Author 
Message 
TAGS:

Hide Tags

Senior Manager
Affiliations: UWC
Joined: 09 May 2012
Posts: 382
Location: Canada
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, 09:27
Question Stats:
84% (01:32) correct 16% (02:18) wrong based on 225 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
Official Answer and Stats are available only to registered users. Register/ Login.



Math Expert
Joined: 02 Sep 2009
Posts: 49231

If n is a positive integer and if (n^3  n)/(n+1) = 240, the
[#permalink]
Show Tags
28 May 2012, 00:45



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1835
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, 23:33
\(\frac{n^3 n}{n+1} = 240\) \(\frac{n(n+1)(n1)}{n+1} = 240\) \(n^2  n  240 = 0\) \(n^2  16n + 15n  240 = 0\) n = 16 Answer = B
_________________
Kindly press "+1 Kudos" to appreciate



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4011
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

If n is a positive integer and if (n^3  n)/(n+1) = 240, the
[#permalink]
Show Tags
24 Nov 2015, 12:28
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, \(n\) = \(16\) Hence answer is definitely (B)
_________________
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 )



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2835

Re: If n is a positive integer and if (n^3  n)/(n+1) = 240, the
[#permalink]
Show Tags
29 Sep 2017, 10:30
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 Answer: B
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Intern
Joined: 25 May 2017
Posts: 6
Concentration: General Management, Strategy
GPA: 3

Re: If n is a positive integer and if (n^3  n)/(n+1) = 240, the
[#permalink]
Show Tags
05 Oct 2017, 18:23
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 \(\frac{n^3n}{n+1}=240\) > \(\frac{n(n1)(n+1)}{n+1}=240\) > \(n(n1)=240\) > 240 is the product of two positive consecutive integers \(n1\) and \(n\) > \(n=16\) (16*15=240). Answer: B. 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?



Math Expert
Joined: 02 Sep 2009
Posts: 49231

Re: If n is a positive integer and if (n^3  n)/(n+1) = 240, the
[#permalink]
Show Tags
05 Oct 2017, 21:07
sharadvatsey wrote: 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 \(\frac{n^3n}{n+1}=240\) > \(\frac{n(n1)(n+1)}{n+1}=240\) > \(n(n1)=240\) > 240 is the product of two positive consecutive integers \(n1\) and \(n\) > \(n=16\) (16*15=240).Answer: B. 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 \(n(n1)=240\) we wouldn't be able to use the logic in highlighted part because if it were given that n is an integer, then \(n1\) and \(n\) might not be consecutive integers and we would be left with quadratics to solve. We'd get the same answer though.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 03 May 2017
Posts: 106

Re: If n is a positive integer and if (n^3  n)/(n+1) = 240, the
[#permalink]
Show Tags
05 Oct 2017, 23:05
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 \(n(n1)=240\) we wouldn't be able to use the logic in highlighted part because if it were given that n is an integer, then \(n1\) 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.



Math Expert
Joined: 02 Sep 2009
Posts: 49231

If n is a positive integer and if (n^3  n)/(n+1) = 240, the
[#permalink]
Show Tags
05 Oct 2017, 23:10



Manager
Status: Enjoying the Journey
Affiliations: ND
Joined: 26 Sep 2017
Posts: 114
WE: Marketing (Consulting)

If n is a positive integer and if (n^3  n)/(n+1) = 240, the
[#permalink]
Show Tags
05 Oct 2017, 23:27
Bunuel wrote: We would but after getting \(n(n1)=240\) we wouldn't be able to use the logic in highlighted part because if it were given that n is an integer, then \(n1\) 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
_________________
"it takes more time to fix a mistake than to avoid one" "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/gmatclublive5principlesforfastmath251028.html#p1940045 YouTube sessions by GMATNinja: https://gmatclub.com/forum/verballivewithgmatninjascpronounsthatparallelism250568.html#p1936104 The Best SC strategies  Amazing 4 videos by Veritas: https://gmatclub.com/forum/thebestscstrategiesamazing4videosbyveritas250377.html#p1934575



Intern
Joined: 25 May 2017
Posts: 6
Concentration: General Management, Strategy
GPA: 3

Re: If n is a positive integer and if (n^3  n)/(n+1) = 240, the
[#permalink]
Show Tags
06 Oct 2017, 00:13
[/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 \(n(n1)=240\) we wouldn't be able to use the logic in highlighted part because if it were given that n is an integer, then \(n1\) 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




Re: If n is a positive integer and if (n^3  n)/(n+1) = 240, the &nbs
[#permalink]
06 Oct 2017, 00:13






