What is the gcd of a, b, and c

[gmat_guy666]

What is the gcd of a, b, and c

(1) gcd(a, b) = 3
(2) gcd(b, c) = 4

OAc

[GMATinsight]

What is the gcd of a, b, and c

(1) gcd(a, b) = 3
(2) gcd(b, c) = 4

OAc

Question : GCD of (a, b, and c) = ?

Statement 1) GCD (a, b) = 3
Information about c is absent therefore
INSUFFICIENT

Statement 2) GCD (b, c) = 4
Information about a is absent therefore
INSUFFICIENT

Combining the Two statements
GCD (b, c) = 4 i.e. there is NO common factor between b and c except 4
i.e. if b = 4x then c = 4y where x and y DO NOT share any common factor other than 1

AND
GCD (a, b) = 3 i.e. there is NO common factor between a and b except 3
i.e. if a = 3z then b = 3w where z and w DO NOT share any common factor other than 1

i.e. b = multiple of 12
and a = odd multiple of 3
and c = multiple of 4 BUT NOT MULTIPLE OF 3

Therefore, GCD of (a,b,c) = 1
SUFFICIENT

Answer: Option C

[theCodeToGMAT]

To find GCD (A,B,C)

Statement 1:
GCD (A,B) = 3
A = 3 x _
B = 3 x _
We cannot deduce anything
INSUFFICIENT

Statement 2:
GCD (B,C) = 4
B = 4 x _
C = 4 x _
We cannot deduce anything
INSUFFICIENT

Combining...
A = 3 x _
B = 3 x 4 x _
C = 4 x _
GCD = 1
SUFFICIENT

{C}

[GMATinsight]

What is the gcd of a, b, and c

(1) gcd(a, b) = 3
(2) gcd(b, c) = 4

OAc

ALTERNATE METHOD :

Question : GCD of (a, b, and c) = ?

Statement 1) GCD (a, b) = 3
Information about c is absent therefore
INSUFFICIENT

Statement 2) GCD (b, c) = 4
Information about a is absent therefore
INSUFFICIENT

Combining the Two statements
If a = 3 then b = 12 (To satisfy statement 1 and 2 both) and c = 4

Therefore, GCD of (a,b,c) = 1
SUFFICIENT

Answer: Option C

[Brent@GMATPrepNow]

Combining the Two statements
GCD (b, c) = 4 i.e. there is NO common factor between b and c except 4
i.e. if b = 4x then c = 4y where x and y DO NOT share any common factor other than 1

Since there's a risk of leading students astray with the above statement in green, I'd like to point out that, if the Greatest Common Divisor (GCD) of b and c is 4, then there are two other divisors (factors) that b and c could have in common. They could also share a common factor of 2 and, of course, share a common factor of 1.
For example, if b = 4 and c = 12, then b and c have 1, 2 and 4 as common factors (of which, 4 is the greatest)

Cheers,
Brent

[Brent@GMATPrepNow]

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