JDesai01 wrote:
What is the greatest common divisor of positive integers m and n?
(1) m is a prime number
(2) 2n = 7m
Thought I'd post a full solution to this question.
Statement 1:
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 know nothing about n, statement 1 is not sufficient.
Statement 2:
If 2n = 7m then we can rearrange the equation to get n = (7/2)m
Important aside: 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. Similarly, if m=11, then n=77/2.
For n to be an integer, m must be even.
If m must be even, it could be the case that m=2 and n=7, in which case the GCD=1
Or it could be the case that m=4 and n=14, in which case the GCD=2
Or it could be the case that m=10 and n=35, in which case the GCD=5 . . . and so on.
Since we cannot determine the GCD with any 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 determine the GCD with certainty, statements 1 & 2 combined are sufficient, and the answer is
C
Cheers,
Brent
