in total.
Kaplan Promo CodeKnewton GMAT Discount CodesManhattan GMAT Discount Codes
Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 5678
Location: Pune, India
Followers: 1412

Kudos [?]: 7308 [0], given: 186

Re: q^2 - 5 [#permalink] New post 08 Jan 2011, 20:14
Expert's post
dimitri92: Didn't see your response since it was on page 2. But yes, that is exactly how I would think about it too. (Thought I think there is a small typo. You have a '+4' rather than a '-4')
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 5332
Followers: 310

Kudos [?]: 60 [0], given: 0

Premium Member
Re: For some integer q, q^2 - 5 is divisible by all of the follo [#permalink] New post 03 Oct 2013, 19:32
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 5332
Followers: 310

Kudos [?]: 60 [0], given: 0

Premium Member
Re: For some integer q, q^2 - 5 is divisible by all of the follo [#permalink] New post 31 Oct 2014, 21:37
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: For some integer q, q^2 - 5 is divisible by all of the follo   [#permalink] 31 Oct 2014, 21:37

Go to page   Previous    1   2   [ 24 posts ] 

    Similar topics Author Replies Last post
Similar
Topics:
38 Experts publish their posts in the topic T is the set of all numbers that can be written as the follo honchos 9 01 Dec 2013, 16:34
12 Experts publish their posts in the topic The positive integer q is divisible by 15. If the product of alchemist009 11 05 Jun 2012, 18:12
Experts publish their posts in the topic Is 0 divisable by all integers? amitjash 4 16 Oct 2010, 03:19
Wed Q2 - Exponents hogann 4 14 Oct 2009, 05:29
Experts publish their posts in the topic Tuesday Q2 - Interns hogann 6 13 Oct 2009, 05:25
Display posts from previous: Sort by

For some integer q, q^2 - 5 is divisible by all of the follo

  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®.