Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: What is the greatest common divisor of the positive integers [#permalink]
02 Mar 2012, 11:20

3

This post received KUDOS

Expert's post

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

(1) m is a prime number --> if m=2=prime and n=1 then GCD(m,n)=1 but if m=2=prime and n=4 then GCD(m,n)=2. Two different answers, hence not sufficient.

(2) 2n=7m --> \frac{m}{n}=\frac{2}{7} --> m is a multiple of 2 and n is a multiple of 7, but this is still not sufficient: if m=2 and n=7 then GCD(m,n)=1 (as both are primes) but if m=4 and n=14 then GCD(m,n)=2 (basically as \frac{m}{n}=\frac{2x}{7x} then as 2 and 7 are primes then GCD(m, n)=x). Two different answers, hence not sufficient.

(1)+(2) Since from (1) m=prime and from (2) \frac{m}{n}=\frac{2}{7} then m=2=prime and n=7, hence GCD(m,n)=1. Sufficient.

1) no info about n (insuf) 2) n=7m/2. To make n an integer, m=2b (b is an pos integer). With b=1,2,3...we have varied GCD of m and n (insuf) Together we have m=2, n=7 GCD=1, suf

Re: What is the greatest common divisor of positive integers m [#permalink]
24 Sep 2012, 21:02

1) This statement says that M is Prime no, So N can be Prime/Composite. If N is Prime , clearly GCD will be 1, If N is composite also GCD will be 1( Except when M itself is a divisor of N, means N<>kM(not equals)), If N=kM then GCD(M,N) will be M it self.(where k is an integer)

2)2N=7M, its clearly not sufficient.

Combining:

From the statement 1, if we can get N=kM or not(where k is an integer) then we will be sure whats the GCD. As from the statement 2, we can see that N=7/2 M, and 7/2 is not an integer. So clearly GCD will be 1.

Re: What is the greatest common divisor of the positive integers [#permalink]
24 Sep 2013, 10:07

Bunuel wrote:

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

(1) m is a prime number --> if m=2=prime and n=1 then GCD(m,n)=1 but if m=2=prime and n=4 then GCD(m,n)=2. Two different answers, hence not sufficient.

(2) 2n=7m --> \frac{m}{n}=\frac{2}{7} --> m is a multiple of 2 and n is a multiple of 7, but this is still not sufficient: if m=2 and n=7 then GCD(m,n)=1 (as both are primes) but if m=4 and n=14 then GCD(m,n)=2 (basically as \frac{m}{n}=\frac{2x}{7x} then as 2 and 7 are primes then GCD(m, n)=x). Two different answers, hence not sufficient.

(1)+(2) Since from (1) m=prime and from (2) \frac{m}{n}=\frac{2}{7} then m=2=prime and n=7, hence GCD(m,n)=1. Sufficient.

Answer: C.

Greatest Common divisor and Highest common factor are same thing Bunuel?

Because n= 7m/2 (Taking both this is true only for m = 2) So Greatest common divisor is 2 not 1, Isn't it?
_________________

Re: What is the greatest common divisor of the positive integers [#permalink]
24 Sep 2013, 14:12

Expert's post

honchos wrote:

Bunuel wrote:

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

(1) m is a prime number --> if m=2=prime and n=1 then GCD(m,n)=1 but if m=2=prime and n=4 then GCD(m,n)=2. Two different answers, hence not sufficient.

(2) 2n=7m --> \frac{m}{n}=\frac{2}{7} --> m is a multiple of 2 and n is a multiple of 7, but this is still not sufficient: if m=2 and n=7 then GCD(m,n)=1 (as both are primes) but if m=4 and n=14 then GCD(m,n)=2 (basically as \frac{m}{n}=\frac{2x}{7x} then as 2 and 7 are primes then GCD(m, n)=x). Two different answers, hence not sufficient.

(1)+(2) Since from (1) m=prime and from (2) \frac{m}{n}=\frac{2}{7} then m=2=prime and n=7, hence GCD(m,n)=1. Sufficient.

Answer: C.

Greatest Common divisor and Highest common factor are same thing Bunuel?

Because n= 7m/2 (Taking both this is true only for m = 2) So Greatest common divisor is 2 not 1, Isn't it?

Yes, GCD and GCF are the same thing.

But couldn't understand your second point: the greatest common divisor of 2 and 7 is 1. How can it be 2? Is 7 divisible by 2?
_________________