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Easy but good one

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by itsmebharat » Tue May 31, 2011 1:02 am
If X and Y are positive intergers such that X = 8Y + 12, what is the common divisor of X and Y?

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

OA is B
I am not an Expert, please feel free to suggest if there is an error.
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Source: — Data Sufficiency |
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by Frankenstein » Tue May 31, 2011 2:18 am
Hi,
From(1): if u=3, x=36 then y=3. common divisor of x,y is 3
if u=5, x=60 then y=6. common divisor of x,y is 6 or 3 or 2
Not Sufficient
From(2): y=12z, so x=8(12z)+12 = 12(8z+1).
8z+1 always leaves remainder when divided by z. so, z and 8z+1 do not have any common divisor. So, x=12(8z+1) and y=12z have common divisor of 2,3,4,6,12 only for any value of x,y.
Sufficient

Hence, B
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