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# If a and b are positive integers, and a=2b+6, the greatest

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Senior Manager
Joined: 21 Oct 2013
Posts: 414
If a and b are positive integers, and a=2b+6, the greatest  [#permalink]

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22 Jul 2014, 05:11
1
6
00:00

Difficulty:

45% (medium)

Question Stats:

62% (01:43) correct 38% (01:24) wrong based on 199 sessions

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If a and b are positive integers, and a=2b+6, the greatest common divisor of a and b CANNOT be

A. 1
B. 2
C. 3
D. 6
E. 12
Math Expert
Joined: 02 Sep 2009
Posts: 55670
Re: If a and b are positive integers, and a=2b+6, the greatest  [#permalink]

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22 Jul 2014, 05:30
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2
goodyear2013 wrote:
If a and b are positive integers, and a=2b+6, the greatest common divisor of a and b CANNOT be

A. 1
B. 2
C. 3
D. 6
E. 12

If b is 1, 2, 3, or 6, then GCD of a and b is 1, 2, 3, and 6 respectively. So, by POE the answer must be E.

Still: if b is a multiple of 12, then a is 6 greater than a multiple of 12, so not a multiple of 12, so both of them cannot be divisive by 12.

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Math Expert
Joined: 02 Sep 2009
Posts: 55670
Re: If a and b are positive integers, and a=2b+6, the greatest  [#permalink]

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22 Jul 2014, 05:34
Intern
Joined: 25 Jun 2014
Posts: 6
GMAT 1: 700 Q50 V33
Re: If a and b are positive integers, and a=2b+6, the greatest  [#permalink]

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22 Jul 2014, 05:43
since a =2b + 6,
so we can say b = (a/2 -3).

So we need to find not possible gcd values for a , (a/2 -3).
A. 1, We can easily get this value by making a = 8.
B. 2. we can again get this value as GCD by keeping a =10
C. 3 We will get this as GCD by keeping a =12
D. 6 We can get GCD 6 by keeping (a/2-3) = 6 and a as 18.
E. 12 This is not possible as for 12(2^2*3 ) to be GCD = 2^2*3 both a and a/2-3 should be divisible by 4 and 3 . So a has to be a multiple of 4 . this means a/2 has to be even and Even - odd will be odd and odd number wont be divisible by 4.

This 12 cant be the GCD.

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Re: If a and b are positive integers, and a=2b+6, the greatest  [#permalink]

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17 Sep 2018, 05:16
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Re: If a and b are positive integers, and a=2b+6, the greatest   [#permalink] 17 Sep 2018, 05:16
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