CAT 2022 Slot 2 Paper

Let the number of questions attempted be $\mathrm{x}+\mathrm{y}$ out of which $\mathrm{x}$ are correct and $\mathrm{y}$ are incorrect and the number of questions unattempted be $\mathit{z}$
It is given,
$\mathit{x}+\mathit{y}+\mathit{z}=75$ $...\left(\mathit{i}\right)$
$3\mathit{x}-\mathit{y}+\mathit{z}=97$ $...\left(\mathit{i}\mathit{i}\right)$
$\mathrm{Eqs}\left(\mathit{i}\mathit{i}\right)-\left(\mathit{i}\right)\Rightarrow \mathit{x}-\mathit{y}=11$
$\mathrm{Eqs}\left(\mathit{i}\right)+\left(\mathit{i}\mathit{i}\right)\Rightarrow 2\mathit{x}+\mathit{z}=86$
$\mathit{z}>\mathit{x}+\mathit{y}$
$\mathit{z}>75-\mathit{z}$
$\mathit{z}>37.5$
Minimum possible value of $\mathit{z}$ is 38
$2\mathit{x}+38=86$
$2\mathit{x}=48$
$\mathit{x}=24$
The maximum number of correct answers is 24 .