For how many different positive integers n is a divisor of n : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 18 Jan 2017, 10:20

# STARTING SOON:

Open Admission Chat with MBA Experts of Personal MBA Coach - Join Chat Room to Participate.

### 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

# For how many different positive integers n is a divisor of n

Author Message
TAGS:

### Hide Tags

Intern
Joined: 07 Feb 2009
Posts: 14
Followers: 0

Kudos [?]: 31 [1] , given: 13

For how many different positive integers n is a divisor of n [#permalink]

### Show Tags

27 Oct 2010, 20:19
1
KUDOS
10
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

56% (02:01) correct 44% (01:05) wrong based on 417 sessions

### HideShow timer Statistics

For how many different positive integers n is a divisor of n^3 + 8?

A. None
B. One
C. Two
D. Three
E. Four
[Reveal] Spoiler: OA

Last edited by Bunuel on 09 Jul 2013, 07:58, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 36545
Followers: 7076

Kudos [?]: 93089 [7] , given: 10542

Re: PS - Integers and divisors [#permalink]

### Show Tags

27 Oct 2010, 20:25
7
KUDOS
Expert's post
2
This post was
BOOKMARKED
For how many different positive integers n is a divisor of n^3 + 8?

A. None
B. One
C. Two
D. Three
E. Four

The question asks for how many different positive integers $$n$$, $$n^3+8$$ is divisible by $$n$$.

Well the first term $$n^3$$ is divisible by $$n$$, the second term, 8, to be divisible by $$n$$, should be a factor of 8.

$$8=2^3$$ hence it has 3+1=4 factors: 1, 2, 4, and 8. Therefore $$n^3+8$$ is divisible by $$n$$ for 4 values of $$n$$: 1, 2, 4, and 8.

_________________
Intern
Joined: 28 May 2012
Posts: 29
Concentration: Finance, General Management
GMAT 1: 700 Q50 V35
GPA: 3.28
WE: Analyst (Investment Banking)
Followers: 1

Kudos [?]: 46 [1] , given: 84

Re: For how many different positive integers n is a divisor of n [#permalink]

### Show Tags

09 Jul 2013, 19:33
1
KUDOS
n^3 + 8 = (n+2)(n^2-2n+4)
--> 2 divisors possible, plus 1 and n
we have 4 divisors.
Intern
Joined: 08 Oct 2011
Posts: 42
Followers: 0

Kudos [?]: 20 [0], given: 38

Re: PS - Integers and divisors [#permalink]

### Show Tags

27 Oct 2013, 08:56
Bunuel wrote:
For how many different positive integers n is a divisor of n^3 + 8?

A. None
B. One
C. Two
D. Three
E. Four

The question asks for how many different positive integers $$n$$, $$n^3+8$$ is divisible by $$n$$.

Well the first term $$n^3$$ is divisible by $$n$$, the second term, 8, to be divisible by $$n$$, should be a factor of 8.

$$8=2^3$$ hence it has 3+1=4 factors: 1, 2, 4, and 8. Therefore $$n^3+8$$ is divisible by $$n$$ for 4 values of $$n$$: 1, 2, 4, and 8.

Bunnel at first I got the answer 4.

Then I plugged in n=3 and got zero. PS questions are supposed to have one right answer. Why are we using only $$2$$ here ?
Math Expert
Joined: 02 Sep 2009
Posts: 36545
Followers: 7076

Kudos [?]: 93089 [2] , given: 10542

Re: PS - Integers and divisors [#permalink]

### Show Tags

27 Oct 2013, 23:24
2
KUDOS
Expert's post
2
This post was
BOOKMARKED
aakrity wrote:
Bunuel wrote:
For how many different positive integers n is a divisor of n^3 + 8?

A. None
B. One
C. Two
D. Three
E. Four

The question asks for how many different positive integers $$n$$, $$n^3+8$$ is divisible by $$n$$.

Well the first term $$n^3$$ is divisible by $$n$$, the second term, 8, to be divisible by $$n$$, should be a factor of 8.

$$8=2^3$$ hence it has 3+1=4 factors: 1, 2, 4, and 8. Therefore $$n^3+8$$ is divisible by $$n$$ for 4 values of $$n$$: 1, 2, 4, and 8.

Bunnel at first I got the answer 4.

Then I plugged in n=3 and got zero. PS questions are supposed to have one right answer. Why are we using only $$2$$ here ?

You cannot pick arbitrary numbers here.

The question asks "for how many different positive integers n is a divisor of n^3 + 8", so for how many different n's $$\frac{n^3 + 8}{n}=integer$$.

Now, $$\frac{n^3 + 8}{n}=n^2+\frac{8}{n}$$ to be an integer n must be a factor of 8. 8 has 4 factors, thus for 4 values of n $$\frac{n^3 + 8}{n}$$ will be an integer: if n is 1, 2, 4, or 8.

Hope it's clear.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13437
Followers: 575

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

Re: For how many different positive integers n is a divisor of n [#permalink]

### Show Tags

23 Nov 2014, 11:13
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 Legend
Joined: 09 Sep 2013
Posts: 13437
Followers: 575

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

Re: For how many different positive integers n is a divisor of n [#permalink]

### Show Tags

13 Dec 2015, 13:52
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: For how many different positive integers n is a divisor of n   [#permalink] 13 Dec 2015, 13:52
Similar topics Replies Last post
Similar
Topics:
If n is a positive integer and the greatest common divisor of n and 30 3 13 Sep 2016, 01:17
2 For how many positive integers n is it true that... 2 06 Jul 2016, 05:41
1 For how many positive integers is the number of positive divisors 3 23 Apr 2016, 06:11
3 If n is a prime number between 0 and 100, how many positive divisors 6 20 Apr 2016, 00:03
6 If n is a positive integer and the greatest common divisor 3 24 Mar 2014, 02:19
Display posts from previous: Sort by