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

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

by Gmat_mission » Sat Mar 17, 2018 8:54 am
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

[spoiler]OA=B[/spoiler].

Since the greatest common divisor or 2 and 3 is 1, it shouldn't be A the answer? I got confused. Experts, I'd appreciate your help here. Thanks.

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by Brent@GMATPrepNow » Sat Mar 17, 2018 4:49 pm
Gmat_mission 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
Consider these two cases.

case 1: x = 3 and y = 2. This satisfies the condition that 1 is the greatest common divisor of x and y
In this case 2x = 2(3) = 6, and 3y = 3(2) = 6
So, the greatest common divisor of 2x and 3y is 6

case 2: x = 1 and y = 1. This satisfies the condition that 1 is the greatest common divisor of x and y
In this case 2x = 2(1) = 2, and 3y = 3(1) = 3
So, the greatest common divisor of 2x and 3y is 1

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by Jeff@TargetTestPrep » Thu Mar 22, 2018 2:54 pm
Gmat_mission 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

If x = 3 and y = 2, then 2x = 6 and 3y = 6, and their greatest common divisor is 6.

However, if x = 5 and y = 6, then 2x = 10 and 3y = 18, and their greatest common divisor is 2.

Jeffrey Miller
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by ceilidh.erickson » Fri Mar 23, 2018 8:34 am
Gmat_mission 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

[spoiler]OA=B[/spoiler].

Since the greatest common divisor or 2 and 3 is 1, it shouldn't be A the answer? I got confused. Experts, I'd appreciate your help here. Thanks.
Here's a general rule: if you see "cannot be determined" in PS answer choices, ask yourself - can I think of different cases that would both fit the given information? Can I try to DISPROVE? Brent showed exactly how to do so on this problem.

Here's another example: https://www.beatthegmat.com/ratio-of-tw ... 86618.html

Ceilidh Erickson
Manhattan Prep GMAT & GRE instructor
EdM in Mind, Brain, and Education