CAT Quantitative Aptitude Questions | Questions for CAT - Coordinate Geometry

CAT Questions | CAT Coordinate Geometry | Geometric Probability

The question is from CAT Coordinate Geometry. It combines coordinate geometry with probability. Our task is to find out the probability of abscissa of a given point being greater than 2. A sample space can be described as a region. This region can be defined using coordinate geometry. This fabulous question does both. Take Geometry, add one unit of algebra; take a diagram, explain it with x's and y's. For the purists, it is geometry without the romance, for the pragmatists it is Geometry with expanded scope. CAT exam does test one on ideas from CAT Coordinate Geometry once in a while.

Question 2: Region R is defined as the region in the first quadrant satisfying the condition 3x + 4y < 12. Given that a point P with coordinates (r, s) lies within the region R, what is the probability that r > 2?

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

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Explanatory Answer

Method of solving this CAT Question from CAT Coordinate Geometry : A sample space can be described as a region. This region can be defined using coordinate geometry. This fabulous question does both.

Line 3x + 4y =12 cuts the x-axis at (4, 0) and y axis at (0, 3).
The region in the first quadrant satisfying the condition 3x + 4y < 12 forms a right triangle with sides 3, 4 and 5. Area of this triangle = 6 sq.units.

The lines x = 2 and 3x + 4y = 12 intersect at (2, 1.5). So, the region r > 2, 3x + 4y < 12 also forms a right triangle. This right triangle has base sides 2, 1.5. Area of this triangle = 1.5
Probability of the point lying in said region = \\frac{1.5}{6}\\) = \\frac{1}{4}\\)

The question is "Given that a point P with coordinates (r, s) lies within the region R, what is the probability that r > 2?"

Hence, the answer is \\frac{1}{4}\\).

Choice A is the correct answer.

 

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