• 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

If n is a positive integer, which of the following could be

This topic has 3 expert replies and 0 member replies

GMAT/MBA Expert

If n is a positive integer, which of the following could be

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



[Math Revolution GMAT math practice question]

If n is a positive integer, which of the following could be the value of (n+1)^3 - n^3?

A. 629
B. 630
C. 631
D. 632
E. 633

_________________

Math Revolution
Finish GMAT Quant Section with 10 minutes to spare.
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Only $99 for 3 month Online Course
Free Resources-30 day online access & Diagnostic Test
Unlimited Access to over 120 free video lessons-try it yourself
Email to : info@mathrevolution.com

  • +1 Upvote Post
  • Quote
  • Flag
Post
Max@Math Revolution wrote:
[Math Revolution GMAT math practice question]

If n is a positive integer, which of the following could be the value of (n+1)^3 - n^3?

A. 629
B. 630
C. 631
D. 632
E. 633
$$n \ge 1\,\,{\mathop{\rm int}} \,\,\left( * \right)$$
$$?\,\,:\,\,\,{\left( {n + 1} \right)^3} - {n^3}\,\,\underline {{\rm{could}}} \,\,{\rm{be}}$$

$${\left( {n + 1} \right)^3} - {n^3}\,\,\, = \,\,\, \ldots \,\,\, = \,\,\,3{n^2} + 3n + 1\,\,\, = \,\,\,3\left( {{n^2} + n} \right) + 1\,\,\, = \,\,\,3Q + 1\,\,\,,\,\,\,\,Q\mathop \ge \limits^{\left( * \right)} 2\,\,\,{\mathop{\rm int}} $$

$$?\,\,\,\,:\,\,\,{\rm{remainder}}\,\,{\rm{1}}\,\,{\rm{when}}\,\,{\rm{divided}}\,\,{\rm{by}}\,\,{\rm{3}}\,\,\,\,\, \Rightarrow \,\,\,{\rm{only}}\,\,\left( {\rm{C}} \right)$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

_________________
Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or https://GMATH.com.br (Portuguese version)
Course release PROMO : finish our test drive till 30/Dec with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount!

  • +1 Upvote Post
  • Quote
  • Flag
Post
Max@Math Revolution wrote:
[Math Revolution GMAT math practice question]

If n is a positive integer, which of the following could be the value of (n+1)^3 - n^3?

A. 629
B. 630
C. 631
D. 632
E. 633
Among the five options, we have to find out the possible value of (n+1)^3 - n^3.

So, we have (n+1)^3 - n^3

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

= [3n(n + 1)] + 1

Since is n a positive integer and n and (n + 1) are consecutive integers, one of n and (n + 1) is even. Thus, we can conclude that 3n(n + 1) is even and a multiple of 3*2 = 6. Thus, Between the two even numbers 630 and 632, only 630 is divisible by 6. So, 630 + 1 = 631 must the correct answer.

The correct answer: C

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: Manhattan Review Mumbai | Hyderabad | GRE Prep Warangal | Begumpet GRE Coaching | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Legendary Member
Joined
24 Jul 2015
Posted:
1840 messages
Followed by:
28 members
Upvotes:
19
GMAT Score:
Most Active Expert
Post
=>

Recall that x^3 - y^3 = (x-y)(x^2+xy+y^2).’
Now,
(n+1)^3 - n^3
= ( n + 1 - n ) ( (n+1)^2 + (n+1)n + n^2 )
= (n+1)^2 + (n+1)n + n2
= n^2 + 2n + 1 + n^2 + n + n2
= 3n^2 + 3n + 1
= 3n(n+1) + 1
Thus (n+1)^3 - n^3 has remainder 1 when it is divided by 3.
631 is the only answer choice with remainder 1 when it is divided by 3.

Therefore, the answer is C.
Answer: C

_________________

Math Revolution
Finish GMAT Quant Section with 10 minutes to spare.
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Only $99 for 3 month Online Course
Free Resources-30 day online access & Diagnostic Test
Unlimited Access to over 120 free video lessons-try it yourself
Email to : info@mathrevolution.com

  • +1 Upvote Post
  • Quote
  • Flag
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer

Top First Responders*

1 Brent@GMATPrepNow 64 first replies
2 fskilnik@GMATH 58 first replies
3 Jay@ManhattanReview 46 first replies
4 GMATGuruNY 34 first replies
5 Rich.C@EMPOWERgma... 24 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description fskilnik@GMATH

GMATH Teacher

120 posts
2 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

99 posts
3 image description Max@Math Revolution

Math Revolution

88 posts
4 image description Jay@ManhattanReview

Manhattan Review

82 posts
5 image description Rich.C@EMPOWERgma...

EMPOWERgmat

65 posts
See More Top Beat The GMAT Experts