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# If a and b are positive integers divisible by 6, is 6 the

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If a and b are positive integers divisible by 6, is 6 the [#permalink]

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05 Aug 2008, 19:21
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If a and b are positive integers divisible by 6, is 6 the greatest common divisor of a and b?

(1) a = 2b + 6

(2) a = 3b
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05 Aug 2008, 20:18
young_gun wrote:
If a and b are positive integers divisible by 6, is 6 the greatest common divisor of a and b?

(1) a = 2b + 6

(2) a = 3b

S1. take b = 6, 12, 18 and any multiple of six
You will always get that six is the greatest common divisor

42 = 2(18) +6 so here six is the greatest common divisor

S2. 36 = 3(12)
here the greatest common 12 divisor is 12. Whatever the value of B is that is the greatest common divisor.

IMO A
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06 Aug 2008, 04:50
young_gun wrote:
If a and b are positive integers divisible by 6, is 6 the greatest common divisor of a and b?

(1) a = 2b + 6

(2) a = 3b

I get A.

(1) Suff

a = 2(6k) + 6 = 2*3*(2k + 1)
b = 2*3*k

2k+1 and k will never have the same prime factors. Thereforce, gcf of a and b is 2*3

(2) Insuff

a = 3*6k = 2*3*3*k
b = 6k = 2*3*k

Gcf of a and b is 2*3*k.
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06 Aug 2008, 16:51
x97agarwal wrote:
young_gun wrote:
If a and b are positive integers divisible by 6, is 6 the greatest common divisor of a and b?

(1) a = 2b + 6

(2) a = 3b

S1. take b = 6, 12, 18 and any multiple of six
You will always get that six is the greatest common divisor

42 = 2(18) +6 so here six is the greatest common divisor

S2. 36 = 3(12)
here the greatest common 12 divisor is 12. Whatever the value of B is that is the greatest common divisor.

IMO A

a and b are divisible by 6
hence
(1) a=2b+6 => say b=6k k is any integer =>
a=2(6k)+6 => a=(2k+1)6
again to get the greatest common factor other than 6 here
k =2k+1=> k=-1
hence a=-6 a,b are posiive hence this is ruled out SUFFI 6 is greatest common divisor

(2)a=3b =>say b=6k a=18k k can be anything hence greatest common divisor can be any integer other than 6 too INSUFFI

IMO A
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Re: PS GCF   [#permalink] 06 Aug 2008, 16:51
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