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Number properties

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Number properties

by awilhelm » Thu Jan 29, 2009 8:30 pm
If x & y are positive integers such that x = 8y + 12, what is the greatest common divisor of x & y?

1) x = 12u, where u is an integer
2) y = 12z, where z is an integer

How can I solve for the GCD?
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by krisraam » Thu Jan 29, 2009 10:03 pm
B alone is sufficient.

x = 8y + 12 ==> x when divided by y leaves a remainder of 12 so y should be greater than 12.

1) x = 12u
12u = 8y + 12 ==> 3(u-1)/2 = y

Let u = 15 and 17 y = 21 and 24 the GCD are 3 and 12.

Not sufficient.

2) y =12z

x = 8*12Z+ 12
=12(8*z + 1)
12 is factor of x and y . If z and 8*z+1 has a common multiple then GCD is 12 * Common multiple.

For z = 2 to 9 z and 8*z + 1 does not have a common multiple.

So GCD is 12.

B is sufficeint.

Thanks
Raama
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by maihuna » Mon Feb 09, 2009 8:55 am
I also encountered this question, but dont agree wit RAAMMMMA explanation though...

I can make this ebn with B:

x = 12(8z+1) where y = 12z

We know 8z+1 will be always odd, 12 need two 2's which will never come..and so B is sufficient...
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