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the greatest common divisor

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the greatest common divisor

by sanju09 » Wed Apr 08, 2009 4:05 am
x and y are positive integers such that x = 8 y + 12, what is the greatest common divisor of x and y?

(1) x = 12 u, where u is an integer.

(2) y = 12 z, where z is an integer.



OA B
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by bluementor » Wed Apr 08, 2009 4:50 am
Statement 1:

12u = 8y + 12
3u = 2y + 3
u = 2y/3 + 1
therefore, 2y/3 must be an integer. following this, y must be divisible by 3.

if y = 3, gcd(x,y) = 3
if y = 12, gcd(x,y) = 12 Insufficient.

Statement 2:

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

y = 12z

Since z is not a factor of 8z+1, then gcd(x,y) = 12. Sufficient.

Choose B

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