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is 0 an even integer?

This topic has 3 expert replies and 8 member replies
CITI29 Senior | Next Rank: 100 Posts Default Avatar
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is 0 an even integer?

Post Sun Jul 13, 2008 4:18 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    was wondering if 0 is an even interger for a question like this:

    If n is an integer, is n even?
    (1) n2 −1 is an odd integer.
    (2) 3n + 4 is an even integer.

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    Ian Stewart GMAT Instructor
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    Post Mon Jul 14, 2008 1:19 am
    Yes, 0 is always an even integer.

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    aniruddhkashyap Newbie | Next Rank: 10 Posts Default Avatar
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    Post Sun Apr 18, 2010 11:13 pm
    Ian Stewart wrote:
    Yes, 0 is always an even integer.
    This is one of the problem from the "tough math problems set" floating around on this site......


    51. How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3?

    A.14 B.15. C.16 D.17 E.18

    Soln: if we arrange this in AP, we get
    4+7+10+.......+49

    so 4+(n-1)3=49: n=16
    C is my pick


    They have not considered 1 as one of the options......is this incorrect?

    ajith Legendary Member
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    Post Sun Apr 18, 2010 11:20 pm
    aniruddhkashyap wrote:
    Ian Stewart wrote:
    Yes, 0 is always an even integer.
    This is one of the problem from the "tough math problems set" floating around on this site......


    51. How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3?

    A.14 B.15. C.16 D.17 E.18

    Soln: if we arrange this in AP, we get
    4+7+10+.......+49

    so 4+(n-1)3=49: n=16
    C is my pick


    They have not considered 1 as one of the options......is this incorrect?
    1 has to be a part of it since it leaves a remainder of 1 when divided by 3

    so the solution quoted is incorrect, in my opinion

    n=17 is the correct answer

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    eaakbari Master | Next Rank: 500 Posts
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    Post Mon Apr 19, 2010 12:43 am
    CITI29 wrote:
    was wondering if 0 is an even interger for a question like this:

    If n is an integer, is n even?
    (1) n2 -1 is an odd integer.
    (2) 3n + 4 is an even integer.
    (1)
    Implies n^2 is even which means n is even
    Hence Suff.

    (2)
    Since 3n+4 is even
    and even + even = even
    Hence 3n must be even, that means n is even
    Hence Suff

    Answer D

    And to reiterate what Ian said, 0 zero is a non-positive, non -negative even integer.

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    sanju09 GMAT Instructor
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    Post Mon Apr 19, 2010 1:18 am
    aniruddhkashyap wrote:
    Ian Stewart wrote:
    Yes, 0 is always an even integer.
    This is one of the problem from the "tough math problems set" floating around on this site......


    51. How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3?

    A.14 B.15. C.16 D.17 E.18

    Soln: if we arrange this in AP, we get
    4+7+10+.......+49

    so 4+(n-1)3=49: n=16
    C is my pick


    They have not considered 1 as one of the options......is this incorrect?
    A positive integer divisor n has exactly n number of possible remainders to succumb. In case the dividend is smaller than the divisor, the remainder happens to be same in value as the dividend. In the presented example, 1 is a member of list so the account is erroneous.

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    Post Tue Oct 02, 2012 6:32 pm
    Is zero positive?

    anuprajan5 Master | Next Rank: 500 Posts
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    Post Tue Oct 02, 2012 8:25 pm
    Claudia,

    0 is a non negative even integer.

    Regards
    Anup

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    sanju09 GMAT Instructor
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    Post Wed Oct 03, 2012 1:32 am
    claudia.minoiu@gmail.com wrote:
    Is zero positive?
    (A) 0 is an even integer.

    (B) 0 is a neutral integer too, hence 0 is neither positive nor negative.

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    Post Wed Oct 03, 2012 6:04 am
    CITI29 wrote:
    If n is an integer, is n even?
    (1) n^2 -1 is an odd integer.
    (2) 3n + 4 is an even integer.
    Target question: Is n even?

    Statement 1: n^2 -1 is an odd integer.
    If n^2 -1 is an odd integer, then n^2 must be an even integer.
    If n^2 is an even integer, then n must be even.
    Rationale: (odd)^2 - odd, but (even)^2 = even
    As such, statement 1 is SUFFICIENT

    Statement 2: 3n + 4 is an even integer.
    If 3n + 4 is an even integer, then 3n must be an even integer (since Even + Even = Even).
    If 3n must be an even integer, then n must be even.
    Rationale: (odd)(even) = even and
    As such, statement 2 is SUFFICIENT

    Answer = D

    Cheers,
    Brent

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    Post Wed Oct 03, 2012 6:06 am

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    GMAT Kolaveri Master | Next Rank: 500 Posts
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    Post Wed Oct 03, 2012 7:49 am
    CITI29 wrote:
    was wondering if 0 is an even interger for a question like this:

    If n is an integer, is n even?
    (1) n2 -1 is an odd integer.
    (2) 3n + 4 is an even integer.
    Type of Question: Yes or No
    We need to find out whether n is even.

    ST 1: n^2 - 1 is odd. Therefore n^2 and 1 should have opposite parity. 1 is odd. hence n^2 should be even. n is even. Is n even? We have a definite YES! SUFFICIENT.

    ST 2: 3n + 4 is even. In this case too both the numbers should have the same parity. 4 is even. 3n should be even. 3 is odd. Hence n should be even. Is n even? We have a definite YES! SUFFICIENT.

    OA: D



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