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(n - 1) (n + 1) is divided by 24

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sanju09 GMAT Instructor
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(n - 1) (n + 1) is divided by 24 Post Fri Apr 10, 2009 6:06 am
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    If n is a positive integer and r is the remainder when (n - 1) (n + 1) is divided by 24, what is the value of r?

    (1) n is not divisible by 2.

    (2) n is not divisible by 3.




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    Nailya Rising GMAT Star
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    Post Fri Apr 10, 2009 10:30 am
    Try picking numbers

    1) n is not divisible by 2
    n=3 (3-1)(3+1)=8 8:24=0+8 r=8
    n=5 (5-1)(5+1)=24 24:24=1+0 r=0
    Two different values of r, this means that the condition is insufficient

    2) n is not divisible by 3
    n=2 (2-1)(2+1)=3 3:24=0+3 r=3
    n=5, as we know already r=0
    Two different values, means condition is insufficient

    1 and 2) n is not divisible by 2 and 3
    n=5 r=0
    n=7 (7-1)(7+1)=48 48:24=2 r=0
    n=11 (11-1)(11+1)= 120 120:24=5 r=0
    We can try other numbers and the result will yield to r=0, therefore answer is C.

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    Post Fri Apr 10, 2009 2:08 pm
    (n-1), n, (n+1) are consecutive numbers.

    24 = 3*(2^3)

    St 1: n is odd
    That means (n-1) and (n+1) are even
    48*50 when divided by 24 the remainder is 0
    26*28 when divided by 24 the remainder is not 0

    Insuff

    St 2: n is not divisible by 3
    which means either (n-1) or (n+1) is divisible by 3, because if there are 3 consecutive numbers then one of the numbers is divisible by 3.
    25*27 when divided by 24 the remainder is not 0
    24*26 when divided by 24 the remainder is 0

    Insuff

    Combining 1 and 2
    We know (n-1) and (n+1) are even and one of them is divisible by 3.
    36*38 when divided by 24 remainder is 0
    72*74 when divided by 24 remainder is 0

    Suff

    Answer is C.

    Thanked by: crazy4gmat

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    sanju09 GMAT Instructor
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    Post Sat Apr 11, 2009 3:16 am
    Nailya's nice; mals24's marvelous!!

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    Post Fri Jun 07, 2013 1:27 pm
    what is the remainder when 0/24 ?

    i thought it would be 0/24= quiotent 0 dividend 24 remainder 24

    if n=1 (not a multiple of 2 or 3 )

    (n-1)(n+1)=0

    0/24 = 0 R 24

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    Post Tue Jun 11, 2013 12:26 am
    J N wrote:
    what is the remainder when 0/24 ?

    i thought it would be 0/24= quiotent 0 dividend 24 remainder 24
    0 is divisible by every number.
    So, when 0 is divided by any number, the remainder is 0.

    Apart from that, when an integer M is divided by some integer N, then the resulting operation will be of the form M = qN + r, where q and r are also integers and M = dividend, N = divisor, q = quotient, and r = remainder. And r < q < M.

    In this case, 0 = 0*24 + 0
    As we are dividing 0 by 24, the resulting remainder cannot be greater than 0 - this should have been your clue that remainder cannot be 24.

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