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

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Intern
Joined: 11 Feb 2012
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If x and y are positive integers, each of the following [#permalink]

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29 Sep 2012, 12:41
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75% (hard)

Question Stats:

47% (01:55) correct 53% (00:54) wrong based on 230 sessions

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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.
[Reveal] Spoiler: OA
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Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
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Kudos [?]: 786 [7] , given: 43

Re: If x and y are positive integers, each of the following [#permalink]

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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 $$15y.$$

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Joined: 02 Sep 2009
Posts: 33523
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Kudos [?]: 73588 [2] , given: 9902

Re: If x and y are positive integers, each of the following [#permalink]

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01 Oct 2012, 06:23
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Expert's post
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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Joined: 04 Oct 2013
Posts: 90
Location: Brazil
GMAT 1: 660 Q45 V35
GMAT 2: 710 Q49 V38
Followers: 2

Kudos [?]: 54 [0], given: 45

Re: If x and y are positive integers, each of the following [#permalink]

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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.
Math Expert
Joined: 02 Sep 2009
Posts: 33523
Followers: 5935

Kudos [?]: 73588 [2] , given: 9902

Re: If x and y are positive integers, each of the following [#permalink]

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29 Nov 2013, 13:25
2
KUDOS
Expert's post
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.
_________________
Manager
Joined: 04 Oct 2013
Posts: 90
Location: Brazil
GMAT 1: 660 Q45 V35
GMAT 2: 710 Q49 V38
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Kudos [?]: 54 [0], given: 45

Re: If x and y are positive integers, each of the following [#permalink]

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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.
Math Expert
Joined: 02 Sep 2009
Posts: 33523
Followers: 5935

Kudos [?]: 73588 [1] , given: 9902

Re: If x and y are positive integers, each of the following [#permalink]

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29 Nov 2013, 13:41
1
KUDOS
Expert's post
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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Joined: 21 Jul 2014
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Kudos [?]: 1 [0], given: 13

Re: If x and y are positive integers, each of the following [#permalink]

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10 Aug 2014, 11:34
Bunuel wrote:
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

Hello Bunuel,
Can you please explain algebraically how we arrive at the correct answer C?

Regards.
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Re: If x and y are positive integers, each of the following [#permalink]

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15 Aug 2015, 14:05
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Re: If x and y are positive integers, each of the following [#permalink]

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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
Re: If x and y are positive integers, each of the following   [#permalink] 14 Mar 2016, 09:10
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