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What is the greatest common factor of positive integers x an

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What is the greatest common factor of positive integers x an  [#permalink]

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New post 21 Jun 2013, 22:29
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What is the greatest common factor of positive integers x and y?

(1) The greatest common factor of x/2 and y/2 is 5.
(2) x and y are even.

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Re: What is the greatest common factor of positive integers x an  [#permalink]

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New post 21 Jun 2013, 22:48
fozzzy wrote:
What is the greatest common factor of positive integers x and y?

(1) The greatest common factor of \(x/2\)and \(y/2\) is 5.

(2) x and y are even.


Statement 1.
GCF of x/2 & y/2 is 5 defines that x& y are even and they must end with 0.
When GCF is 5 for those 2 numbers when both of them are divided by 2, it makes the it obvious that GCF is 10.
Sufficient

Statement 2:
Is not sufficient.
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Re: What is the greatest common factor of positive integers x an  [#permalink]

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New post 21 Jun 2013, 23:37
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fozzzy wrote:
What is the greatest common factor of positive integers x and y?

(1) The greatest common factor of \(x/2\)and \(y/2\) is 5.

(2) x and y are even.


From F.S 1 we know that HCF of\(x/2\) and \(y/2\) is 5. Thus, \(x/2\) = 5a and \(y/2\) = 5b , where a and b are co-primes.

Thus, x = 10a and y = 10b and their HCF is 10. Sufficient.

From F.S 2, for x = 4 and y = 8 , the hcf is 4. However, for x = 2 and y = 4, the hcf is 2. Insufficient.

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Re: What is the greatest common factor of positive integers x an  [#permalink]

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New post 31 Aug 2018, 04:55
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Re: What is the greatest common factor of positive integers x an &nbs [#permalink] 31 Aug 2018, 04:55
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