CAT 2024 Slot 3 QA Q18 Inequalities & Modulus

Question 18 of the Quantitative Ability (QA) section, CAT 2024 Slot 3, with CAT's official answer and a worked solution.

The number of distinct real values of \(x\), satisfying the equation \(\max \{x, 2\}-\min \{x, 2\}=|x+2|-|x-2|\), is

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

Answer: 2 Inequalities & Modulus TITA

Solution

  1. \(\max\{x,2\} - \min\{x,2\} = |x - 2|\), so the equation is \(2|x-2| = |x+2|\).
  2. \(x \ge 2\): \(2x - 4 = x + 2 \Rightarrow x = 6\). \(-2 \le x < 2\): \(4 - 2x = x + 2 \Rightarrow x = \frac23\). \(x < -2\): \(4 - 2x = -x - 2 \Rightarrow x = 6\), rejected.
  3. Two solutions.

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