BTGmoderatorDC wrote:If n is an integer, what is the greatest common divisor of 12 and n ?

(1) The product of 12 and n is 432.
(2) The greatest common divisor of 24 and n is 12.

Statement 1:
12n = 432.
Since we can solve for n, the GCF of 12 and n can be determined.
SUFFICIENT.

Statement 2:
24 = 2*2*2*3.
Since the GCF of n and 24 is the blue product (12) without the red factor (2), n must be a multiple of 12 that does NOT include an additional factor of 2.
In other words:
n = 12a, where a is an ODD positive integer.
Options for n:
12*1, 12*3, 12*5, 12*7, 12*9...
In every case, the GCF of n and 12 is the value in green (12).
SUFFICIENT.

The correct answer is D.

BTGmoderatorDC wrote:If n is an integer, what is the greatest common divisor of 12 and n ?

(1) The product of 12 and n is 432.
(2) The greatest common divisor of 24 and n is 12.

We need to determine the greatest common divisor or the greatest common factor (GCF) of 12 and n. If we can determine the value of n, then we can determine the GCF of 12 and n.

Statement One Alone:

The product of 12 and n is 432

Since 12n = 432, n = 432/12 = 36. So the GCF of 12 and 36 is 12.

Statement one alone is sufficient.

Statement Two Alone:

The greatest common divisor of 24 and n is 12.

Since the GCF of 24 and n is 12, that means n itself is a multiple of 12. Therefore, the GCF of 12 and n must be also 12.

Statement two is sufficient.

Answer: D