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

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Director
Joined: 21 Aug 2005
Posts: 785

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

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21 Oct 2005, 22:21
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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?
a) x=12u, u is an integer
b) y=12z, z is an integer

Kudos [?]: 31 [0], given: 0

Director
Joined: 13 Nov 2003
Posts: 788

Kudos [?]: 64 [0], given: 0

Location: BULGARIA

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22 Oct 2005, 00:50
x=8y+12 and x=12u then 12u=8y+12 or y=[12*(u-1)]/8 or y=[3*(u-1)]/2 since u ia an integer when u=1 y=0 x=12 the greatest GCD is 12 when u=3,y=3 x=36 GCD is 3 so A) is insuff
Same reasoning can be applied to B)
Even when combined A) and B) are not enough So E) is my choice

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Current Student
Joined: 28 Dec 2004
Posts: 3345

Kudos [?]: 325 [0], given: 2

Location: New York City
Schools: Wharton'11 HBS'12

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22 Oct 2005, 07:57
this is B

(1) well 12u=8y+12

OK so xis a multiple of 12...

lets if y=0, then x=12...then GCD=0

if y=3, x=36, GCD=3, y=6, x=60, GCD=6...Insuff

(2)
x=8(12z)+12 well, what does this mean; it means X and Y both are multiples of 12....therefor GCD will be 12...i.e. say y=12 and x=8.12+12, GCD=12...say y=24 x=8.24+12...GCD=12

Sufficient

Kudos [?]: 325 [0], given: 2

22 Oct 2005, 07:57
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