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(x - a)^2 + (y - b)^2 = 16 is a circle with center at (a,b) and radius of 4.

1. a^2 + b^2 > 16 presents a plane with a hole at the center of coordinates. So, we can choose (a,b) at Y-axis and far away Y- axis. Insufficient.

2. a = |b| + 5 presents a semi-plane with a>=5. Therefore, any circle with the center at the semi-pane and radius 4 will not intersect Y-axis. Sufficient.
_________________

I don't understand those plane explanations, Walker. If this is a GMAT problem, there has to be an easier explanations.

I paraphrase the question to ask is a in [-4,4], meaning it intersects the Y-axis, or is it not? a is the distance of moving left or right on the X-axis and since we know the radius is 4, a can tell us if the circle intersects the Y-axis.

1. Not sufficient because a can be a number in the interval and outside of it as well.

2. Sufficient because it says a > 5 and that means, a is outside the interval and therefore cannot intersect the Y-axis.
_________________

Chinese Democracy is misunderstood...at your nearest BestBuy.

(x - a)^2 + (y - b)^2 = 16 is a circle with center at (a,b) and radius of 4.

1. a^2 + b^2 > 16 presents a plane with a hole at the center of coordinates. So, we can choose (a,b) at Y-axis and far away Y- axis. Insufficient.

2. a = |b| + 5 presents a semi-plane with a>=5. Therefore, any circle with the center at the semi-pane and radius 4 will not intersect Y-axis. Sufficient.

Walker or anyone: if you could explain how to draw these equations on a plane, it would be very helpful.