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Math Expert V
Joined: 02 Sep 2009
Posts: 58435
If x and y are both positive integers, what is their greatest common  [#permalink]

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Difficulty:   85% (hard)

Question Stats: 26% (01:01) correct 74% (00:54) wrong based on 152 sessions

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If x and y are both positive integers, what is their greatest common factor?

(1) x and y are prime numbers.

(2) x and y share only one common divisor.

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Retired Moderator G
Joined: 26 Nov 2012
Posts: 571
Re: If x and y are both positive integers, what is their greatest common  [#permalink]

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Bunuel wrote:
If x and y are both positive integers, what is their greatest common factor?

(1) x and y are prime numbers.

(2) x and y share only one common divisor.

To find the GCD, we need to prime factorization.

Stat 1: Clearly insufficient...as we don't have x and y values...only they are prime...

Stat 2: Sufficient...

Note : Every common divisor of a and b is a divisor of GCD (a, b)....in our case common division of x and y is a divisor of GCD(x,y)..

IMO option B.
Director  S
Joined: 21 Mar 2016
Posts: 505
Re: If x and y are both positive integers, what is their greatest common  [#permalink]

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1
Stat 1 : any two prime nos share only one common divisor ,that is 1 sufficient

stat2 : every number has 1 as common divisor, since the statement says, one common divisor, GCD is 1
sufficient

IMO D
Retired Moderator G
Joined: 26 Nov 2012
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If x and y are both positive integers, what is their greatest common  [#permalink]

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mohshu wrote:
Stat 1 : any two prime nos share only one common divisor ,that is 1 sufficient

stat2 : every number has 1 as common divisor, since the statement says, one common divisor, GCD is 1
sufficient

IMO D

Your stat 1 is incorrect.

If you take x and y are 2 and 3 respectively...then GCD is 1

if x and y are both 3 and 3...then GCD is 3.... It is not mentioned that x and y are not equal...

Hope this clears..
Intern  Joined: 11 May 2016
Posts: 1
Location: United Kingdom
Re: If x and y are both positive integers, what is their greatest common  [#permalink]

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If x and y are both positive integers, what is their greatest common factor?

(1) x and y are prime numbers.

(2) x and y share only one common divisor.

My answer is (d), both statements are sufficient, because 2 prime numbers will have one common divisor that is 1.
The second statement also means 1 is a common advisor, so both are sufficient.
Intern  B
Joined: 13 Dec 2015
Posts: 7
Re: If x and y are both positive integers, what is their greatest common  [#permalink]

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Even I thought the answer is D.

But, the only reason I can think of D not being the correct answer choice, is no where in the question it being mentioned that they are "Distinct" +ve integers.

Any one who can clarify?
Current Student B
Joined: 24 Jul 2016
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GMAT 1: 730 Q51 V40 GPA: 3.6
Re: If x and y are both positive integers, what is their greatest common  [#permalink]

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msk0657 wrote:
mohshu wrote:
Stat 1 : any two prime nos share only one common divisor ,that is 1 sufficient

stat2 : every number has 1 as common divisor, since the statement says, one common divisor, GCD is 1
sufficient

IMO D

Your stat 1 is incorrect.

If you take x and y are 2 and 3 respectively...then GCD is 1

if x and y are both 3 and 3...then GCD is 3.... It is not mentioned that x and y are not equal...

Hope this clears..
Aah you are absolutely correct. Answer will be B then

Sent from my iPhone using GMAT Club Forum mobile app
Manager  S
Joined: 11 Oct 2016
Posts: 75
Location: India
GMAT 1: 610 Q47 V28 Re: If x and y are both positive integers, what is their greatest common  [#permalink]

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mohit_w wrote:
Even I thought the answer is D.

But, the only reason I can think of D not being the correct answer choice, is no where in the question it being mentioned that they are "Distinct" +ve integers.

Any one who can clarify?

You are correct mohit_w.
Unless its not mentioned , we cannot assume .
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Joined: 17 Jul 2014
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Re: If x and y are both positive integers, what is their greatest common  [#permalink]

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msk0657 wrote:
mohshu wrote:
Stat 1 : any two prime nos share only one common divisor ,that is 1 sufficient

stat2 : every number has 1 as common divisor, since the statement says, one common divisor, GCD is 1
sufficient

IMO D

Your stat 1 is incorrect.

If you take x and y are 2 and 3 respectively...then GCD is 1

if x and y are both 3 and 3...then GCD is 3.... It is not mentioned that x and y are not equal...

Hope this clears..

good example of why you shouldn't make additional assumptions when you are not required to!!!
I definitely fell for D, but now I see why B is the correct answer!
We were NEVER told that x and y are distinct integers!
Manager  G
Joined: 31 Jan 2019
Posts: 172
Location: Switzerland
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GPA: 3.9
Re: If x and y are both positive integers, what is their greatest common  [#permalink]

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Bunuel wrote:
If x and y are both positive integers, what is their greatest common factor?

(1) x and y are prime numbers.

(2) x and y share only one common divisor.

Option 1 is insufficient since:
If x=2 and y=2 than GCF=2=x=y
If X=2 and y=3 than GCF=1

Option 2

This statement tells us that GCF=1
Hence sufficient Re: If x and y are both positive integers, what is their greatest common   [#permalink] 01 Oct 2019, 12:52
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