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If x and y are positive integers, and 1 is the greatest common divisor

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If x and y are positive integers, and 1 is the greatest common divisor  [#permalink]

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New post 18 Oct 2010, 10:02
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If x and y are positive integers, and 1 is the greatest common divisor of x and y, what is the greatest common divisor of 2x and 3y?

A. 1
B. Cannot be determined
C. 2
D. 5
E. 6

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Re: If x and y are positive integers, and 1 is the greatest common divisor  [#permalink]

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New post 18 Oct 2010, 10:12
shrive555 wrote:
If x and y are positive integers, and 1 is the greatest common divisor of x and y, what is the greatest common divisor of 2x and 3y ?

:x


According to me it should be 1.

As x and y dont have any other common divisor rather than 1.So 2x and 3y will also have only one common divisor i.e 1.( As 2 and 3 also dont have any common divisor except 1)


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Re: If x and y are positive integers, and 1 is the greatest common divisor  [#permalink]

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New post 18 Oct 2010, 10:30
isn;t the value of 2x and 3y depend on the value of x and y. changing the values of x and y will change the GCD ?
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Re: If x and y are positive integers, and 1 is the greatest common divisor  [#permalink]

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New post 18 Oct 2010, 10:48
shrive555 wrote:
isn;t the value of 2x and 3y depend on the value of x and y. changing the values of x and y will change the GCD ?



If x and y are positive integers, and 1 is the greatest common divisor of x and y.Hence whatever value we will take for x and y, their common divisor should be one only and it doesnt make any difference after that.
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Re: If x and y are positive integers, and 1 is the greatest common divisor  [#permalink]

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New post 19 Oct 2010, 12:38
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ankitranjan wrote:
shrive555 wrote:
If x and y are positive integers, and 1 is the greatest common divisor of x and y, what is the greatest common divisor of 2x and 3y ?

:x


According to me it should be 1.

As x and y dont have any other common divisor rather than 1.So 2x and 3y will also have only one common divisor i.e 1.( As 2 and 3 also dont have any common divisor except 1)


Consider KUDOS if it helped u in some way.


That's not correct.

Given: \(x\) and \(y\) are co-prime - do not share any common factor but 1.

If \(x=1\) (or any other non multiple of 3) and \(y=1\) (or any other non multiple of 2) then \(GCD(2x,3y)=GCD(2,3)=1\);
If \(x=1\) (or any other non multiple of 3) and \(y=2\) (or any other multiple of 2) then \(GCD(2x,3y)=GCD(2,6)=2\);
If \(x=3\) (or any other multiple of 3) and \(y=1\) (or any other non multiple of 2) then \(GCD(2x,3y)=GCD(6,3)=3\);
If \(x=3\) (or any other multiple of 3) and \(y=2\) (or any other multiple of 2) then \(GCD(2x,3y)=GCD(6,6)=6\).

Hope it helps.
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Re: If x and y are positive integers, and 1 is the greatest common divisor  [#permalink]

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New post 01 Apr 2015, 03:46
shrive555 wrote:
If x and y are positive integers, and 1 is the greatest common divisor of x and y, what is the greatest common divisor of 2x and 3y?

A. 1
B. Cannot be determined
C. 2
D. 5
E. 6



My explanation: from question stem we know that nothing is common between X and Y , X and Y are two prime numbers eg: X=2, Y=3 and their GCD(2,3) =1 and so 2X and 3Y will have a GCD(2X,3Y) = 1 . what if either X or Y was 1, eg: X=1,Y=4 then GCD(1,4) =1 , but GCD(2,12) = 2.
and hence answer B

btw, i posted the same question but some goof up happened while posting it .
i have deleted my post now.
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Re: If x and y are positive integers, and 1 is the greatest common divisor  [#permalink]

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New post 04 Aug 2019, 02:20
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Re: If x and y are positive integers, and 1 is the greatest common divisor   [#permalink] 04 Aug 2019, 02:20
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