• Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • 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
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • 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

Problem Solving - Q

This topic has 2 expert replies and 2 member replies
gettingstarted Newbie | Next Rank: 10 Posts Default Avatar
Joined
21 Jul 2011
Posted:
2 messages

Problem Solving - Q

Post Thu Jul 21, 2011 11:10 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    What is the best way to solve the Question below, is it by testing numbers or is there any other approach that can be tried, please suggest and explain the approach. Thanks

    Q ) If n is an integer greater than 6, which of the following must be divisible by 3?

    A) n(n+1)(n-4)
    B) n(n+2)(n-1)
    C) n(n+3)(n-5)
    D) n(n+4)(n-2)
    E) n(n+5)(n-6)

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Thu Jul 21, 2011 11:44 am
    gettingstarted wrote:
    What is the best way to solve the Question below, is it by testing numbers or is there any other approach that can be tried, please suggest and explain the approach. Thanks

    Q ) If n is an integer greater than 6, which of the following must be divisible by 3?

    A) n(n+1)(n-4)
    B) n(n+2)(n-1)
    C) n(n+3)(n-5)
    D) n(n+4)(n-2)
    E) n(n+5)(n-6)
    We can plug in numbers and eliminate any answer that is not a multiple of 3.

    Let n=7:
    A) n(n+1)(n-4) = 7*8*3, which is a multiple of 3. Hold onto A.
    B) n(n+2)(n-1) = 7*9*6, which is a multiple of 3. Hold onto B.
    C) n(n+3)(n-5) = 7*10*5, which is not a multiple of 3. Eliminate C.
    D) n(n+4)(n-2) = 7*11*5, which is not a multiple of 3. Eliminate D.
    E) n(n+5)(n-6) = 7*12*1, which is a multiple of 3. Hold onto E.

    Let n=8:
    A) n(n+1)(n-4) = 8*9*4, which is a multiple of 3. Hold onto A.
    B) n(n+2)(n-1) = 8*10*7, which is not a multiple of 3. Eliminate B.
    E) n(n+5)(n-6) = 8*13*2, which is not a multiple of 3. Eliminate E.

    The correct answer is A.

    We also could reason our way to the correct answer.

    Of every 3 consecutive integers, exactly one will be a multiple of 3:
    1,2,3
    2,3,4
    3,4,5
    4,5,6

    Answer choice A includes n(n+1).
    Of n-1, n, and n+1 -- three consecutive integers -- exactly one will be a multiple of 3.
    If either n or n+1 is a multiple of 3, then n(n+1) will be a multiple of 3.
    If neither n nor n+1 is a multiple of 3, then n-1 must be a multiple of 3.
    If n-1 is a multiple of 3, so is n-4, since the distance between them = (n-1) - (n-4) = 3.
    If n-4 is a multiple of 3, then n(n+1)(n-4) is a multiple of 3.

    Thus, whatever the scenario, answer choice A must be a multiple of 3.

    I think plugging in numbers is MUCH easier.

    _________________
    Mitch Hunt
    GMAT Private Tutor
    GMATGuruNY@gmail.com
    If you find one of my posts helpful, please take a moment to click on the "Thank" icon.
    Available for tutoring in NYC and long-distance.
    For more information, please email me at GMATGuruNY@gmail.com.



    Last edited by GMATGuruNY on Sat Sep 10, 2011 4:48 am; edited 2 times in total

    Thanked by: ravirajsitaram, arvysri
    Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.
    gettingstarted Newbie | Next Rank: 10 Posts Default Avatar
    Joined
    21 Jul 2011
    Posted:
    2 messages
    Post Fri Jul 22, 2011 10:10 am
    Thanks for the reply. Its was really helpful.

    leumas Senior | Next Rank: 100 Posts
    Joined
    21 Aug 2011
    Posted:
    44 messages
    Thanked:
    3 times
    Test Date:
    12/28/2011
    Target GMAT Score:
    800
    GMAT Score:
    NA
    Post Sat Sep 10, 2011 5:20 am
    GMATGuruNY wrote:
    Q ) If n is an integer greater than 6, which of the following must be divisible by 3?

    A) n(n+1)(n-4)
    B) n(n+2)(n-1)
    C) n(n+3)(n-5)
    D) n(n+4)(n-2)
    E) n(n+5)(n-6)

    We can plug in numbers and eliminate any answer that is not a multiple of 3.

    Let n=7:
    A) n(n+1)(n-4) = 7*8*3, which is a multiple of 3. Hold onto A.
    B) n(n+2)(n-1) = 7*9*6, which is a multiple of 3. Hold onto B.
    C) n(n+3)(n-5) = 7*10*5, which is not a multiple of 3. Eliminate C.
    D) n(n+4)(n-2) = 7*11*5, which is not a multiple of 3. Eliminate D.
    E) n(n+5)(n-6) = 7*12*1, which is a multiple of 3. Hold onto E.

    Let n=8:
    A) n(n+1)(n-4) = 8*9*4, which is a multiple of 3. Hold onto A.
    B) n(n+2)(n-1) = 8*10*7, which is not a multiple of 3. Eliminate B.
    E) n(n+5)(n-6) = 8*13*2, which is not a multiple of 3. Eliminate E.

    The correct answer is A.

    We also could reason our way to the correct answer.

    Of every 3 consecutive integers, exactly one will be a multiple of 3:
    1,2,3
    2,3,4
    3,4,5
    4,5,6

    Answer choice A includes n(n+1).
    Of n-1, n, and n+1 -- three consecutive integers -- exactly one will be a multiple of 3.
    If either n or n+1 is a multiple of 3, then n(n+1) will be a multiple of 3.
    If neither n nor n+1 is a multiple of 3, then n-1 must be a multiple of 3.
    If n-1 is a multiple of 3, so is n-4, since the distance between them = (n-1) - (n-4) = 3.
    If n-4 is a multiple of 3, then n(n+1)(n-4) is a multiple of 3.

    Thus, whatever the scenario, answer choice A must be a multiple of 3.

    I think plugging in numbers is MUCH easier.
    Hi Gmatguru Thanks!! Now I got Anurag that n-4 can be written as -3+ (N-1),

    Then we should ignore the info given in the question that the integer is greater than 6.
    Is this right approach?

    Post Sat Sep 10, 2011 2:01 pm
    leumas wrote:
    GMATGuruNY wrote:
    Q ) If n is an integer greater than 6, which of the following must be divisible by 3?

    A) n(n+1)(n-4)
    B) n(n+2)(n-1)
    C) n(n+3)(n-5)
    D) n(n+4)(n-2)
    E) n(n+5)(n-6)

    We can plug in numbers and eliminate any answer that is not a multiple of 3.

    Let n=7:
    A) n(n+1)(n-4) = 7*8*3, which is a multiple of 3. Hold onto A.
    B) n(n+2)(n-1) = 7*9*6, which is a multiple of 3. Hold onto B.
    C) n(n+3)(n-5) = 7*10*5, which is not a multiple of 3. Eliminate C.
    D) n(n+4)(n-2) = 7*11*5, which is not a multiple of 3. Eliminate D.
    E) n(n+5)(n-6) = 7*12*1, which is a multiple of 3. Hold onto E.

    Let n=8:
    A) n(n+1)(n-4) = 8*9*4, which is a multiple of 3. Hold onto A.
    B) n(n+2)(n-1) = 8*10*7, which is not a multiple of 3. Eliminate B.
    E) n(n+5)(n-6) = 8*13*2, which is not a multiple of 3. Eliminate E.

    The correct answer is A.

    We also could reason our way to the correct answer.

    Of every 3 consecutive integers, exactly one will be a multiple of 3:
    1,2,3
    2,3,4
    3,4,5
    4,5,6

    Answer choice A includes n(n+1).
    Of n-1, n, and n+1 -- three consecutive integers -- exactly one will be a multiple of 3.
    If either n or n+1 is a multiple of 3, then n(n+1) will be a multiple of 3.
    If neither n nor n+1 is a multiple of 3, then n-1 must be a multiple of 3.
    If n-1 is a multiple of 3, so is n-4, since the distance between them = (n-1) - (n-4) = 3.
    If n-4 is a multiple of 3, then n(n+1)(n-4) is a multiple of 3.

    Thus, whatever the scenario, answer choice A must be a multiple of 3.

    I think plugging in numbers is MUCH easier.
    Hi Gmatguru Thanks!! Now I got Anurag that n-4 can be written as -3+ (N-1),

    Then we should ignore the info given in the question that the integer is greater than 6.
    Is this right approach?
    When we plug in, we must comply with whatever conditions are given in the problem.
    In the problem here, n must be greater than 6.
    In my solution, I plugged in n=7 and n=8, both of which are greater than 6.

    _________________
    Mitch Hunt
    GMAT Private Tutor
    GMATGuruNY@gmail.com
    If you find one of my posts helpful, please take a moment to click on the "Thank" icon.
    Available for tutoring in NYC and long-distance.
    For more information, please email me at GMATGuruNY@gmail.com.

    Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.

    Best Conversation Starters

    1 Vincen 180 topics
    2 lheiannie07 65 topics
    3 Roland2rule 49 topics
    4 ardz24 44 topics
    5 LUANDATO 23 topics
    See More Top Beat The GMAT Members...

    Most Active Experts

    1 image description Brent@GMATPrepNow

    GMAT Prep Now Teacher

    147 posts
    2 image description Rich.C@EMPOWERgma...

    EMPOWERgmat

    103 posts
    3 image description GMATGuruNY

    The Princeton Review Teacher

    102 posts
    4 image description EconomistGMATTutor

    The Economist GMAT Tutor

    94 posts
    5 image description DavidG@VeritasPrep

    Veritas Prep

    76 posts
    See More Top Beat The GMAT Experts