Does the curve (x - a)^2 + (y - b)^2 = 16 intersect the Y axis?
1) a^2 + b^2 > 16
2) a = |b| + 5
I read this question on another forum but couldn't understand explanation of solution. Can anybody help me to solve it.
Here is the solution,
[spoiler]Given equation is an equation of a circle centered at with radius 4.
 Statement (1) by itself is insufficient. S1 says that the center of the circle is further than 4 units away from the origin but it doesn't specify whether the circle is far enough from the axis not to intersect it.
 Statement (2) by itself is sufficient. From S2 it follows that and thus the center of the circle is at least 5 units away from the axis. As the radius of the circle is only 4
units, we can conclude that the circle does not intersect the axis.
 The correct answer is B. Statement 2 is sufficient.[/spoiler]
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Coordinate Geometry Data Sufficiency Problem
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That solution relies on a knowledge of coordinate geometry far beyond what you need on the GMAT.saleem.kh 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
I read this question on another forum but couldn't understand explanation of solution. Can anybody help me to solve it.
In this question, we are asked about y-intercepts. To find y-intercepts, we plug in x=0. So we want to know if there are any solutions to
(0 - a)^2 + (y - b)^2 = 16
a^2 + (y - b)^2 = 16
(y-b)^2 = 16 - a^2
Now, the left side of this equation cannot be negative, since it is a square. So this equation will have no solutions if the right side is negative.
From Statement 1, we have that 16 - a^2 < b^2. So certainly 16-a^2 could be negative, but could also be positive, and we don't know if we have solutions to our equation: not sufficient.
From Statement 2, we know that a = |b| + 5. Since |b| is at least 0, this guarantees that a is at least 5, so we know 16 - a^2 is negative, and the equation (y-b)^2 = 16 - a^2 cannot possibly have a solution. Sufficient - the answer is B.
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mirantdon
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very good question +1 for B.
Try maximizing on the value of a for X axis so that it doesnt touch Y axis .
(Anything greater than the radius of the circle r=4)
try to prove insufficiency ..
Try maximizing on the value of a for X axis so that it doesnt touch Y axis .
(Anything greater than the radius of the circle r=4)
try to prove insufficiency ..
