NinetynineCAT 2024 Slot 3 QA Q1 Inequalities & Modulus
Question 1 of the Quantitative Ability (QA) section, CAT 2024 Slot 3, with CAT's official answer and a worked solution.
The number of distinct integer solutions \((x, y)\) of the equation \(|x+y|+|x-y|=2\), is
TITA: type in the answer. There are no options and no negative marking.
Answer: 8 Inequalities & Modulus TITA
Solution
- \(|x+y| + |x-y| = 2\max(|x|, |y|)\), so the equation is \(\max(|x|,|y|) = 1\).
- Integer points with \(\max(|x|,|y|) = 1\) are the \(3 \times 3\) grid around the origin minus \((0,0)\): \(9 - 1 = 8\).
Shortcut. The graph is the square with vertices \((\pm1,\pm1)\); count its lattice points.