## What is the greatest common divisor of positive integers $$m$$ and $$n?$$

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### What is the greatest common divisor of positive integers $$m$$ and $$n?$$

by VJesus12 » Thu Apr 08, 2021 12:14 pm

00:00

A

B

C

D

E

## Global Stats

What is the greatest common divisor of positive integers $$m$$ and $$n?$$

(1) $$m$$ is a prime number
(2) $$2n = 7m$$

Source: GMAT Prep

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### Re: What is the greatest common divisor of positive integers $$m$$ and $$n?$$

by [email protected] » Sat Apr 10, 2021 6:01 am

00:00

A

B

C

D

E

## Global Stats

VJesus12 wrote:
Thu Apr 08, 2021 12:14 pm
What is the greatest common divisor of positive integers $$m$$ and $$n?$$

(1) $$m$$ is a prime number
(2) $$2n = 7m$$

Source: GMAT Prep
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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