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If x and y are positive integers, each of the following

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smartass666
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If x and y are positive integers, each of the following [#permalink] New post   29 Sep 2012, 12:41
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If x and y are positive integers, each of the following could be the greatest common divisor of 30x and 15y EXCEPT

A. 30x.
B. 15y.
C. 15(x + y).
D. 15(x - y).
E. 15,000.
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C
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EvaJager
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Re: If x and y are positive integers, each of the following [#permalink] New post   29 Sep 2012, 13:29
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smartass666 wrote:
If x and y are positive integers, each of the following could be the greatest common divisor of 30x and 15y EXCEPT

30x.
15y.
15(x + y).
15(x - y).
15,000.


The greatest common divisor must be smaller than each number.
\(15(x+y)>15y\), so for sure, \(15(x+y)\) cannot be a divisor of \(15y.\)

Answer C.
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Re: If x and y are positive integers, each of the following [#permalink] New post   01 Oct 2012, 06:23
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smartass666 wrote:
If x and y are positive integers, each of the following could be the greatest common divisor of 30x and 15y EXCEPT

A. 30x.
B. 15y.
C. 15(x + y).
D. 15(x - y).
E. 15,000.


Similar questions to practice:
which-of-the-following-cannot-be-the-greatest-common-divisor-108865.html
if-x-and-y-are-positive-integers-which-of-the-following-74924.html
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Re: If x and y are positive integers, each of the following [#permalink] New post   29 Nov 2013, 13:25
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nechets wrote:
Wait a minute, picking numbers:

If x= 1 and y =1 , both positive integers, why this could not be the base case for C?


smartass666 wrote:
If x and y are positive integers, each of the following could be the greatest common divisor of 30x and 15y EXCEPT

A. 30x.
B. 15y.
C. 15(x + y).
D. 15(x - y).
E. 15,000.


If x=1 and y=1, then 30x=30 and 15y=15. The GCD of 30 and 15 is 15, while (C) gives 15(x+y)=30.

Hope it's clear.
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Re: If x and y are positive integers, each of the following [#permalink] New post   29 Nov 2013, 13:41
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nechets wrote:
Fantastic Bunuel, great catch.

Is it the case that x/(x+y) or y/(x+y) will never be integer? Is this the right way to elimate C algebraically? Or how would you do so?


Bunuel wrote:
nechets wrote:
Wait a minute, picking numbers:

If x= 1 and y =1 , both positive integers, why this could not be the base case for C?


If x and y are positive integers, each of the following could be the greatest common divisor of 30x and 15y EXCEPT

A. 30x.
B. 15y.
C. 15(x + y).
D. 15(x - y).
E. 15,000.


If x=1 and y=1, then 30x=30 and 15y=15. The GCD of 30 and 15 is 15, while (C) gives 15(x+y)=30.

Hope it's clear.


Both x and y are positive integers, thus \(\frac{15y}{15(x+y)}=\frac{y}{x+y}\neq{integer}\) because the denominator is greater than the numerator. Thus 15(x+y) cannot be a divisor of 15y.

Check similar questions to practice:
which-of-the-following-cannot-be-the-greatest-common-divisor-108865.html
if-x-and-y-are-positive-integers-which-of-the-following-74924.html

Hope this helps.
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Re: If x and y are positive integers, each of the following [#permalink] New post   29 Nov 2013, 13:22
Wait a minute, picking numbers:

If x= 1 and y =1 , both positive integers, why this could not be the base case for C?


smartass666 wrote:
If x and y are positive integers, each of the following could be the greatest common divisor of 30x and 15y EXCEPT

A. 30x.
B. 15y.
C. 15(x + y).
D. 15(x - y).
E. 15,000.
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nechets
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Re: If x and y are positive integers, each of the following [#permalink] New post   29 Nov 2013, 13:31
Fantastic Bunuel, great catch.

Is it the case that x/(x+y) or y/(x+y) will never be integer? Is this the right way to elimate C algebraically? Or how would you do so?


Bunuel wrote:
nechets wrote:
Wait a minute, picking numbers:

If x= 1 and y =1 , both positive integers, why this could not be the base case for C?


smartass666 wrote:
If x and y are positive integers, each of the following could be the greatest common divisor of 30x and 15y EXCEPT

A. 30x.
B. 15y.
C. 15(x + y).
D. 15(x - y).
E. 15,000.


If x=1 and y=1, then 30x=30 and 15y=15. The GCD of 30 and 15 is 15, while (C) gives 15(x+y)=30.

Hope it's clear.
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Re: If x and y are positive integers, each of the following [#permalink] New post   14 Mar 2016, 09:10
I arrived at the answer as i did not find any pairs for 15(x+y)

also 15(x-y)is feasible for x=2 and y=1
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Re: If x and y are positive integers, each of the following [#permalink] New post   07 Sep 2020, 15:12
Bunuel wrote:
nechets wrote:
Wait a minute, picking numbers:

If x= 1 and y =1 , both positive integers, why this could not be the base case for C?


smartass666 wrote:
If x and y are positive integers, each of the following could be the greatest common divisor of 30x and 15y EXCEPT

A. 30x.
B. 15y.
C. 15(x + y).
D. 15(x - y).
E. 15,000.


If x=1 and y=1, then 30x=30 and 15y=15. The GCD of 30 and 15 is 15, while (C) gives 15(x+y)=30.

Hope it's clear.
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Re: If x and y are positive integers, each of the following [#permalink] New post   13 May 2023, 10:15
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Re: If x and y are positive integers, each of the following [#permalink]
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