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Greatest Common Divisor

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josh80 Senior | Next Rank: 100 Posts Default Avatar
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Greatest Common Divisor

Post Wed Dec 11, 2013 4:26 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    What is the greatest common divisor of positive integers m and n?

    1) m is a prime number

    2) 2n = 7m

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    Post Wed Dec 11, 2013 4:35 pm
    josh80 wrote:
    What is the greatest common divisor of positive integers m and n?

    1) m is a prime number
    2) 2n = 7m
    Target question: What is the GCD of m and n?

    Statement 1: m is a prime number
    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 cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT.

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

    IMPORTANT: 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 (n is not an integer). Similarly, if m = 11, then n = 77/2 (n is not an integer). So, in order for n to be an INTEGER, m must be EVEN.

    If m must be EVEN, there are several possible values for m and n. Consider these two cases:
    case a: m = 2 and n = 7, in which case the GCD = 1
    case b: m = 4 and n = 14, in which case the GCD=2
    Since we cannot answer the target question with 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 answer the target question with certainty, statements 1 & 2 combined are sufficient, and the answer is C

    Cheers,
    Brent

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