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If x and y are positive integers, what is the greatest common divisor

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If x and y are positive integers, what is the greatest common divisor  [#permalink]

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New post 07 May 2017, 09:20
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If x and y are positive integers, what is the greatest common divisor of x and y?

(1) x and y are both prime Numbers
(2) x + y is odd.
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Re: If x and y are positive integers, what is the greatest common divisor  [#permalink]

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New post 07 May 2017, 09:32
ans is A
as prime numbers, greatest common divisor must be 1.

2 doesn't serve any purpose.


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Re: If x and y are positive integers, what is the greatest common divisor  [#permalink]

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New post 07 May 2017, 09:34
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If x and y are positive integers, what is the greatest common divisor of x and y?

(1) x and y are both prime numbers. If x and y are different primes, say 2 and 3, then the the greatest common divisor of x and y will be 1 but if x and y are the same prime, say 2 and 2, then the the greatest common divisor of x and y will be that prime. Not sufficient.

Note here that unless it is explicitly stated otherwise, different variables CAN represent the same number.

(2) x + y is odd. This implies that one is odd and another is even. Clearly not sufficient. For example, x = 1 and y = 2, then GCF = 1 but x = 3 and y = 6, then GCF = 3.

(1)+(2) From (2) it follows that x and y cannot be the same prime, because in this case x + y would be even. Thus x and y are different primes, which implies that the greatest common divisor of x and y is 1. Sufficient.

Answer: C.

Hope it's clear.
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Re: If x and y are positive integers, what is the greatest common divisor  [#permalink]

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New post 25 Sep 2018, 19:27
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If x and y are positive integers, what is the greatest common divisor &nbs [#permalink] 25 Sep 2018, 19:27
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