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If x and y are positive integers, each of the following [#permalink ]
29 Sep 2012, 11:41

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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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Re: If x and y are positive integers, each of the following [#permalink ]
29 Sep 2012, 12:29
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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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Re: If x and y are positive integers, each of the following [#permalink ]
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.

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Re: If x and y are positive integers, each of the following [#permalink ]
29 Nov 2013, 12:25
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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 ]
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.

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Re: If x and y are positive integers, each of the following [#permalink ]
29 Nov 2013, 12:41
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 MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!! PLEASE READ AND FOLLOW: 11 Rules for Posting!!! RESOURCES: [GMAT MATH BOOK ]; 1. Triangles ; 2. Polygons ; 3. Coordinate Geometry ; 4. Factorials ; 5. Circles ; 6. Number Theory ; 7. Remainders ; 8. Overlapping Sets ; 9. PDF of Math Book ; 10. Remainders ; 11. GMAT Prep Software Analysis NEW!!! ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!! ; 12. Tricky questions from previous years. NEW!!! ;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 ? 25 extra-hard Quant Tests Get the best GMAT Prep Resources with GMAT Club Premium Membership

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