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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.

Re: What is the greatest common divisor of positive integers m [#permalink]

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04 Oct 2016, 08:58

1

This post received KUDOS

puchku wrote:

abhimahna wrote:

puchku wrote:

I marked B for this question.

My reasoning is - 2n = 7m Since 2 and 7 don't have any common factors other than 1, 'm' must be a multiple of 2 and 'n' a multiple of 7. So GCD(m,n) = m/2 = n/7

My doubt is, in such questions are we not allowed to deduce an answer in terms of variables 'm' and 'n'?

Try taking the values of m = 2,4,6 and as we know n = 7m/2, we can have n = 7,14,21, and so on.

When combined with Statement 1, we can say m could be only 2. Thus n could be only 7. Hence, HCF= 1.

But even without considering Statement 1, on the basis of Statement 2 we can say that GCM(m.n) will be m/2

For example m=2 => n=7 => GCD(2,7) = m/2 = 1 m=4 => n=14 => GCD(4,14) = m/2 = 2

Now, even though the actual values are different here, can't we assume that we know the values of 'm' and 'n' (since we want to find their GCD), and thus, in turn, we know the value of GCD which is m/2

But since this is an official question and the answer is C, I am guessing that in DS questions, we have to be able to determine exact values and not such relations

Highlighted line above is the rule for DS questions. We should have a definite answer to arrive at any conclusion.
_________________

Re: What is the greatest common divisor of positive integers m [#permalink]

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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]

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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?
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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?
_________________

Re: What is the greatest common divisor of positive integers m [#permalink]

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03 Oct 2016, 08:19

I marked B for this question.

My reasoning is - 2n = 7m Since 2 and 7 don't have any common factors other than 1, 'm' must be a multiple of 2 and 'n' a multiple of 7. So GCD(m,n) = m/2 = n/7

My doubt is, in such questions are we not allowed to deduce an answer in terms of variables 'm' and 'n'?

Re: What is the greatest common divisor of positive integers m [#permalink]

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03 Oct 2016, 08:52

puchku wrote:

I marked B for this question.

My reasoning is - 2n = 7m Since 2 and 7 don't have any common factors other than 1, 'm' must be a multiple of 2 and 'n' a multiple of 7. So GCD(m,n) = m/2 = n/7

My doubt is, in such questions are we not allowed to deduce an answer in terms of variables 'm' and 'n'?

Try taking the values of m = 2,4,6 and as we know n = 7m/2, we can have n = 7,14,21, and so on.

When combined with Statement 1, we can say m could be only 2. Thus n could be only 7. Hence, HCF= 1.
_________________

Re: What is the greatest common divisor of positive integers m [#permalink]

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03 Oct 2016, 11:14

abhimahna wrote:

puchku wrote:

I marked B for this question.

My reasoning is - 2n = 7m Since 2 and 7 don't have any common factors other than 1, 'm' must be a multiple of 2 and 'n' a multiple of 7. So GCD(m,n) = m/2 = n/7

My doubt is, in such questions are we not allowed to deduce an answer in terms of variables 'm' and 'n'?

Try taking the values of m = 2,4,6 and as we know n = 7m/2, we can have n = 7,14,21, and so on.

When combined with Statement 1, we can say m could be only 2. Thus n could be only 7. Hence, HCF= 1.

But even without considering Statement 1, on the basis of Statement 2 we can say that GCM(m.n) will be m/2

For example m=2 => n=7 => GCD(2,7) = m/2 = 1 m=4 => n=14 => GCD(4,14) = m/2 = 2

Now, even though the actual values are different here, can't we assume that we know the values of 'm' and 'n' (since we want to find their GCD), and thus, in turn, we know the value of GCD which is m/2

But since this is an official question and the answer is C, I am guessing that in DS questions, we have to be able to determine exact values and not such relations

Re: What is the greatest common divisor of positive integers m [#permalink]

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26 Jan 2017, 11:07

(1) No info about n but we could test below values as well that will make this statement insufficient.

if m = 3 (which is prime) and n = 6, then the gcf is 3. if m = 3 (which is prime) and n = 5, then the gcf is 1. insufficient.

(2)In the case of this statement, you can divide by 2m on both sides, to give n/m = 7/2. (you could also divide by 7n, to give m/n = 2/7.)

so, the ratio of n to m is 7:2. if they're actually 7 and 2, the gcf is 1. if they're multiples of these numbers, then the gcf is not 1. (for instance, if they're 14 and 4, the gcf is 2.) insufficient.

--

(together) if you need a prime, and the ratio is 7 to 2, then the numbers must actually be 7 and 2. sufficient.
_________________

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

(1) m is a prime number (2) 2n=7m

We need to determine the greatest common divisor, or the greatest common factor (GCF), of integers m and n.

Statement One Alone:

m is a prime number.

Since we don’t know anything about n, statement one is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

2n = 7m

We can manipulate the equation 2n = 7m:

n = 7m/2

n/m = 7/2

Even with the equation rewritten, we see that there are many options for m and n, and thus there are many different GCFs for m and n. For instance, if n = 7 and m = 2, then the GCF is 1. However, if n = 14 and m = 4, then the GCF is 2. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

Using statements one and two, we know that m is prime and that n/m = 7/2. Therefore, m must equal 2 and n must equal 7. When m is 2 and n is 7, the GCF is 1.

Answer: C
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