Set T consists of all points (x, y) such that x^2 + y^2 = 1 . If point (a, b) is randomly selected from set T , what is the probability that b > a + 1 ? A. \frac{1}{4} B. \frac{1}{3} C. \frac{1}{2} D. \frac{3}{5} E. \frac{2}{3}

Here is a very simple calculation. The values of X and Y that will satisfy the given equation is if X is 0, Y is 1 X is 1 Y will be 0 If X is -1, Y will be 0 And if X is 0, Y will be -1 4 combinations. The only combination for b > a+1 is if a is -1 then b will definitely be 1 That makes the answer 1/4 Posted from my mobile device

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

How is a circle derived from any of this info? I see some comments saying x^2+y^2=1, but how is a circle derived from this? Posted from my mobile device

Circle on a plane In an x-y Cartesian coordinate system, the circle with center (a, b) and radius r is the set of all points (x, y) such that: (x-a)^2+(y-b)^2=r^2 https://gmatclub.com/forum/download/file.php?id=10337 This equation of the circle follows from the Pythagorean theorem applied to any point on the circle: as shown in the diagram above, the radius is the hypotenuse of a right-angled triangle whose other sides are of length x-a and y-b. If the circle is centered at the origin (0, 0) , then the equation simplifies to: x^2+y^2=r^2 24. Coordinate Geometry Theory Math: Coordinate Geometry Beauty of Coordinate geometry Dealing with Tangents on the GMAT Questions DS Questions PS Questions For more check: ALL YOU NEED FOR QUANT ! ! ! Ultimate GMAT Quantitative Megathread Hope it helps.

x^2+y^2=1. x^2= 1-y^2 and y^2=1-^x2. Therefore, 1-y^2>0 and 1-x^2>0 thus -1 y or 1/4 chance. So a total of 1/2+1/4 =3/4 chance that x+1>y or 1/4 chance y<x+1

I like the solution - it’s helpful.

bb , I don't think the answer is coming 1/4. I think the options has to be changed.

1/4 is correct. You can review the discussion for more details or check the other thread for alternative solutions: https://gmatclub.com/forum/set-t-consis ... 15626.html

Is the domain of this question is Geometry or Probability... means whether such type of questions can still be tested under new Gmat syllabus..?? I got this question in Gmat club test.. Bunuel KarishmaB

Note that while Geometry is not tested on GMAT Focus, Coordinate Geometry is tested under the Functions and Graphing sections found in the Official Guide for GMAT Focus Edition.