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

Cheers,
Brent

vishugogo wrote:Brent if the 2 numbers x and y take values 6 and 30, then they also share a common factor 6 only.

In that case is statement 1 sufficient?

As far as statement 1 goes, it cannot be the case that x = 6 and y = 30, because we're told that x and y share only one common factor.
6 and 30 have four common factors. Notice that 1, 2, 3, and 6 are factors of both 6 and 30

So, for example, it could be the case that x = 7 and y = 30, because the only factor that they share is 1. (so 7 and 30 share only one common factor)
Likewise, it could be the case that x = 16 and y = 25, because the only factor that they share is 1. (so 16 and 25 share only one common factor)

I hope that helps.

Cheers,
Brent