Data Sufficiency - 46

What is the greatest common divisor of positive integers a and b?

(1) a and b share exactly one common factor
(2) a and b are both prime numbers


Answer: A

From statement (1): we know that a and b have only one common factor, and we also know that all positive integers share the common factor 1 only, so we know it must be 1...hence sufficient

From Statement (2): we know that a and b are both prime, this implies the greatest common factor will have to be 1 or if a = b could be the same prime number then the GCF would be a (=b). ...hence insufficient

NOTE: You cannot assume that a and b are different integers if the question stem does not states the same