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

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Intern
Joined: 11 Feb 2012
Posts: 12
If x and y are positive integers, each of the following  [#permalink]

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29 Sep 2012, 11:41
3
9
00:00

Difficulty:

65% (hard)

Question Stats:

54% (01:37) correct 46% (01:31) wrong based on 392 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.
Director
Joined: 22 Mar 2011
Posts: 601
WE: Science (Education)
Re: If x and y are positive integers, each of the following  [#permalink]

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29 Sep 2012, 12:29
9
6
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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##### General Discussion
Math Expert
Joined: 02 Sep 2009
Posts: 51072
Re: If x and y are positive integers, each of the following  [#permalink]

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01 Oct 2012, 05:23
3
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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Current Student
Joined: 04 Oct 2013
Posts: 75
Location: Brazil
GMAT 1: 660 Q45 V35
GMAT 2: 710 Q49 V38
Re: If x and y are positive integers, each of the following  [#permalink]

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29 Nov 2013, 12:22
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: 51072
Re: If x and y are positive integers, each of the following  [#permalink]

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29 Nov 2013, 12:25
3
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.
_________________
Current Student
Joined: 04 Oct 2013
Posts: 75
Location: Brazil
GMAT 1: 660 Q45 V35
GMAT 2: 710 Q49 V38
Re: If x and y are positive integers, each of the following  [#permalink]

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29 Nov 2013, 12:31
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: 51072
Re: If x and y are positive integers, each of the following  [#permalink]

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29 Nov 2013, 12:41
1
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: 12 Aug 2015
Posts: 2630
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: If x and y are positive integers, each of the following  [#permalink]

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14 Mar 2016, 08:10
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Joined: 09 Sep 2013
Posts: 9101
Re: If x and y are positive integers, each of the following  [#permalink]

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11 Aug 2018, 04:29
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If x and y are positive integers, each of the following &nbs [#permalink] 11 Aug 2018, 04:29
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