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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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17 Jun 2007, 01:35
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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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17 Jun 2007, 05:55

Stmt1: a =2b +6
the gcd between a and 2b may be 6, 12, 18....
But 2b+6 makes 'a' to be divisible by 6 not by the higher multiples of 6.
Hence the gcd of a and b is 6.
Suff

Stmt2: Clearly insuff.
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17 Jun 2007, 08:23
A is sufficient
Bis not

Bis clearly not sufficient. Think like this - a = 3b,
b can be anything 6,12,18,24.. similarly GCD can be 6,12,18...

a = 2b+6 means that 6 will always be the GCD no matter what the value of b. g
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17 Jun 2007, 09:06
go with E.

a,b are given to be divisible by 6

St1: a = 2b+6

say b=6 => a = 18 ; GCD = 6

say b=12 => a = 36; GCD = 12

hence INSUFF

St2: a = 3b

choosing the same set of #s as in St1, St2 is INSUFF

(1) + (2) is INSUFF as well.
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17 Jun 2007, 13:34
oh darn ! wat was i thinking ..

guess shud think twice before I refute vshaunak's answer haha
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18 Jun 2007, 10:41
OA is A
18 Jun 2007, 10:41
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