What is the greatest common divisor of positive integers...

[cschmidlapp]

What is the greatest common divisor of positive integers m and n?

1) m is a prime number

2) 2n=7m


Answer is C.

1) insufficient - says nothing about n

2) can simplify to m/n = 2/7, but because numbers are in this ratio, can't determine greatest common divisor because it could be any multiple of both 2 and 7 [is this the right reasoning?]

C - both statements together - if m is prime, than m must be 2, and GCD is 1?

Can someone help me confirm or correct the reasoning here?

Thanks

[RonPurewal]

This approach is pretty much perfect.

As for this:

2) can simplify to m/n = 2/7, but because numbers are in this ratio, can't determine greatest common divisor because it could be any multiple of both 2 and 7 [is this the right reasoning?]

On just about any DS number-properties problem, if you are not 100.000000% absolutely sure of what's going on, START TESTING SPECIFIC NUMBERS.

So, yeah, m:n is 2:7. So just pick some numbers in that ratio, throw them at the problem, and watch what falls out.

If m = 2 and n = 7, then the greatest common factor is 1.
If m = 4 and n = 14, then the greatest common factor is 2. Which is not 1.
DONE
TWO DIFFERENT ANSWERS
NOT SUFFICIENT

That wasn't very hard.

Remember -- if you are 99.999% sure, that's still not 100% sure. Test numbers.

C - both statements together - if m is prime, than m must be 2, and GCD is 1?

Yes.

[jnelson0612]

.