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Divisibility by 3

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knight247 GMAT Destroyer!
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Divisibility by 3 Post Tue Feb 14, 2012 9:54 am
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  • Lap #[LAPCOUNT] ([LAPTIME])
    If n is a positive integer, is n-1 divisible by 3?
    (1)n²+n is not divisible by 6
    (2)3n=k+3, where k is a positive multiple of 3

    The OA is A

    Here is where I have a problem with the OA.
    If n=1 then n²+n=2 which isn't divisible by 6. So n=1 is a valid case. But n-1 would equal zero which obviously isn't divisible by 3. All the other values like n=4, n=7 ETC seem to meet the requirement. But n=1 clearly proves the insufficiency of (1). Hoping to get a clear explanation.

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    rijul007 GMAT Destroyer!
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    Post Tue Feb 14, 2012 10:23 am
    knight247 wrote:
    If n is a positive integer, is n-1 divisible by 3?
    (1)n²+n is not divisible by 6
    (2)3n=k+3, where k is a positive multiple of 3

    The OA is A

    Here is where I have a problem with the OA.
    If n=1 then n²+n=2 which isn't divisible by 6. So n=1 is a valid case. But n-1 would equal zero which obviously isn't divisible by 3. All the other values like n=4, n=7 ETC seem to meet the requirement. But n=1 clearly proves the insufficiency of (1). Hoping to get a clear explanation.
    Actually Zero is divisible by 3.

    When N divided by X gives a remainder 0, we say N is divisible by X.

    Similarly 0 divided by 3 would give us a remainder 0. Hence, 0 is divisible by 3.

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    Brent@GMATPrepNow GMAT Instructor
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    Post Tue Feb 14, 2012 10:26 am
    knight247 wrote:
    If n is a positive integer, is n-1 divisible by 3?
    (1)n²+n is not divisible by 6
    (2)3n=k+3, where k is a positive multiple of 3

    The OA is A

    Here is where I have a problem with the OA.
    If n=1 then n²+n=2 which isn't divisible by 6. So n=1 is a valid case. But n-1 would equal zero which obviously isn't divisible by 3. All the other values like n=4, n=7 ETC seem to meet the requirement. But n=1 clearly proves the insufficiency of (1). Hoping to get a clear explanation.
    Yes, zero is definitely divisible by 3.

    Here's my solution.


    Target question: Is n-1 divisible by 3?

    Statement 1: n²+n is not divisible by 6
    This statement is testing two things.
    First, there's are great rule that says: If we have n consecutive integers, then one of those integers must be divisible by n.
    So, for example, if we have 5 consecutive integers, one of those numbers will be divisible by 5.
    Second, it's testing our ability to see that n^2 + n = n(n+1), and that n and n+1 are two consecutive integers.

    Now, for n(n+1)to be divisible by 6, it would have to be divisible by 2 and by 3
    Since n and n+1 are two consecutive integers, then one must be divisible by 2, so n(n+1)is definitely divisible by 2.
    However, we are told that n(n+1)is not divisible by 6, which means that neither n nor n+1 is divisible by 3.

    Now recognize that n-1, n and n+1 are three consecutive integers. Since we now know that neither n nor n+1 is divisible by 3, it must be true that n-1 is divisible by 3.
    So statement 1 is SUFFICIENT

    Statement 2: 3n=k+3, where k is a positive multiple of 3
    Let's plug in some numbers here.
    case a: k=3, which means n=2, which means n-1 is not divisible by 3
    case b: k=9, which means n=4, which means n-1 is divisible by 3
    So statement 2 is INSUFFICIENT

    The answer is A

    Cheers,
    Brent

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    LalaB GMAT Destroyer!
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    Post Tue Feb 14, 2012 10:37 am
    I didnt get u .why 0 cant be divisible by 3? 0/3=0



    If n is a positive integer, is n-1 divisible by 3?
    (1)n²+n is not divisible by 6
    (2)3n=k+3, where k is a positive multiple of 3


    stmt 1 - n²+n =n(n+1) <--consecutive numbers . so we have 3 consecutive numbers (n-1 ) n (n+1)

    cases-
    0 1 2
    3 4 5
    6 7 8

    smtnt2 -
    3n=k+3
    3n-3=k
    n-1=k/3

    k is divisible by 3. let k =3 then n-1=1 not divisible by 3
    let k =9 then n-1=3 divisible by 3. so insuff

    oops, I am late Smile . the q. is answered already

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