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

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

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

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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]

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

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

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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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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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]

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New post 29 Nov 2013, 13:41
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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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New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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

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

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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] 14 Mar 2016, 09:10
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