LUANDATO wrote:If the greatest common factor of positive integers A and B is 20, what is the value of A - B?

(1) The least common multiple of A and B is 400.
(2) A = 80

Target question: What is the value of A - B?

Given: The greatest common factor of positive integers A and B is 20

Statement 1: The least common multiple of A and B is 400
USEFUL RULE: (greatest common factor x and y)(least common multiple of x and y) = xy
So, (greatest common factor A and B)(least common multiple of A and B) = AB
Replace values to get: (20)(400) = AB
In other words, AB = 8000
Is knowing the value of AB enough to determine the value of A - B?
No.
There are several values of A and B that satisfy statement 1 (and the given information). Here are two:
Case a: A = 20 and B = 400, in which case A - B = 20 - 400 = -380
Case b: A = 400 and B = 20, in which case A - B = 400 - 20 = 380
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: A = 80
There's no information about B, so statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that AB = 8000
Statement 2 tells us that A = 80
This means that B = 100
So, A - B = 80 - 100 = -20
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent