## What is the greatest common factor of positive integers x and y?

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### What is the greatest common factor of positive integers x and y?

by BTGmoderatorDC » Tue May 30, 2023 12:17 am

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## Global Stats

What is the greatest common factor of positive integers x and y?

(1) The greatest common factor of x/2 and y/2 is 5.
(2) x and y are even.

OA A

Source: Princeton Review

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### Re: What is the greatest common factor of positive integers x and y?

by swerve » Tue May 30, 2023 12:04 pm

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## Global Stats

BTGmoderatorDC wrote:
Tue May 30, 2023 12:17 am
What is the greatest common factor of positive integers x and y?

(1) The greatest common factor of x/2 and y/2 is 5.
(2) x and y are even.

OA A

Source: Princeton Review
From 1:
Since, $$5$$ is the GCF of both $$x/2$$ and $$y/2 \Rightarrow 5$$ is also a common factor of $$x$$ and $$y$$
In addition, we can infer from above that $$2$$ is a common factor of $$x$$ and $$y$$.
Therefore, GCF of $$x$$ and y is $$5\cdot 2 = 10$$. Sufficient $$\Large{\color{green} \checkmark}$$

From 2:
$$2$$ is definitely a factor of $$x$$ and $$y$$ but we can have other factors such as $$4, 8$$ etc as GCF of $$x$$ and $$y$$. Not sufficient $$\Large{\color{red}\chi}$$

Therefore, A

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