GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 20 Jun 2019, 12:52

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.

Close

Request Expert Reply

Confirm Cancel

If n is a positive integer, is n^3 + 4n^2 – 5n divisible by

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Manager
Manager
User avatar
Status: Never ever give up on yourself.Period.
Joined: 23 Aug 2012
Posts: 136
Location: India
Concentration: Finance, Human Resources
GMAT 1: 570 Q47 V21
GMAT 2: 690 Q50 V33
GPA: 3.5
WE: Information Technology (Investment Banking)
If n is a positive integer, is n^3 + 4n^2 – 5n divisible by  [#permalink]

Show Tags

New post Updated on: 14 Jan 2013, 06:42
3
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

63% (02:40) correct 38% (02:25) wrong based on 154 sessions

HideShow timer Statistics

If n is a positive integer, is n^3 + 4n^2 - 5n divisible by 8 ?

(1) n = 4b + 1, where b is a positive integer.

(2) n^2 – n is divisible by 24.

_________________
Don't give up on yourself ever. Period.
Beat it, no one wants to be defeated (My journey from 570 to 690) : http://gmatclub.com/forum/beat-it-no-one-wants-to-be-defeated-journey-570-to-149968.html

Originally posted by daviesj on 14 Jan 2013, 06:40.
Last edited by Bunuel on 14 Jan 2013, 06:42, edited 1 time in total.
Edited the question.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55732
Re: If n is a positive integer, is n^3 + 4n^2 – 5n divisible by  [#permalink]

Show Tags

New post 14 Jan 2013, 06:49
If n is a positive integer, is n^3 + 4n^2 - 5n divisible by 8 ?

\(n^3 + 4n^2 - 5n=n(n^2+4n-5)=n(n-1)(n+5)\)

(1) n = 4b + 1, where b is a positive integer --> \(n(n-1)(n+5)=(4b+1)(4b)(4b+6)=(4b+1)(8b)(2b+3)\). Sufficient.

(2) n^2 – n is divisible by 24 --> n(n-1) is divisible by 24, so its also divisible by 8. Thus n(n-1)(n+5) is also divisible by 8. Sufficient.

Answer: D.

Hope it's clear.
_________________
Manager
Manager
avatar
Joined: 06 Jun 2010
Posts: 153
Re: If n is a positive integer, is n^3 + 4n^2 – 5n divisible by  [#permalink]

Show Tags

New post 15 Jan 2013, 11:56
Hi Bunuel,

Can u plz xplain this step:

(4b+1)(4b)(4b+6)= (4b+1)(8b)(2b+3).Sufficient.

Thanks,
Shreeraj
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55732
Re: If n is a positive integer, is n^3 + 4n^2 – 5n divisible by  [#permalink]

Show Tags

New post 15 Jan 2013, 12:08
SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1651
Concentration: Finance
GMAT ToolKit User
Re: If n is a positive integer, is n^3 + 4n^2 – 5n divisible by  [#permalink]

Show Tags

New post 17 Jan 2014, 12:32
daviesj wrote:
If n is a positive integer, is n^3 + 4n^2 - 5n divisible by 8 ?

(1) n = 4b + 1, where b is a positive integer.

(2) n^2 – n is divisible by 24.


The only things to point out or add if you will are the following

Question stem = Factorizing one gets (n)(n+5)(n-1)

Statement 1

n = 4b+1

Replacing (4b+1)(4b+6)(4b)

Now (4b) and (4b+1) are consecutive integers

Therefore one of them must be odd and one even, obviously 4b is the even one

So 4b is a multiple of 4 and 4b +6 is even so we have a multiple of 8

Statement 2

n(n-1) divisible by 24 means that either n or n-1 is divisible by 3 and that one of them, the even one, will be divisible by 8

Since we have both terms in our initial factorization then YES it is a multiple of 8

Hence D

Is this clear?

PS. The answer choice button tab in GMAT Club is awesome!

Cheers!
J :)
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 11398
Re: If n is a positive integer, is n^3 + 4n^2 – 5n divisible by  [#permalink]

Show Tags

New post 16 Sep 2018, 02:54
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 Club Bot
Re: If n is a positive integer, is n^3 + 4n^2 – 5n divisible by   [#permalink] 16 Sep 2018, 02:54
Display posts from previous: Sort by

If n is a positive integer, is n^3 + 4n^2 – 5n divisible by

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne