CAT 2025 Slot 1 QA Q17 Inequalities & Modulus

Question 17 of the Quantitative Ability (QA) section, CAT 2025 Slot 1, with CAT's official answer and a worked solution.

The number of distinct pairs of integers \((x, y)\) satisfying the inequalities \(x>y \geq 3\) and \(x+y<14\) is

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

Answer: 16 Inequalities & Modulus TITA

Solution

For a fixed \(y \ge 3\), \(x\) runs from \(y + 1\) to \(13 - y\): that is \(13 - 2y\) values.
\(y = 3, 4, 5, 6\) give \(7, 5, 3, 1\) (none for \(y \ge 7\)).
Total \(= 16\).