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

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by BTGmoderatorDC » Mon Jun 08, 2020 6:44 pm

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A

B

C

D

E

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

(1) x and y share only one common factor.
(2) x and y are unique prime numbers.


OA D

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

by Jay@ManhattanReview » Mon Jun 08, 2020 10:14 pm
BTGmoderatorDC wrote: ↑
Mon Jun 08, 2020 6:44 pm
 What is the greatest common factor of positive integers x and y?

(1) x and y share only one common factor.
(2) x and y are unique prime numbers.

OA D

Source: Veritas Prep
Let's take each statement one by one.

(1) x and y share only one common factor.

Note that all positive integers have 1 as a common factor. Since x and y share ONLY one common factor, they must be co-prime to each other. So, the greatest common factor of positive integers x and y = 1. Sufficient.

(2) x and y are unique prime numbers.

=> x and y are co-prime to each other. So, the greatest common factor of positive integers x and y = 1. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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