It is currently 14 Dec 2017, 05:18

# Decision(s) Day!:

CHAT Rooms | Wharton R1 | Stanford R1 | Tuck R1 | Ross R1 | Haas R1

### 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 if (n^3 - n)/(n+1) = 240, the

Author Message
TAGS:

### Hide Tags

Senior Manager
Affiliations: UWC
Joined: 09 May 2012
Posts: 393

Kudos [?]: 1681 [0], given: 100

GMAT 1: 620 Q42 V33
GMAT 2: 680 Q44 V38
GPA: 3.43
WE: Engineering (Entertainment and Sports)
If n is a positive integer and if (n^3 - n)/(n+1) = 240, the [#permalink]

### Show Tags

27 May 2012, 08:27
9
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

83% (01:33) correct 17% (02:07) wrong based on 213 sessions

### HideShow timer Statistics

If n is a positive integer and if (n^3 - n)/(n+1) = 240, then what is the value of n?

A. 12
B. 16
C. 17
D. 20
E. 48
[Reveal] Spoiler: OA

Kudos [?]: 1681 [0], given: 100

Math Expert
Joined: 02 Sep 2009
Posts: 42605

Kudos [?]: 135613 [1], given: 12705

If n is a positive integer and if (n^3 - n)/(n+1) = 240, the [#permalink]

### Show Tags

27 May 2012, 23:45
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
macjas wrote:
If n is a positive integer and if (n^3 - n)/(n+1) = 240, then what is the value of n?

A. 12
B. 16
C. 17
D. 20
E. 48

$$\frac{n^3-n}{n+1}=240$$ --> $$\frac{n(n-1)(n+1)}{n+1}=240$$ --> $$n(n-1)=240$$ --> 240 is the product of two positive consecutive integers $$n-1$$ and $$n$$ --> $$n=16$$ (16*15=240).

Note that one other pair of consecutive integers satisfy $$n(n-1)=240$$: -15 and -16 but we are told that n is positive hence this solution is not valid.
_________________

Kudos [?]: 135613 [1], given: 12705

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1849

Kudos [?]: 2788 [1], given: 193

Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If n is a positive integer and if (n^3 - n)/(n+1) = 240, the [#permalink]

### Show Tags

26 Oct 2014, 22:33
1
KUDOS
$$\frac{n^3 -n}{n+1} = 240$$

$$\frac{n(n+1)(n-1)}{n+1} = 240$$

$$n^2 - n - 240 = 0$$

$$n^2 - 16n + 15n - 240 = 0$$

n = 16

_________________

Kindly press "+1 Kudos" to appreciate

Kudos [?]: 2788 [1], given: 193

Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3111

Kudos [?]: 1146 [0], given: 327

Location: India
GPA: 3.5
If n is a positive integer and if (n^3 - n)/(n+1) = 240, the [#permalink]

### Show Tags

24 Nov 2015, 11:28
macjas wrote:
If n is a positive integer and if (n^3 - n)/(n+1) = 240, then what is the value of n?

A. 12
B. 16
C. 17
D. 20
E. 48

$$\frac{(n^3 - n)}{(n+1)}$$ = 240

$$\frac{(n^3 - n)}{(n+1)}$$ = $$(16 )(15)$$

$$\frac{n(n^2 - 1)}{(n+1)}$$ = $$(16 )(15)$$

$$\frac{n(n - 1)(n+1)}{(n+1)}$$= $$(16 )(15)$$

$$n(n - 1)$$ = $$(16 )(15)$$

So, $$n$$ = $$16$$

_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Kudos [?]: 1146 [0], given: 327

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1802

Kudos [?]: 981 [0], given: 5

Re: If n is a positive integer and if (n^3 - n)/(n+1) = 240, the [#permalink]

### Show Tags

29 Sep 2017, 09:30
macjas wrote:
If n is a positive integer and if (n^3 - n)/(n+1) = 240, then what is the value of n?

A. 12
B. 16
C. 17
D. 20
E. 48

We can simplify the given equation:

(n^3 - n)/(n + 1) = 240

n(n^2 - 1)/(n + 1) = 240

n(n + 1)(n - 1)/(n + 1) = 240

n(n - 1) = 240

n^2 - n - 240 = 0

(n - 16)(n + 15) = 0

n = 16 or n = -15

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 981 [0], given: 5

Intern
Joined: 25 May 2017
Posts: 6

Kudos [?]: 6 [0], given: 11

Concentration: General Management, Strategy
GMAT 1: 710 Q49 V36
GPA: 3
Re: If n is a positive integer and if (n^3 - n)/(n+1) = 240, the [#permalink]

### Show Tags

05 Oct 2017, 17:23
Bunuel wrote:
macjas wrote:
If n is a positive integer and if (n^3 - n)/(n+1) = 240, then what is the value of n?

A. 12
B. 16
C. 17
D. 20
E. 48

$$\frac{n^3-n}{n+1}=240$$ --> $$\frac{n(n-1)(n+1)}{n+1}=240$$ --> $$n(n-1)=240$$ --> 240 is the product of two positive consecutive integers $$n-1$$ and $$n$$ --> $$n=16$$ (16*15=240).

What is the significance of "If n is a positive integer" in this question? Would we not cancel (n+1) if n is not a positive integer?

Kudos [?]: 6 [0], given: 11

Math Expert
Joined: 02 Sep 2009
Posts: 42605

Kudos [?]: 135613 [1], given: 12705

Re: If n is a positive integer and if (n^3 - n)/(n+1) = 240, the [#permalink]

### Show Tags

05 Oct 2017, 20:07
1
KUDOS
Expert's post
Bunuel wrote:
macjas wrote:
If n is a positive integer and if (n^3 - n)/(n+1) = 240, then what is the value of n?

A. 12
B. 16
C. 17
D. 20
E. 48

$$\frac{n^3-n}{n+1}=240$$ --> $$\frac{n(n-1)(n+1)}{n+1}=240$$ --> $$n(n-1)=240$$ --> 240 is the product of two positive consecutive integers $$n-1$$ and $$n$$ --> $$n=16$$ (16*15=240).

What is the significance of "If n is a positive integer" in this question? Would we not cancel (n+1) if n is not a positive integer?

We would but after getting $$n(n-1)=240$$ we wouldn't be able to use the logic in highlighted part because if it were given that n is an integer, then $$n-1$$ and $$n$$ might not be consecutive integers and we would be left with quadratics to solve. We'd get the same answer though.
_________________

Kudos [?]: 135613 [1], given: 12705

Manager
Joined: 03 May 2017
Posts: 113

Kudos [?]: 19 [0], given: 14

Re: If n is a positive integer and if (n^3 - n)/(n+1) = 240, the [#permalink]

### Show Tags

05 Oct 2017, 22:05
What is the significance of "If n is a positive integer" in this question? Would we not cancel (n+1) if n is not a positive integer?[/quote]

We would but after getting $$n(n-1)=240$$ we wouldn't be able to use the logic in highlighted part because if it were given that n is an integer, then $$n-1$$ and $$n$$ might not be consecutive integers and we would be left with quadratics to solve. We'd get the same answer though.[/quote]

Hi Bunuel

Great work, you mentioned that we might not be able to get consecutive integers, but -16 and -15 are also consecutive integers and as you have mentioned we would arrive at the same solution. I would lean towards the isolation of a single solution as the significance of the positive integer constraint. As you are well aware of, this would probably be more significant in a DS yes or no or even a DS value question.

Thanks again for the excellent contributions.

Kudos [?]: 19 [0], given: 14

Math Expert
Joined: 02 Sep 2009
Posts: 42605

Kudos [?]: 135613 [1], given: 12705

If n is a positive integer and if (n^3 - n)/(n+1) = 240, the [#permalink]

### Show Tags

05 Oct 2017, 22:10
1
KUDOS
Expert's post
rulingbear wrote:
Great work, you mentioned that we might not be able to get consecutive integers, but -16 and -15 are also consecutive integers and as you have mentioned we would arrive at the same solution. I would lean towards the isolation of a single solution as the significance of the positive integer constraint. As you are well aware of, this would probably be more significant in a DS yes or no or even a DS value question.

Thanks again for the excellent contributions.

Notice that we are not only told that n is an integer but also that n is positive: " n is a positive integer".
_________________

Kudos [?]: 135613 [1], given: 12705

Manager
Status: Enjoying the Journey
Affiliations: ND
Joined: 26 Sep 2017
Posts: 83

Kudos [?]: 33 [0], given: 471

Schools: Rotman '21
WE: Marketing (Consulting)
If n is a positive integer and if (n^3 - n)/(n+1) = 240, the [#permalink]

### Show Tags

05 Oct 2017, 22:27
Bunuel wrote:
We would but after getting $$n(n-1)=240$$ we wouldn't be able to use the logic in highlighted part because if it were given that n is an integer, then $$n-1$$ and $$n$$ might not be consecutive integers and we would be left with quadratics to solve. We'd get the same answer though.

I like the idea of plugging and not solving the quadratic equation...this saves a hell of time
_________________

"Giving kudos" is a decent way to say "Thanks" and motivate contributors. Please use them, it won't cost you anything

High achievement always takes place in the framework of high expectation Charles Kettering
If we chase perfection we can catch excellence Vince Lombardi

GMAT Club Live: 5 Principles for Fast Math: https://gmatclub.com/forum/gmat-club-live-5-principles-for-fast-math-251028.html#p1940045
The Best SC strategies - Amazing 4 videos by Veritas: https://gmatclub.com/forum/the-best-sc-strategies-amazing-4-videos-by-veritas-250377.html#p1934575

Kudos [?]: 33 [0], given: 471

Intern
Joined: 25 May 2017
Posts: 6

Kudos [?]: 6 [0], given: 11

Concentration: General Management, Strategy
GMAT 1: 710 Q49 V36
GPA: 3
Re: If n is a positive integer and if (n^3 - n)/(n+1) = 240, the [#permalink]

### Show Tags

05 Oct 2017, 23:13
[/quote]

What is the significance of "If n is a positive integer" in this question? Would we not cancel (n+1) if n is not a positive integer?[/quote]

We would but after getting $$n(n-1)=240$$ we wouldn't be able to use the logic in highlighted part because if it were given that n is an integer, then $$n-1$$ and $$n$$ might not be consecutive integers and we would be left with quadratics to solve. We'd get the same answer though.[/quote]

Thank you. This helps

Kudos [?]: 6 [0], given: 11

Re: If n is a positive integer and if (n^3 - n)/(n+1) = 240, the   [#permalink] 05 Oct 2017, 23:13
Display posts from previous: Sort by