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If x and y are positive integers, and 1 is the gre

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COolguy101
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If x and y are positive integers, and 1 is the gre [#permalink] New post   26 Jun 2021, 03:39
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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. 2

C. 5

D. 6

E. Cannot be determined
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E
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sagortm
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If x and y are positive integers, and 1 is the gre [#permalink] New post   26 Jun 2021, 17:29
Answer will be E

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COolguy101
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Re: If x and y are positive integers, and 1 is the gre [#permalink] New post   26 Jun 2021, 18:36
sagortm wrote:
Answer will be E

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Hi, Instead posting answer choice only, please post a detailed solution. This will help the forum!
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Re: If x and y are positive integers, and 1 is the gre [#permalink] New post   26 Jun 2021, 23:02
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kumarneupane4344 wrote:
sagortm wrote:
Answer will be E

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Hi, Instead posting answer choice only, please post a detailed solution. This will help the forum!


Sure....
Explanation:
As x & y are the co-prime.

Case 01: x = 1 and y = 1.
Here, 2(x) = 2, and 3(y) = 3
So, the greatest common divisor(GCD)=1

Case 02: x = 1 and y = 2.
Here, 2x = 2, and 3y = 6
So, the GCD=2

Case 03: x = 3 and y = 2.
Here, 2x = 6, and 3y = 6
So, the GCD=6

Case 04: x = 3 and y = 4.
Here, 2x = 6, and 3y = 12
So, the GCD=6

That means GCD is different with different value of x & y.

So the Answer is not fixed; that means "Can not be determined: E"
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If x and y are positive integers, and 1 is the gre [#permalink] New post   30 Oct 2021, 08:43
COolguy101 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. 2
C. 5
D. 6
E. Cannot be determined


Let's test some pairs of values....

case i: x = 1 and y = 1 have a greatest common divisor of 1
Here, 2x = 2(1) = 2, and 3y = 3(1) = 3
So, the greatest common divisor of 2x (2) and 3y (3) is 1

case ii: x = 1 and y = 2 have a greatest common divisor of 1
Here, 2x = 2(1) = 2, and 3y = 3(2) = 6
So, the greatest common divisor of 2x (2) and 3y (6) is 2

Answer: E
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Re: If x and y are positive integers, and 1 is the gre [#permalink] New post   03 Jun 2024, 06:28
You can play around with giving y a 3 or x a 2 in order to get different combinations of shared factors for 2x and 3y, so we don't know:

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Re: If x and y are positive integers, and 1 is the gre [#permalink]
03 Jun 2024, 06:28
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