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If a, b, and c are positive integers, what is the greatest common divi

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If a, b, and c are positive integers, what is the greatest common divi  [#permalink]

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New post 21 Dec 2018, 05:01
1
7
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A
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C
D
E

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If a, b, and c are positive integers, what is the greatest common divisor of a, b and c?


(1) The greatest common divisor of a and b is 3
(2) The greatest common divisor of b and c is 4
Spoiler: OA

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Re: If a, b, and c are positive integers, what is the greatest common divi  [#permalink]

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New post 24 Dec 2018, 00:56
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1
If a, b, and c are positive integers, what is the greatest common divisor of a, b and c?

GCD means the largest number which has all three numbers a, b and c in its table.

(1) The greatest common divisor of a and b is 3
this means GCD of a, b and c can be only 3, but we don't know if 3 is a factor of c or not.
If yes, GCD is 3, otherwise it is 1.
Insufficient

(2) The greatest common divisor of b and c is 4
this means GCD of a, b and c can be only 4, but we don't know if 4 is a factor of a or not.
If yes, GCD is 4, otherwise it is 1.
Insufficient

Combined..
It can be only 1

C
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
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Re: If a, b, and c are positive integers, what is the greatest common divi  [#permalink]

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New post 23 Dec 2018, 03:19
I got E.

Since by St#2 : b = 4x , c = 4y , not enough

And by St#1 : a = 3z , b = 3x , not enough

Combining ,in (c)
a= 3z
b = 3*4*x
c = 4*y

We cannot get common factor from here, hence (e)
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If a, b, and c are positive integers, what is the greatest common divi  [#permalink]

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New post 23 Dec 2018, 07:11
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aru010 wrote:
I got E.

Since by St#2 : b = 4x , c = 4y , not enough

And by St#1 : a = 3z , b = 3x , not enough

Combining ,in (c)
a= 3z
b = 3*4*x
c = 4*y

We cannot get common factor from here, hence (e)


aru010

What about the number 1?

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Re: If a, b, and c are positive integers, what is the greatest common divi  [#permalink]

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New post 24 Dec 2018, 00:16
Bunuel wrote:
If a, b, and c are positive integers, what is the greatest common divisor of a, b and c?


(1) The greatest common divisor of a and b is 3
(2) The greatest common divisor of b and c is 4


Par of GMAT CLUB'S New Year's Quantitative Challenge Set


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Re: If a, b, and c are positive integers, what is the greatest common divi  [#permalink]

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New post 08 Oct 2019, 03:50
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Bunuel wrote:
If a, b, and c are positive integers, what is the greatest common divisor of a, b and c?


(1) The greatest common divisor of a and b is 3
(2) The greatest common divisor of b and c is 4


Asked: If a, b, and c are positive integers, what is the greatest common divisor of a, b and c?


(1) The greatest common divisor of a and b is 3
Since c is unknown
NOT SUFFICIENT

(2) The greatest common divisor of b and c is 4
Since a is unknown
NOT SUFFICIENT

(1) + (2)
(1) The greatest common divisor of a and b is 3
(2) The greatest common divisor of b and c is 4
The greatest common divisor of a, b & c is 1.
SUFFICIENT

IMO C
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Re: If a, b, and c are positive integers, what is the greatest common divi   [#permalink] 08 Oct 2019, 03:50
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