Xavier Aptitude Test 2023 Paper

Given equation, $A=\left| x+3 \right| + \left| x-2 \right| - \left| 2x-8 \right|$.Case (i):- $x+3 \geq 0, x-2 \geq 0 \text{ and } 2x-8 \geq 0$then, $A=x+3+x-2-2x+8=9$.The maximum value of $\left| A \right| = 9$ Case (ii):-$x+3 \geq 0, x-2 \geq 0 \text{ and } 2x-8 < 0$$x \geq -3, x \geq 2 \text{ and } x < 4$then $A=x+3+x-2+2x-8=4x-7$The range of $x$ is $[2,4)$. Hence the value of $A$ varies from $[1,9)$.The maximum value of $\left| A \right| < 9$ Case (iii): $x+3 \geq 0, x-2 < 0 \text{ and } 2x-8 < 0$$x \geq -3, x < 2 \text{ and } x < 4$then $A=x+3-x+2+2x-8=2x-3$.The range of $x$ is $[-3,2)$. Hence the value of $A$ varies from $[-9,1)$.The maximum value of $\left| A \right| = 9$ Case (iv): $x+3 < 0, x-2 < 0 \text{ and } 2x-8 < 0$$x < 3, x < 2 \text{ and } x < 4$then $A=-x-3-x+2+2x-8=-9$.The maximum value of $\left| A \right| = 9$From the above cases, The maximum value of $\left| A \right| = 9$. Option (B) is correct.