CAT 2024 Slot 2 QA Q2 Inequalities & Modulus

Question 2 of the Quantitative Ability (QA) section, CAT 2024 Slot 2, with CAT's official answer and a worked solution.

If \(x\) and \(y\) satisfy the equations \(|x|+x+y=15\) and \(x+|y|-y=20\), then \((x-y)\) equals

A
10
B
5
C
20
D
15

Answer: (D) 15 Inequalities & Modulus MCQ

Solution

If \(x<0\), the first equation gives \(y=15\), and then the second gives \(x=20\), a contradiction. So \(x \ge 0\).
If also \(y \ge 0\): \(2x+y=15\) and \(x=20\), giving \(y=-25<0\), a contradiction. So \(y<0\).
With \(x \ge 0, y<0\): \(2x+y=15\) and \(x-2y=20\). Solving, \(y=-5\), \(x=10\).
\(x-y = 10-(-5) = 15\).