What is the greatest common factor of positive integers x an

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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 is D

I don't understand how can[spoiler] S(1)[/spoiler] also be the answer. Suppose both x and y are multiples of 4 such as 12 and 20, the GCD of (4 *3, 4 *5) = 4
Another example both are consecutive integers such as 2 and 3, then GCD(2,3) = 1
Different values in both the examples.

Another thing, I have checked a lot of questions where they say GCD for 15, 10 is 5. From here we know that both are multiples of 5, and here they share only one factor. Am i correct ?

Thanks
Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Thu Sep 28, 2017 7:22 am
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
Target question: What is the greatest common factor of x and y?

Statement 1: x and y share only one common factor
All integers have 1 as a factor.
So, if x and y share only one common factor, then that common factor must be 1, in which case the greatest common factor of x and y is definitely 1
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x and y are unique prime numbers
If x is prime, the positive factors of x are 1 and x
If y is prime, the positive factors of y are 1 and y
If x does not equal y, then the greatest common factor of x and y must be 1
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

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by Brent@GMATPrepNow » Thu Sep 28, 2017 7:25 am
vinni.k wrote: I don't understand how can[spoiler] S(1)[/spoiler] also be the answer. Suppose both x and y are multiples of 4 such as 12 and 20, the GCD of (4 *3, 4 *5) = 4
Another example both are consecutive integers such as 2 and 3, then GCD(2,3) = 1
Different values in both the examples.

Another thing, I have checked a lot of questions where they say GCD for 15, 10 is 5. From here we know that both are multiples of 5, and here they share only one factor. Am i correct ?

Thanks
Your counterexample above (the numbers are 12 and 20) doesn't satisfy the condition that x and y share only one common factor
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 20: 1, 2, 4, 5, 10, 20
The COMMON factors are 1, 2 and 4, so they share MORE THAN ONE common factor.

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Brent
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by vinni.k » Thu Sep 28, 2017 9:51 am
So, here common factors are 1, 2, and 4, but the greatest common factor (GCD or GCF) is 4 ?

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by Brent@GMATPrepNow » Thu Sep 28, 2017 11:46 am
vinni.k wrote:So, here common factors are 1, 2, and 4, but the greatest common factor (GCD or GCF) is 4 ?
Yes, the GCD = 4
However, the values 12 and 20 share 3 common factors, and statement 1 says that x and y share only 1 common factor.
So, 12 and 20 do not meet the conditions described in statement 1.

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