gmat_guy666 wrote:What is the gcd of a, b, and c
(1) gcd(a, b) = 3
(2) gcd(b, c) = 4
Just to be clear, the test-makers would never assume that test-takers are aware of the notation in this question. An official GMAT question would probably look more like this:
If a, b and c are positive integers, what is the greatest common divisor of a, b and c?
1) The greatest common divisor of a and b is 3
2) The greatest common divisor of b and c is 4
For this question, I'll apply the following concept:
If N is the greatest common divisor of a and b, then a and b also have all factors of N in common.
Target question: What is the greatest common divisor of a, b and c?
Statement 1: The greatest common divisor of a and b is 3
No information about c, so statement 1 is NOT SUFFICIENT
Statement 2: The greatest common divisor of b and c is 4
No information about a, so statement 2 is NOT SUFFICIENT:
Statements 1 and 2 combined
Statement 1: Applying the
green rule above, a and b have the following divisors in common:
1 and
3.
Statement 2: Applying the
green rule above, b and c have the following divisors in common:
1,
2 and
4.
We're looking for a divisor in common with a, b AND c. The only factor they
all share is
1.
So,
the greatest common divisor of a, b and c is 1.
Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer =
C
Cheers,
Brent
