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Which is the divisor of n?

This topic has 2 expert replies and 1 member reply
Which is the divisor of n? Post Thu Dec 25, 2014 12:51 pm
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    When the positive integer n is divided by 45, the remainder is 18. Which of the following must be a divisor of n?

    A) 11

    B) 9

    C) 7

    D) 6

    E) 4

    Is there a formula of some sort to solve this problem? Any help is appreciated.

    Thanks,

    -Andy

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    Post Thu Dec 25, 2014 1:04 pm
    AndrewRivera7793 wrote:
    When the positive integer n is divided by 45, the remainder is 18. Which of the following must be a divisor of n?

    A) 11

    B) 9

    C) 7

    D) 6

    E) 4

    Is there a formula of some sort to solve this problem? Any help is appreciated.

    Thanks,

    -Andy
    When the positive integer n is divided by 45, the remainder is 18.
    In other words, n is multiple of 45 plus 18:
    n = 45a + 18, where a is a nonnegative integer.

    Simplifying n = 45a + 18, we get:
    n = 45a + 18 = 9(5a + 2).
    Thus, n must be a multiple of 9.

    The correct answer is B.

    We can also TEST options for n.

    If a=0, then n = 45a + 18 = 45*0 + 18 = 18.
    Since 18 is not a multiple of 11, 7, or 4, eliminate A, C and E.
    If a=1, then n = 45a + 18 = 45*1 + 18 = 63.
    Since 63 is a not multiple of 6, eliminate D.

    The correct answer is B.

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    Last edited by GMATGuruNY on Thu Dec 25, 2014 1:08 pm; edited 1 time in total

    Thanked by: AndrewRivera7793
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    Post Thu Dec 25, 2014 1:05 pm
    AndrewRivera7793 wrote:
    When the positive integer n is divided by 45, the remainder is 18. Which of the following must be a divisor of n?

    A) 11
    B) 9
    C) 7
    D) 6
    E) 4

    When it comes to remainders, we have a nice rule that says:

    If N divided by D, leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
    For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

    Here, we are told that n divided by 45 leaves a remainder of 18, so the possible values of n are: 18, 63, 108,... etc.

    IMPORTANT: the question asks, "Which of the following must be a divisor of n?
    So, let's test the smallest possible value of n, which is 18, and check the answer choices.

    18 is NOT divisible by 11, 7 or 4, so we can ELIMINATE A, C and E.
    So, the correct answer is either B or D

    Now test the next possible value of n, which is 63.
    63 is NOT divisible by 6, so we can ELIMINATE D

    So, by the process of elimination, the correct answer is B

    Cheers,
    Brent

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    Thanked by: AndrewRivera7793
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    Post Thu Dec 25, 2014 1:12 pm
    Wow, Thank you both for the excellent methods to solve this problem! I've "Thanked" you both. Merry Xmas Smile

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