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Divisor = Factor?

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JDesai01 Just gettin' started! Default Avatar
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Divisor = Factor? Post Mon Jul 28, 2008 5:03 pm
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    Am I missing something when I conclude that a divisor is the same thing as a factor?

    eg
    What is the greatest common divisor of positive integers m and n?
    (1) m is a prime number
    (2) 2n = 7m

    I probably wasted 30 seconds trying to figure out what they meant by divisor. Aren't they just asking for the greatest common factor?

    BTW- answer is C (need both)

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    sauryk Just gettin' started! Default Avatar
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    Post Mon Jul 28, 2008 8:00 pm
    You are correct in assuming that divisor is the same as factor. Greatest Common Divisor (GCD) is same as greatest common factor (GCF) or highest common factor (HCF).

    artistocrat Really wants to Beat The GMAT! Default Avatar
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    Post Mon Sep 01, 2008 6:50 am
    The answer is C: If m is prime, the only way for 2n to be a factor of m is if m itself is 2, meaning n must be 7.

    Post Fri Aug 19, 2011 6:20 am
    JDesai01 wrote:
    What is the greatest common divisor of positive integers m and n?
    (1) m is a prime number
    (2) 2n = 7m

    Thought I'd post a full solution to this question.

    Statement 1:
    If m is a prime number, it has exactly 2 divisors (1 and m), so this tells us that the GCD of m and n must be either 1 or m.
    Since we know nothing about n, statement 1 is not sufficient.

    Statement 2:
    If 2n = 7m then we can rearrange the equation to get n = (7/2)m

    Important aside: Notice that if m were to equal an odd number, then n would not be an integer. For example, if m=3, then n=21/2. Similarly, if m=11, then n=77/2. For n to be an integer, m must be even.

    If m must be even, it could be the case that m=2 and n=7, in which case the GCD=1
    Or it could be the case that m=4 and n=14, in which case the GCD=2
    Or it could be the case that m=10 and n=35, in which case the GCD=5 . . . and so on.
    Since we cannot determine the GCD with any certainty, statement 2 is not sufficient.

    Statements 1 & 2 combined
    From statement 1, we know that m is prime, and from statement 2, we know that m is even.
    Since 2 is the only even prime number, we can conclude that m must equal 2.
    If m=2, then n must equal 7, which means that the GCD must be 1.
    Since we are able to determine the GCD with certainty, statements 1 & 2 combined are sufficient, and the answer is C

    Cheers,
    Brent

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