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

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VP
Joined: 30 Jun 2008
Posts: 1022
If x and y are positive integers such that x=8y+12, what is [#permalink]

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25 Oct 2008, 00:58
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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.
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"You have to find it. No one else can find it for you." - Bjorn Borg

Senior Manager
Joined: 28 Feb 2007
Posts: 296

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25 Oct 2008, 01:25
Edited (I made a silly mistake again. 0 is not POSITIVE INTEGER that question stem emphasizes.). B.
Mathematic approach is as follows:
st1) x=12t, t IS positive INTERGER
x=8y+12 12t=8y+12 t=2y/3 +1, Y can be ( 3,6,9,12, ..), GCD=y Insuff.

st2) y=12z, z is positive integer. x=12(8z+1). Despite the value of Z, GCD=12. SUFF.

Last edited by UMB on 25 Oct 2008, 02:06, edited 1 time in total.
VP
Joined: 30 Jun 2008
Posts: 1022

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25 Oct 2008, 01:53
Not E.

UMB, you came close .....
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SVP
Joined: 17 Jun 2008
Posts: 1507

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25 Oct 2008, 04:42
B.

From stmt1: x = 12m and 12m = 8y + 12 or 3m = 2y + 3 and y is a multiple of 3...not sufficient as x = 12, y = 3 and GCD = 3, x = 12, y = 6, GCD = 6.

From stmt2: y = 12n and x = 12(8n + 1).

For y = 0 12 12*2 12*3
x = 12 12*9 12*17 12*25

and GCD will always be 12.. Hence, sufficient.
Retired Moderator
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25 Oct 2008, 05:17
amitdgr 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.

B

X IS DEVISABLE BY 4 , Y IS DEVIABLE BY 3 AND 4

Re: DS : GCD   [#permalink] 25 Oct 2008, 05:17
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