josh80 wrote:What is the greatest common divisor of positive integers m and n?
1) m is a prime number
2) 2n = 7m
Target question: What is the GCD of m and n?
Statement 1: m is a prime number
If m is a prime number, it has exactly 2 divisors (1 and m), so this tells us that the
GCD of m and n must be either 1 or m.
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT.
Statement 2: 2n = 7m
If 2n = 7m then we can rearrange the equation to get n = (7/2)m
IMPORTANT: Notice that if m were to equal an ODD number, then n would not be an integer. For example, if m = 3, then n = 21/2 (n is not an integer). Similarly, if m = 11, then n = 77/2 (n is not an integer). So, in order for n to be an INTEGER, m must be EVEN.
If m must be EVEN, there are several possible values for m and n. Consider these two cases:
case a: m = 2 and n = 7, in which case the
GCD = 1
case b: m = 4 and n = 14, in which case the
GCD=2
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT.
Statements 1 & 2 combined
From statement 1, we know that
m is prime, and from statement 2, we know that
m is even.
Since 2 is the only even prime number, we can conclude that m
must equal 2.
If m = 2, then n must equal 7, which means that
the GCD must be 1.
Since we are able to answer the
target question with certainty, statements 1 & 2 combined are sufficient, and the answer is
C
Cheers,
Brent
