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Good question. Stmt 1 points that the common factor is 1 hence (1) is sufficient. Stmt 2 is also sufficient since two primes have 1 as the only common factor. D is the answer.
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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.

Below is my solution. Struggling to understand the official answer. Can someone please help?

Considering statement 1 : If X = 6 and Y = 9 then X = 2*3 and Y = 3 *3 and the GCF is 3 which is the common factor shared by both X and Y and of X = 4 and Y = 12 then X = 2^2 and Y = 2^2 * 3. Therefore the GCF is 4. Therefore this statement should be insufficient.

Considering statement 2 : If X = 2 and Y = 3, the GCF is 1 as this is the common factor shared by both.

Hence, I went for B, which is not the case.

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

(1) x and y share only one common factor --> every integer has 1 as a factor, thus since x and y share only one common factor it must be 1. Sufficient.

(2) x and y are unique prime numbers. Two different primes can have only 1 as common factor. Sufficient.

Answer: D.

Hope it's clear.



(BUT) cant the two integers that is x and y be same??
thats y it should be C and not D
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enigma123
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.

Below is my solution. Struggling to understand the official answer. Can someone please help?

Considering statement 1 : If X = 6 and Y = 9 then X = 2*3 and Y = 3 *3 and the GCF is 3 which is the common factor shared by both X and Y and of X = 4 and Y = 12 then X = 2^2 and Y = 2^2 * 3. Therefore the GCF is 4. Therefore this statement should be insufficient.

Considering statement 2 : If X = 2 and Y = 3, the GCF is 1 as this is the common factor shared by both.

Hence, I went for B, which is not the case.

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

(1) x and y share only one common factor --> every integer has 1 as a factor, thus since x and y share only one common factor it must be 1. Sufficient.

(2) x and y are unique prime numbers. Two different primes can have only 1 as common factor. Sufficient.

Answer: D.

Hope it's clear.



(BUT) cant the two integers that is x and y be same??
thats y it should be C and not D

For (2) we are given that x and y are distinct: x and y are unique prime numbers.

As for (1): if x and y are the same number, say 3, then they would share all their factors 1 and 3, not just one.

The OA is correct.
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enigma123
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.

Below is my solution. Struggling to understand the official answer. Can someone please help?

Considering statement 1 : If X = 6 and Y = 9 then X = 2*3 and Y = 3 *3 and the GCF is 3 which is the common factor shared by both X and Y and of X = 4 and Y = 12 then X = 2^2 and Y = 2^2 * 3. Therefore the GCF is 4. Therefore this statement should be insufficient.

Considering statement 2 : If X = 2 and Y = 3, the GCF is 1 as this is the common factor shared by both.

Hence, I went for B, which is not the case.



1. one is the factor for all the values. since both has only one common factor then it should be one. hence suff.

2. two rpime number shares only one as a common factor. hence suff.

Hence answer D.
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we are not asked to find X and Y, just GCF

St1. Share only one factor means that X and Y are coprime. No matter what number they are (5,6 or 2,3) GCF=1.Suff

St2. X and Y unique primes means again that hey are coprime, so GCF=1.Suff

D
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