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

Question

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.

msk0657 · Answer

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.

mohshu · Answer

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

msk0657 · Answer

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..

NS0029 · Answer

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.

mohit_w · Answer

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?

ProfX · Answer

Aah you are absolutely correct. Answer will be B then

Sent from my iPhone using  GMAT Club Forum mobile app

nitiny · Answer

You are correct mohit_w.
Unless its not mentioned , we cannot assume .

mvictor · Answer

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!

auradediligodo · Answer

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

HNS · Answer

how come option B incorrect ?

if x = 3 and y = 3 then common divisors will be 1 and 3 but it is said that x and y share only one common divisor. Then x and y should be distinct prime numbers to share only one common divisor.

Bunuel · Answer

1 is a factor of every integer. So if x and y share only one common divisor, that divisor must be 1. Therefore, the greatest common factor of x and y is 1, and statement (2) alone is sufficient.

Also, x and y do not need to be prime. They only need to be coprime. For example, 4 and 15 or 9 and 22 share exactly one common divisor, which is 1.

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

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GMAT Data Sufficiency (DS) Questions

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

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