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Divisibility

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Divisibility

by selango » Sun Jul 11, 2010 12:32 pm
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

OA A
--Anand--
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Source: — Data Sufficiency |
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by kvcpk » Sun Jul 11, 2010 1:17 pm
a = 6m
b=6n

GCD of 2b+6,b
GCD of 12n+6,6n
GCD of 6(2n+1),6n

n and 2n+1 will never have a common divisor except 1.
Why?
Because, if (2n+1) is divisible by k, say
then 2n is not divisible by k. Because consecutive numbers will not have a common divisor more than 1.
So, if 2n is not divisible by k, then n is not divisible by k.

Hence the GCD of 6(2n+1),6n is 6.

SUFF

a=3b
let b=6,
the a=18
GCD=6

let b=12,
then a=36,
GCD =12

INSUFF

pick A
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