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What is the greatest common divisor of positive integers m

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Re: What is the greatest common divisor of positive integers m  [#permalink]

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New post 22 Dec 2017, 10:54
Top Contributor
lahoosaher 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

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Brent
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Re: What is the greatest common divisor of positive integers m  [#permalink]

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New post 21 Oct 2018, 01:08
(1) m is primer. Insuff
(2) m/n=7/2. m is multiple of 7, n is multiple of 2. GCD=1 but if, 24 and 4 than GCD=4. Insuff

(1)(2) m is prime and m is multiple of 7 So, m is 7
if m is 7, then n is 2
GCD=1
GMAT Club Bot
Re: What is the greatest common divisor of positive integers m &nbs [#permalink] 21 Oct 2018, 01:08

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