What is the greatest common divisor of a, b, and 3a+23b?
1). a=4
2). The greatest common divisor of a, b, and 23a+3b is 4
1). a=4
2). The greatest common divisor of a, b, and 23a+3b is 4
What is the gcd of a, b, and 3a+23b?
1) a=4. plug this in to get 4, b, 12+23b; If b=1, the gcd(4,1,35)=1. If b=4, the gcd(4,4,12+23(4))=4. INSUFFICIENT.
2) The greatest common divisor of a, b, and 23a+3b is 4. This implies that gcd(a,b)=4. If there were some divisor greater than 4, that a and b had in common, then it would also divide 23a+3b. But this would contradict the fact that gcd(a,b,23a+3b)=4. Hence, gcd(a,b)=4.
Back to the original question, the fact that gcd(a,b)=4 implies that 4 is a common divisor of a, b, and 3a+23b. But it also must be the GREATEST common divisor of a, b, 3a+23b, because if there were some common divisor greater than 4, it would contradict the fact that gcd(a,b)=4. SUFFICIENT
Ans: B
