CAT 2020 Slot 1 QA Q16 Coordinate Geometry

Question 16 of the Quantitative Ability (QA) section, CAT 2020 Slot 1, with CAT's official answer and a worked solution.

The area of the region satisfying the inequalities |x| - y ≤ 1, y ≥ 0, and y ≤ 1 is

TITA: type in the answer. There are no options and no negative marking.

Answer: 3 Coordinate Geometry TITA

Solution

  1. \(|x|-y\le1\) means \(|x|\le y+1\). With \(0\le y\le1\), each horizontal slice has width \(2(y+1)\).
  2. The region is a trapezium with parallel sides 2 (at y = 0) and 4 (at y = 1) and height 1.
  3. Area \(= \frac{2+4}{2}\times1 = 3\).

Same concept in other years

See every question on Area of a region bounded by modulus graphs.

More Coordinate Geometry questions from CAT

All 16 Coordinate Geometry questions asked since 2017.