Set T consists of all points (x, y) such that \(x^2+y^2=1\) GMAT Problem Solving

Question: Set T consists of all points (x, y) such that \(x^2+y^2=1\) If point (a, b) is selected from set T at random, what is the probability that b > a + 1?

1. \(\frac{1}{4}\)
2. \(\frac{1}{3}\)
3. \(\frac{1}{2}\)
4. \(\frac{3}{5}\)
5. \(\frac{2}{3}\)

Correct Answer: A

Solution and Explanation:
Approach Solution (1):

Look at the diagram below:

The circle represented by the equation \(x^2+y^2=1\) is centered at the origin and has the radius of \(r=\sqrt1=1\)

So, set T is the circle itself (red curve).

Question is: if point (a, b) is selected from the set T at random, what is the probability that b > a + 1? All points (a, b) which satisfy this condition (belong to T and have y- coordinate and gt; x- coordinate +1) lie above the line y = x + 1 (blue line). You can see that portion of the circle which is above the line is \(\frac{1}{4}\) of the whole circumference, hence P = \(\frac{1}{4}\)

“Set T consists of all points (x, y) such that \(x^2+y^2=1\). If point (a, b) is selected from set T at random, what is the probability that b > a + 1?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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