Remainders

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singhmaharaj Senior | Next Rank: 100 Posts
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Remainders

Post Tue May 06, 2014 1:54 am
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  • Lap #[LAPCOUNT] ([LAPTIME])
    If r is the remainder when the positive integer n is divided by 7, what is the value of r?

    1) When n is divided by 21, the remainder is an odd number.

    2) When n is divided by 28, the remainder is 3

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    theCodeToGMAT Legendary Member
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    Post Tue May 06, 2014 2:03 am
    n/7 ==> Remainder is "r"

    Possible values 1,2,3,4,5,6

    TO find: "r"

    Statement 1:
    n/21 leave "R" ODD Number
    ODD Possible = 1,3,5
    INSUFFICIENT

    Statement 2:
    n/28 leaves remainder = 3
    Possible numbers = 31, 59, 87
    Then, r = 3, 3, 3 ..
    SUFFICIENT

    {B}

    _________________
    R A H U L

    Post Tue May 06, 2014 2:45 am
    singhmaharaj wrote:
    If r is the remainder when the positive integer n is divided by 7, what is the value of r?

    1) When n is divided by 21, the remainder is an odd number.
    2) When n is divided by 28, the remainder is 3
    We can use a variety of divisibility rules to solve this, or we can list possible values of n based on the statements. The rule for listing possible values of n is as follows:
    If, when N is divided by D, the remainder is R, then the possible values of N include: R, R+D, R+2D, R+3D,. . .

    Target question: What is the value of r?

    Statement 1: When n is divided by 21, the remainder is an odd number.
    There are several possible values of n that satisfy this condition. Here are two:
    Case a: n = 1 (since 1 divided by 21 leaves remainder 1, which is odd). Here, r = 1
    Case b: n = 3 (since 3 divided by 21 leaves remainder 3, which is odd). Here, r = 3
    Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

    Statement 2: When n is divided by 28, the remainder is 3
    Possible values of n: 3, 31, 59, 87, . . .
    We can see that for all possible values of n, the remainder is always 3 when n is divided by 7
    Since we can answer the target question with certainty, statement 2 is SUFFICIENT

    Answer = B

    Cheers,
    Brent

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