christoph wrote:
Does the curve (x-a)^2 + (y-b)^2=16 intersect the y-axis ?
(1) a^2+b^2>16
(2) a=|b|+5
What do we mean by 'intersect the y axis'? We mean that the x co-ordinate is 0.
So let's put x = 0 and see what we get:
\((0-a)^2 + (y-b)^2 = 16\)
\(y = b + (16 - a^2)^{1/2}\)
Now what decides whether we get a value for y or not? Obviously, if \((16 - a^2)\) is negative, y will have no real value and the curve will not intersect the y axis. If instead \((16 - a^2)\) is 0 or positive, the curve will intersect the y axis. So we can answer the question asked if we know whether \((16 - a^2)\) is positive/0 or not.
Is \((16 - a^2) >= 0\)
or Is \((a^2 - 16) <= 0\)
Is \(-4 <= a <= 4\)?
We have simplified the question stem as much as we could. Let's go on to the given statements.
(1) \(a^2+b^2>16\)
Doesn't tell us about the value of a. a could be 2 or 10 or many other values.
(2) a=|b|+5
a is 5 or greater since |b| is at least 0. This tells us that 'a' does not lie between -4 and 4. Hence this statement is sufficient to answer the question.
Answer (B)
What does intersect mean? In our Indian education system , we have learnt that intersection means that the arcs/lines cross each other.
forum that on the GMAT intersection would also mean that the line may be a tangent to the arc. .
So in that case, even if |a|=4, then the circle intersects the y axis ..
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