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.
If x and y are positive integers, and 1 is the greatest
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Consider these two cases.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
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
Answer: B
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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.
Answer: B
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- ceilidh.erickson
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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.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 another example: https://www.beatthegmat.com/ratio-of-tw ... 86618.html
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education