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

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If x and y are positive integers such that x=8y+12, what is [#permalink]

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New post 31 Jul 2008, 09:20
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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?
(1) x is divisible by 12.
(2) y is divisible by 12.
A. Statement (1) ALONE is sufficient but Statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient but Statement (1) ALONE is not sufficient.
C. BOTH Statements TOGETHER are sufficient, but NEITHER Statement alone is sufficient.
D. Each Statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
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Re: gcd.... [#permalink]

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New post 31 Jul 2008, 09:39
If x and y are positive integers such that x=8y+12, what is the greatest common divisor of x and y?
(1) x is divisible by 12.
(2) y is divisible by 12

lets look at 1)

if y=3, then x=36 GCD of x and y=3

if y=6 then x=60 gcd=6 ...insuff

lets look at 2)
x=8(12K)+12
x=12(8K+1)
x/12=(8k+1) now pick any value of K, it will never be a multiple of 12..therefore we know that x is divisible by 12 and that the GCD=12..

B is sufficient
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Re: gcd.... [#permalink]

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New post 31 Jul 2008, 11:05
arjtryarjtry wrote:
. If x and y are positive integers such that x=8y+12, what is the greatest common divisor of x and y?
(1) x is divisible by 12.
(2) y is divisible by 12.
A. Statement (1) ALONE is sufficient but Statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient but Statement (1) ALONE is not sufficient.
C. BOTH Statements TOGETHER are sufficient, but NEITHER Statement alone is sufficient.
D. Each Statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.



x=8y+12 --> insufficient
1)x is divisible by 12.

X=12K
Y= 12k-12/8 = 12 (k-1)/8 =3/2 (k-1)

GCD wher (K-1)/2 --> should be integers say( m)
k=2m+1

2*2*3 K, 3/2 (k-1)

12 (2m+1), 3 m
2*2*3*(2m+1) , 3m -- where m>1
2*2*3*3 , 3 -- when m=1 -- GCD --> 3
2*2*3*5 , 3*2 -- when m=2 -- GCD --> 6


2) y is divisible by 12. --- sufficient
y =12q
x= 12q*8+12 = 12 (8q+1)

12 q, 12 (8q+1) -- GCD 12 for any value of q


B
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Re: gcd....   [#permalink] 31 Jul 2008, 11:05
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