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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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18 Oct 2010, 10:02
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Difficulty:

45% (medium)

Question Stats:

56% (01:15) correct 44% (00:54) wrong based on 88 sessions

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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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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 ?

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

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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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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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19 Oct 2010, 12:38
2
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 ?

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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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.

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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04 Aug 2019, 02:20
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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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