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?

(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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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