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x and y are positive integers such that x=8y+12, what is the

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x and y are positive integers such that x=8y+12, what is the [#permalink] New post 29 Jan 2012, 17:25
00:00
A
B
C
D
E

Difficulty:

  55% (medium)

Question Stats:

43% (03:02) correct 56% (01:18) wrong based on 233 sessions
x and y are positive integers such that x=8y+12, what is the greatest common divisor of x and y?

(1) X=12u, where u is an integer.
(2) Y=12z, where z is an integer.

[Reveal] Spoiler:
For me its B and this is how I solved it. Is my solution correct?

Question is asking for GCD of x and y.

GCF or GCD is the product of common prime factors with lowest exponents. for example GF of 12 and 24 is

12 = 2^2 * 3^1
24 = 2^3 * 3^1

GCF = 2^2 * 3^1 = 12

Coming back to the question and considering statement 1

x is a multiple of 12

So if we put different values of x in the our equation GCF will be different. Therefore this statement is INSUFFICIENT.

Considering statement 2

Y=12z, where z is an integer. Y is a multiple of 12. i.e Y can be 12, 24, 36. And therefore x can be 192, 204 etc.

So if y = 12 then x = 108

Prime factors of 12 = 2^2 *3^1
Prime factors of 108 = 2^2 * 3^3
GCF = 2^2 * 3^1 = 12

Now if y = 24, x = 204

Prime factors of 24 = 2^3 * 3 ^1
Prime factors of 204 = 2^2 * 3^1 * 17
GCF = 2^2 * 3 = 12

So GCF or GCF will be 12 and therefore B alone is sufficient to answer this question. Am I right guys? Unfortunately OA is not provided.
[Reveal] Spoiler: OA

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MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610 :-(


Last edited by Bunuel on 16 Dec 2012, 08:11, edited 2 times in total.
Added the OA
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Re: GCD of x & y [#permalink] New post 29 Jan 2012, 17:39
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If x and y are positive integers such that x = 8y + 12, what is the greatest common divisor of x and y?

Given: x=8y+12.

(1) x = 12u, where u is an integer --> x=12u --> 12u=8y+12 --> 3(u-1)=2y --> the only thing we know from this is that 3 is a factor of y. Is it GCD of x and y? Not clear: if x=36, then y=3 and GCD(x,y)=3 but if x=60, then y=6 and GCD(x,y)=6 --> two different answers. Not sufficient.

(2) y = 12z, where z is an integer --> y=12z --> x=8*12z+12 --> x=12(8z+1). So, we have y=12z and x=12(8z+1). Now, as z and 8z+1 do not share any common factor but 1 (8z and 8z+1 are consecutive integers and consecutive integers do not share any common factor 1. As 8z has all factors of z then z and 8z+1 also do not share any common factor but 1). Thus, 12 must be GCD of x and y. Sufficient.

Answer: B.

Hope it's clear.
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Re: If x and y are positive integers such that x=8y+12 [#permalink] New post 23 Mar 2012, 12:23
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dddmba2012 wrote:
If x an y are positive integers such that x = 8y + 12, what is the greatest common divisor of x and y
1. x = 12u where u is an integer
2. y = 12z where z is an integer


Merging similar topics. Please ask if anything remains unclear.

Also discussed:
if-x-and-y-are-positive-integers-such-that-x-8y-12-what-101196.html
if-x-and-y-are-positive-integers-such-that-x-8y-12-what-100138.html

Hope it helps.
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Re: x and y are positive integers such that x=8y+12, what is the [#permalink] New post 12 Feb 2012, 22:35
bunuel where enigma123 is wrong in her explanation , i think her way is also correct, by putting values we can easily get to know relevant options, i think by substitiuing varoius values of Y like Y= 12, 24, 36 it becomes little bit lengthy , plz correct me if i am wrong.

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If x and y are positive integers such that x=8y+12 [#permalink] New post 23 Mar 2012, 12:17
If x an y are positive integers such that x = 8y + 12, what is the greatest common divisor of x and y
1. x = 12u where u is an integer
2. y = 12z where z is an integer
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Re: x and y are positive integers such that x=8y+12, what is the [#permalink] New post 05 Jul 2013, 01:44
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Re: x and y are positive integers such that x=8y+12, what is the [#permalink] New post 26 Aug 2013, 21:51
[quote="enigma123"]x and y are positive integers such that x=8y+12, what is the greatest common divisor of x and y?

(1) X=12u, where u is an integer.
(2) Y=12z, where z is an integer.


1) x = 12u --> 12u = 8y + 12 --> y = 3(u - 1)/2
Keeping in mind y is a positive integer, u = 3, 5, 7... ---> x = 36, 60, 84 and y = 3, 6, 9..and GCD of x and y is = 3, 6, 3 etc. Since GCD is not constant we cannot determine it.

2) y = 12z ---> x = 8 × 12z + 12 = 12(8z + 1). Now z = 1, 2, 3, 4... ---> y = 12, 24, 36, 48... and x = 12 × 9, 12 × 17, 12 × 25...you can see that GCD is 12 for every pair of x and y.

Hence, 2 answers the question.

Source: http://totalgadha.com/mod/forum/discuss.php?d=130
Re: x and y are positive integers such that x=8y+12, what is the   [#permalink] 26 Aug 2013, 21:51
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