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

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

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

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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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swerve: Legendary Member; Posts: 2535; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

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

by swerve » Tue May 30, 2023 12:04 pm

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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