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CAT 2024 Slot 3 QA Question 13

Type-in-the-answer (no negative marking) · Algebra · Modulus · Try it, then check the answer and solution below.

CAT 2024 Slot 3QAAlgebra • ModulusModerate
The number of distinct real values of x, satisfying the equation.
max {x, 2} - min {x, 2} =∣x+2∣−∣x= |x + 2| - |x− 2| , is
TITA Answer:
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Answer and solution

Answer: 2

📌 Core Concept
The equation involves the difference between the maximum and minimum of two numbers, which simplifies based on the relative values of the numbers. Additionally, the equation includes absolute values, which can be evaluated by considering different intervals for x.
🔢 Step-by-Step Solution
1
Case 1: x≥2x \geq 2
Left side: max{x,2}−min{x,2}=x−2\text{max}\{x, 2\} - \text{min}\{x, 2\} = x - 2
Right side: ∣x+2∣−∣x−2∣=(x+2)−(x−2)=4|x + 2| - |x - 2| = (x + 2) - (x - 2) = 4
Equation: x−2=4x - 2 = 4 ⇒ x=6x = 6 (valid since6 ≥ 2)
2
Case 2: x<2x < 2
Left side: max{x,2}−min{x,2}=2−x\text{max}\{x, 2\} - \text{min}\{x, 2\} = 2 - x
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