[email protected] wrote:What is the greatest common factor of x and y

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

NOTE: This question needs to restrict the factors to POSITIVE factors only. If we allow for negative factors, we get a problems since all integers have 1 and -1 as factors. This would make statement 1 impossible.

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

[email protected] wrote:What is the greatest common factor of x and y

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


If we plug in then for example x=6 and y = 4 the common factor is 2
But if x is 5 and y is 7 then common factor 1 just 1; hence a is not sufficient

The values x = 6 and y = 4 do not satisfy the conditions in statement 1. In this case, x and y share TWO common factors (1 and 2), and the statement says that x and y share ONLY ONE common factor.

Cheers,
Brent