• 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
  • 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
  • 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
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • 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

Is zero considered an even integer?

This topic has 5 expert replies and 6 member replies
givemeanid Master | Next Rank: 500 Posts
Joined
17 Jun 2007
Posted:
277 messages
Followed by:
1 members
Thanked:
6 times

Is zero considered an even integer?

Post Sun Jul 01, 2007 5:59 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    GMAT considers 0 as an even integer. Is that correct?

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    jayhawk2001 Community Manager
    Joined
    28 Jan 2007
    Posted:
    789 messages
    Followed by:
    1 members
    Thanked:
    30 times
    Post Sun Jul 01, 2007 7:50 pm
    Well, not just GMAT Smile. Zero is generally considered even.

    An integer n is called even if there exists an integer m such that n = 2m, and odd if n+1 is even.

    Thanked by: Joseph_Alexander
    montz Senior | Next Rank: 100 Posts Default Avatar
    Joined
    11 Aug 2007
    Posted:
    30 messages
    Thanked:
    1 times
    Target GMAT Score:
    750
    GMAT Score:
    700
    Post Mon Aug 20, 2007 10:34 am
    I always thought zero is neither odd nor even. The properties of even/odd nos. -

    Even => 2n and Odd => 2n-1 where 'n' is a natural number.

    But as per OG zero is even Confused

    Post Fri Aug 31, 2007 4:53 am
    however one thing to note is that zero is neither +ve nor -ve

    samirpandeyit62 Master | Next Rank: 500 Posts Default Avatar
    Joined
    25 Mar 2007
    Posted:
    460 messages
    Thanked:
    27 times
    Post Wed Sep 05, 2007 9:49 am
    As far as sign of 0 is concerned it is generally accepted that 0 can be both +ve as well as -ve as +0 =0 & -0 = 0 hence both would be the same nos,
    I believe specially on a DS question if it is asked to check some value is +ve or -ve and if it comes out to be 0 or can possibly be 0, I think we can simply use it as required by the question & not against it i.e if question wants +ve value, use it as +ve and vice versa.

    Post Thu Apr 07, 2016 6:00 am
    alstonamos wrote:
    I always thought zero is neither odd nor even. The properties of even/odd nos. -



    waleeed
    Zero is definitely even. In fact, this concept is tested often on the GMAT.
    An integer is considered even if it can be written as the product of 2 and another integer.
    Since, 0 = (2)(0), zero is considered even.

    Zero, however, is neither positive nor negative.

    Cheers,
    Brent

    _________________
    Brent Hanneson – Founder of GMATPrepNow.com
    Use our video course along with Beat The GMAT's free 60-Day Study Guide

    Check out the online reviews of our course
    Come see all of our free resources

    GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
    Post Thu Apr 07, 2016 5:26 pm
    Hi Waleed,

    0 is called a 'null value' since it's neither positive nor negative.
    0 is even because on a number line, integers vary odd-even-odd-even-etc. (e.g.. -3, -2, -1, 0, 1, 2, etc.)

    When a question uses a phrase such as "X is a non-negative integer', you should ABSOLUTELY consider the possibility that X is 0.

    GMAT assassins aren't born, they're made,
    Rich

    _________________
    Contact Rich at Rich.C@empowergmat.com

    GMAT/MBA Expert

    Post Fri Apr 15, 2016 1:38 pm
    I'd go even further and say that if you see the word 'nonnegative' instead of 'positive', considering 0 is *almost definitely* crucial to solving the problem.

    (This goes for 'nonpositive' too, I suppose, though I can't remember seeing that term in a GMAT problem.)

    Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!
    800_or_bust Master | Next Rank: 500 Posts Default Avatar
    Joined
    26 Apr 2014
    Posted:
    199 messages
    Followed by:
    4 members
    Thanked:
    16 times
    Test Date:
    7/9/2016
    GMAT Score:
    780
    Post Wed May 04, 2016 6:49 pm
    Matt@VeritasPrep wrote:
    I'd go even further and say that if you see the word 'nonnegative' instead of 'positive', considering 0 is *almost definitely* crucial to solving the problem.

    (This goes for 'nonpositive' too, I suppose, though I can't remember seeing that term in a GMAT problem.)
    Probably should remind the other instructors of this. I was watching the recorded stream from last night's free sample class, and noticed an error in the first example.

    The prompt was "If n is a nonnegative integer, then n(n+1)(n+2) is ..." And the correct answer was given as (E) Divisible by 12 whenever n is even.

    But this is clearly not correct, because if n=0, then n(n+1)(n+2) evaluates to be 2 which is not divisible by 12. Zero is both a nonnegative integer (as required by the prompt) and even (as required in the selected answer choice), and proves that (E) is not necessarily true.

    Other than that, it was good. Brian was pretty entertaining. Seemed like he was battling a bit of a cough though!

    _________________
    800 or bust!

    800_or_bust Master | Next Rank: 500 Posts Default Avatar
    Joined
    26 Apr 2014
    Posted:
    199 messages
    Followed by:
    4 members
    Thanked:
    16 times
    Test Date:
    7/9/2016
    GMAT Score:
    780
    Post Thu May 05, 2016 3:05 am
    800_or_bust wrote:
    Matt@VeritasPrep wrote:
    I'd go even further and say that if you see the word 'nonnegative' instead of 'positive', considering 0 is *almost definitely* crucial to solving the problem.

    (This goes for 'nonpositive' too, I suppose, though I can't remember seeing that term in a GMAT problem.)
    Probably should remind the other instructors of this. I was watching the recorded stream from last night's free sample class, and noticed an error in the first example.

    The prompt was "If n is a nonnegative integer, then n(n+1)(n+2) is ..." And the correct answer was given as (E) Divisible by 12 whenever n is even.

    But this is clearly not correct, because if n=0, then n(n+1)(n+2) evaluates to be 2 which is not divisible by 12. Zero is both a nonnegative integer (as required by the prompt) and even (as required in the selected answer choice), and proves that (E) is not necessarily true.

    Other than that, it was good. Brian was pretty entertaining. Seemed like he was battling a bit of a cough though!
    Actually, I'm the moron. I guess it was too late to be doing anything GMAT related last night... Of course, that expression actually evaluates to zero, not 2. And yes, zero is divisible by 12 so (E) is always true. Zero is divisible by any number. Oops.

    _________________
    800 or bust!

    GMAT/MBA Expert

    Post Thu May 26, 2016 1:47 pm
    800_or_bust wrote:
    The prompt was "If n is a nonnegative integer, then n(n+1)(n+2) is ..." And the correct answer was given as (E) Divisible by 12 whenever n is even.

    But this is clearly not correct, because if n=0, then n(n+1)(n+2) evaluates to be 2 which is not divisible by 12. Zero is both a nonnegative integer (as required by the prompt) and even (as required in the selected answer choice), and proves that (E) is not necessarily true.

    Other than that, it was good. Brian was pretty entertaining. Seemed like he was battling a bit of a cough though!
    Sorry to have missed this response!

    If n is even, you'll have n even, (n + 2) even, and one of the three consecutive integers divisible by 3 (though you don't know which one it will be). So you have two factors of 2 and one factor of 3, making n * (n + 1) * (n + 2) always divisible by 12.

    Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

    GMAT/MBA Expert

    Post Thu May 26, 2016 1:49 pm
    We could also think of this algebraically. Suppose n is even, so we can write n = 2k, where k is some integer we don't care about.

    2k * (2k + 1) * (2k + 2) =>

    4k * (2k + 1) * (k + 1)

    So clearly this is divisible by 4. We're left with

    k * (k + 1) * (2k + 1)

    If k has remainder 0 by 3, then the k term divides by 3.

    If k has remainder 1 by 3, then the (2k + 1) term divides by 3.

    If k has remainder 2 by 3, then the (k + 1) term divides by 3.

    Since these three cases are exhaustive, our product must divide by 3 and by 4, and hence by 12.

    Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

    Best Conversation Starters

    1 lheiannie07 111 topics
    2 ardz24 64 topics
    3 LUANDATO 62 topics
    4 swerve 60 topics
    5 AAPL 57 topics
    See More Top Beat The GMAT Members...

    Most Active Experts

    1 image description Brent@GMATPrepNow

    GMAT Prep Now Teacher

    160 posts
    2 image description EconomistGMATTutor

    The Economist GMAT Tutor

    130 posts
    3 image description Rich.C@EMPOWERgma...

    EMPOWERgmat

    122 posts
    4 image description GMATGuruNY

    The Princeton Review Teacher

    122 posts
    5 image description Scott@TargetTestPrep

    Target Test Prep

    118 posts
    See More Top Beat The GMAT Experts