XAT 2023 — QA & DI Question 19
ModulusEasy
Given A = |x + 3| + |x - 2| - |2x - 8|. The maximum value of |A| is:
Answer & solution
- A
111
9
- C
6
- D
3
- E
∞
Solution
A = |x + 3| + |x - 2| - |2x - 8|
The critical points are -3, 2 and 4.
Case 1: x ≥ 4
∴ A = x + 3 + x - 2 - (2x - 8)
⇒ A = 2x + 1 - 2x + 8
⇒ A = 9
Case 2: 2 ≤ x < 4
∴ A = x + 3 + x - 2 + (2x - 8)
⇒ A = 2x + 1 + 2x - 8
⇒ A = 4x - 7
∴ A ∈ [1, 9)
Case 3: -3 ≤ x < 2
∴ A = x + 3 - (x - 2) + (2x - 8)
⇒ A = x + 3 - x + 2 + 2x - 8
⇒ A = 2x - 3
∴ A ∈ [-9, 1)
Case 4: x < -3
∴ A = - (x + 3) - (x - 2) + (2x - 8)
⇒ A = - x - 3 - x + 2 + 2x - 8
⇒ A = - 9
From the above cases, The maximum value of |A| = 9
Hence, option (b).