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What is the greatest common factor of positive integers x

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What is the greatest common factor of positive integers x [#permalink] New post 15 Mar 2008, 12:26
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What is the greatest common factor of positive integers x and y?

1) The GCF of x/2 and y/2 is 5?
2) x and y are even.
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Re: PS: Greatest Common Factor [#permalink] New post 15 Mar 2008, 14:20
jimmyjamesdonkey wrote:
What is the greatest common factor of positive integers x and y?

1) The GCF of x/2 and y/2 is 5?
2) x and y are even.


A shd be it.

St1: If the GCF is 5, then with X and Y, the GCF will be 10...Suff.

St2: Even: X = 10, Y = 20, GCF = 10.
X = 18, Y = 24, GCF = 6.
Not suff.

Whats OA ?
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Re: PS: Greatest Common Factor [#permalink] New post 15 Mar 2008, 14:44
The answer should be 10.
If x/2 and y/2 have the GCF of 5, it means that x/2 and y/2 should both be divisible by 5. This implies that x and y should both be divisible by 10. As an example you can take 10 and 20 or 20 and 30 or 30 and 40 and so on. If you take alternate 10s like 20 and 40, then 10 and 20 do not have the GCF of 5 but have the GCF of 10. That contradicts our first condition.
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Re: PS: Greatest Common Factor [#permalink] New post 24 May 2011, 04:00
FOR ME:

X/2=5*A X=2*5*A
Y/2=5*B Y=2*5*B HENCE :2 AND 5ARE THE GCF
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Re: PS: Greatest Common Factor [#permalink] New post 24 May 2011, 04:13
Clean A .

X/2 and Y/2 has 5 as GCF , which mean x, y will have 10 GCF,
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Re: PS: Greatest Common Factor [#permalink] New post 24 May 2011, 04:43
ok so i agree statement 2 is insufficient, however i do have a quick question regarding statement 1, you have said if x/2 and y/2 have a GCF of 5, then the GCF of x and y is 10. However i didnt really apply the straight forward technique so need your help here, please find below my technique

assuming
x= 20
y=10

x/2= 10
y/2= 5

10= 2*5
5= 5*1

Hence GCF would be the common numbers with the lowest exponent, i.e. 5^1=5.
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Re: PS: Greatest Common Factor [#permalink] New post 25 May 2011, 22:46
its a 10 using A here.
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Re: PS: Greatest Common Factor   [#permalink] 25 May 2011, 22:46
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